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School Finance Reform and the Distribution of Student Achievement * November 2015 Julien Lafortune University of California, Berkeley [email protected] Jesse Rothstein University of California, Berkeley and NBER [email protected] Diane Whitmore Schanzenbach Northwestern University and NBER [email protected] ABSTRACT We study the impact of post-1990 school finance reforms, during the so-called “adequacy” era, on the distribution of school spending and student achievement between high-income and low-income school districts. Using an event study design, we find that reform events – court orders and legislative reforms – lead to sharp, immediate, and sustained increases in mean school spending and in relative spending in low-income school districts. Using test score data from the National Assessment of Educational Progress, we also find that reforms cause gradual increases in the relative achievement of students in low-income school districts, consistent with the goal of improving educational opportunity for these students. The implied effect of school resources on educational achievement is large. * This research was supported by funding from the Spencer Foundation and the Washington Center for Equitable Growth. We are grateful to Apurba Chakraborty, Elora Ditton, and Patrick Lapid for excellent research assistance. We thank Tom Downes, Kirabo Jackson, Rucker Johnson, and conference and seminar participants at APPAM, AEFP, and Brookings for helpful comments and discussions.

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Page 1: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

SchoolFinanceReformandtheDistributionofStudentAchievement

November2015

JulienLafortune

UniversityofCaliforniaBerkeleyjulieneconberkeleyedu

JesseRothstein

UniversityofCaliforniaBerkeleyandNBER

rothsteinberkeleyedu

DianeWhitmoreSchanzenbachNorthwesternUniversity

andNBERdwsnorthwesternedu

ABSTRACT

Westudytheimpactofpost-1990schoolfinancereformsduringtheso-calledldquoadequacyrdquoeraonthedistributionofschoolspendingandstudentachievementbetweenhigh-incomeandlow-incomeschooldistrictsUsinganeventstudydesignwefindthatreformeventsndashcourtordersandlegislativereformsndashleadtosharpimmediateandsustainedincreasesinmeanschoolspendingandinrelativespendinginlow-incomeschooldistrictsUsingtestscoredatafromtheNationalAssessmentofEducationalProgresswealsofindthatreformscausegradualincreasesintherelativeachievementofstudentsinlow-incomeschooldistrictsconsistentwiththegoalofimprovingeducationalopportunityforthesestudentsTheimpliedeffectofschoolresourcesoneducationalachievementislarge

ThisresearchwassupportedbyfundingfromtheSpencerFoundationandtheWashingtonCenterforEquitableGrowthWearegratefultoApurbaChakrabortyEloraDittonandPatrickLapidforexcellentresearchassistanceWethankTomDownesKiraboJacksonRuckerJohnsonandconferenceandseminarparticipantsatAPPAMAEFPandBrookingsforhelpfulcommentsanddiscussions

2

Introduction

Schoolsareakeylinkinthetransmissionofeconomicstatusfromgeneration

togenerationChildrenfromlow-incomefamilieshavelowertestscoreslower

ratesofhighschoolandcollegecompletionandeventuallylowerearnings2The

achievementgapbetweenrichandpoorchildrenhaswidenedinrecentyearseven

asracialgapshaveshrunk(Reardon2011)Onepotentialcontributingfactorto

gapsineducationaloutcomesisinequityinschoolresourcesUSschoolsare

traditionallyfundedoutoflocalpropertytaxesandbecausewealthierfamiliestend

toliveinrichercommunitieswithlargertaxbasestheirchildrenhavetendedto

attendschoolsthatspendmorethandothoseattendedbythechildrenoflow-

incomefamilies

Theproductivityofadditionalschoolresourcesisthesubjectoflongstanding

debateintheeducationpolicyliterature(seeegHanushek2003Krueger2003

Burtless1996)Timeseriesandcross-districtobservationalcomparisonstendto

showsmallorzeroeffectsofspendingonacademicachievement(Hanushek2006

Colemanetal1966)thoughstate-levelcomparisons(CardandKrueger1992a)and

randomizedexperiments(Krueger1999Chettyetal2011)aremorepositive

Compensatoryfundingndashadditionalstateaidfordisadvantagedschool

districtsndashwouldcreateadownwardbiasintheestimatedeffectofschoolresources

fromobservationaldesignsButitisexactlythistypeofprogramthatisofinterest

forpolicyevaluationasthestatefundingformulaisthemainpolicytoolavailableto

addressinequitiesinacademicoutcomesIndeedstatefundingformulashavebeen2SeeBarrowandSchanzenbach(2012)forareviewofthisliterature

3

alocusforreformeffortsBeginningwiththe1971SerranovPriestdecisionin

whichafederalcourtfoundCaliforniarsquosschoolfinancesystemunconstitutional

manyUSstateshavemovedawayfromlocalfundingtomorecentralizedsystems

aimedatincreasingopportunityforlow-incomestudents3

Financereformsarearguablythemostimportantpolicyforpromoting

equalityofeducationalopportunitysincetheturnawayfromschooldesegregation

inthe1980sAlongliteratureexaminestheimplicationsofthesereformsforthe

distributionofschoolspending(seeegLaddandFiske2015Hanushekand

Lindseth2009CorcoranandEvans2015)MostrelevantforourstudyCorcoran

andEvans(2015seealsoCorcoranetal2004)findthatplaintiffcourtvictories

reduceinequalityofspendingacrossdistrictsFischel(1989)andHoxby(2001)

arguethatpoorlydesignedreformssometimesledtoldquolevelingdownrdquoofthetopof

thedistributionratherthantoabsoluteincreasesinspendinginlow-income

districtsNeverthelessCorcoranandEvans(2015)findthatplaintiffvictorieslead

toincreasesatthebottomofthespendingdistributionwhileCardandPayne

(2002)findincreasedrelativespendingindistrictswithlowfamilyincomes(which

mayormaynotbelow-spendingdistricts)

Levelingdownwaspossiblebecausereformsinthe1970sand1980swere

focusedonreducinggapsinfundingbetweendistrictsAnewwaveofreformsinthe

1990swasbasedonadifferentlegaltheoryThatstateconstitutionsrequirednot

justequitableeducationspendingbutanadequatelevelofeducationalqualityIn

3CascioandReber(2013)andCascioGordonandReber(2013)examineanearlierformofschoolfinancereformtheintroductionoffederalTitleIfundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct

4

judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso

therewaslessscopetoleveldowninresponsetoanadverseruling

Althoughattentionhasshiftedinrecentyearstoaccountabilityandother

processreformsasmoreimportantleversforeducationalopportunityfinance

policychangesremainquiteimportantwithatleast20schoolfinancereformcases

decidedsince2000Severalauthorshaveexaminedindividualadequacy-based

reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans

(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa

grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle

knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending

Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance

reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature

attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut

schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence

spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso

discreteeventswithtimingduemoretolegalprocessesthantopotentially

endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem

attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof

spendingonoutcomesThebarriertothishasbeentheabsenceofnationally

comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby

examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing

ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan

5

andPayne2002)orbyexamininglessproximateoutcomeslikeeventual

educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand

PersicoforthcomingCandelariaandShores2015)

Weprovidethefirstevidencefromnationallyrepresentativedataregarding

theimpactofschoolfinancereformsonstudentachievementWerelyonrarely

usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also

knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage

studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool

districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof

theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform

Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms

Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative

spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy

frameworkwefindthatfinancereformsleadtosharpimmediateandsustained

increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns

ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally

positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent

reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms

havepositiveeffectsontotalrevenuesforatleastadozenyears

Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem

theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold

5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere

6

incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth

quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore

progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)

followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly

aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity

ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand

persistorevengrowoveratleastthenextdecade

Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe

relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome

intheschooldistrictUsingoureventstudyframeworkwefindthatthe

ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income

districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform

indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused

productivelyThe(local)averageeffectofanextra$1000inper-pupilannual

spendingistoraisestudenttestscorestenyearslaterby018standarddeviations

Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending

intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms

correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies

thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool

6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 2: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

2

Introduction

Schoolsareakeylinkinthetransmissionofeconomicstatusfromgeneration

togenerationChildrenfromlow-incomefamilieshavelowertestscoreslower

ratesofhighschoolandcollegecompletionandeventuallylowerearnings2The

achievementgapbetweenrichandpoorchildrenhaswidenedinrecentyearseven

asracialgapshaveshrunk(Reardon2011)Onepotentialcontributingfactorto

gapsineducationaloutcomesisinequityinschoolresourcesUSschoolsare

traditionallyfundedoutoflocalpropertytaxesandbecausewealthierfamiliestend

toliveinrichercommunitieswithlargertaxbasestheirchildrenhavetendedto

attendschoolsthatspendmorethandothoseattendedbythechildrenoflow-

incomefamilies

Theproductivityofadditionalschoolresourcesisthesubjectoflongstanding

debateintheeducationpolicyliterature(seeegHanushek2003Krueger2003

Burtless1996)Timeseriesandcross-districtobservationalcomparisonstendto

showsmallorzeroeffectsofspendingonacademicachievement(Hanushek2006

Colemanetal1966)thoughstate-levelcomparisons(CardandKrueger1992a)and

randomizedexperiments(Krueger1999Chettyetal2011)aremorepositive

Compensatoryfundingndashadditionalstateaidfordisadvantagedschool

districtsndashwouldcreateadownwardbiasintheestimatedeffectofschoolresources

fromobservationaldesignsButitisexactlythistypeofprogramthatisofinterest

forpolicyevaluationasthestatefundingformulaisthemainpolicytoolavailableto

addressinequitiesinacademicoutcomesIndeedstatefundingformulashavebeen2SeeBarrowandSchanzenbach(2012)forareviewofthisliterature

3

alocusforreformeffortsBeginningwiththe1971SerranovPriestdecisionin

whichafederalcourtfoundCaliforniarsquosschoolfinancesystemunconstitutional

manyUSstateshavemovedawayfromlocalfundingtomorecentralizedsystems

aimedatincreasingopportunityforlow-incomestudents3

Financereformsarearguablythemostimportantpolicyforpromoting

equalityofeducationalopportunitysincetheturnawayfromschooldesegregation

inthe1980sAlongliteratureexaminestheimplicationsofthesereformsforthe

distributionofschoolspending(seeegLaddandFiske2015Hanushekand

Lindseth2009CorcoranandEvans2015)MostrelevantforourstudyCorcoran

andEvans(2015seealsoCorcoranetal2004)findthatplaintiffcourtvictories

reduceinequalityofspendingacrossdistrictsFischel(1989)andHoxby(2001)

arguethatpoorlydesignedreformssometimesledtoldquolevelingdownrdquoofthetopof

thedistributionratherthantoabsoluteincreasesinspendinginlow-income

districtsNeverthelessCorcoranandEvans(2015)findthatplaintiffvictorieslead

toincreasesatthebottomofthespendingdistributionwhileCardandPayne

(2002)findincreasedrelativespendingindistrictswithlowfamilyincomes(which

mayormaynotbelow-spendingdistricts)

Levelingdownwaspossiblebecausereformsinthe1970sand1980swere

focusedonreducinggapsinfundingbetweendistrictsAnewwaveofreformsinthe

1990swasbasedonadifferentlegaltheoryThatstateconstitutionsrequirednot

justequitableeducationspendingbutanadequatelevelofeducationalqualityIn

3CascioandReber(2013)andCascioGordonandReber(2013)examineanearlierformofschoolfinancereformtheintroductionoffederalTitleIfundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct

4

judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso

therewaslessscopetoleveldowninresponsetoanadverseruling

Althoughattentionhasshiftedinrecentyearstoaccountabilityandother

processreformsasmoreimportantleversforeducationalopportunityfinance

policychangesremainquiteimportantwithatleast20schoolfinancereformcases

decidedsince2000Severalauthorshaveexaminedindividualadequacy-based

reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans

(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa

grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle

knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending

Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance

reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature

attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut

schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence

spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso

discreteeventswithtimingduemoretolegalprocessesthantopotentially

endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem

attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof

spendingonoutcomesThebarriertothishasbeentheabsenceofnationally

comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby

examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing

ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan

5

andPayne2002)orbyexamininglessproximateoutcomeslikeeventual

educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand

PersicoforthcomingCandelariaandShores2015)

Weprovidethefirstevidencefromnationallyrepresentativedataregarding

theimpactofschoolfinancereformsonstudentachievementWerelyonrarely

usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also

knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage

studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool

districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof

theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform

Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms

Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative

spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy

frameworkwefindthatfinancereformsleadtosharpimmediateandsustained

increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns

ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally

positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent

reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms

havepositiveeffectsontotalrevenuesforatleastadozenyears

Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem

theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold

5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere

6

incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth

quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore

progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)

followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly

aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity

ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand

persistorevengrowoveratleastthenextdecade

Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe

relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome

intheschooldistrictUsingoureventstudyframeworkwefindthatthe

ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income

districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform

indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused

productivelyThe(local)averageeffectofanextra$1000inper-pupilannual

spendingistoraisestudenttestscorestenyearslaterby018standarddeviations

Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending

intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms

correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies

thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool

6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 3: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

3

alocusforreformeffortsBeginningwiththe1971SerranovPriestdecisionin

whichafederalcourtfoundCaliforniarsquosschoolfinancesystemunconstitutional

manyUSstateshavemovedawayfromlocalfundingtomorecentralizedsystems

aimedatincreasingopportunityforlow-incomestudents3

Financereformsarearguablythemostimportantpolicyforpromoting

equalityofeducationalopportunitysincetheturnawayfromschooldesegregation

inthe1980sAlongliteratureexaminestheimplicationsofthesereformsforthe

distributionofschoolspending(seeegLaddandFiske2015Hanushekand

Lindseth2009CorcoranandEvans2015)MostrelevantforourstudyCorcoran

andEvans(2015seealsoCorcoranetal2004)findthatplaintiffcourtvictories

reduceinequalityofspendingacrossdistrictsFischel(1989)andHoxby(2001)

arguethatpoorlydesignedreformssometimesledtoldquolevelingdownrdquoofthetopof

thedistributionratherthantoabsoluteincreasesinspendinginlow-income

districtsNeverthelessCorcoranandEvans(2015)findthatplaintiffvictorieslead

toincreasesatthebottomofthespendingdistributionwhileCardandPayne

(2002)findincreasedrelativespendingindistrictswithlowfamilyincomes(which

mayormaynotbelow-spendingdistricts)

Levelingdownwaspossiblebecausereformsinthe1970sand1980swere

focusedonreducinggapsinfundingbetweendistrictsAnewwaveofreformsinthe

1990swasbasedonadifferentlegaltheoryThatstateconstitutionsrequirednot

justequitableeducationspendingbutanadequatelevelofeducationalqualityIn

3CascioandReber(2013)andCascioGordonandReber(2013)examineanearlierformofschoolfinancereformtheintroductionoffederalTitleIfundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct

4

judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso

therewaslessscopetoleveldowninresponsetoanadverseruling

Althoughattentionhasshiftedinrecentyearstoaccountabilityandother

processreformsasmoreimportantleversforeducationalopportunityfinance

policychangesremainquiteimportantwithatleast20schoolfinancereformcases

decidedsince2000Severalauthorshaveexaminedindividualadequacy-based

reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans

(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa

grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle

knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending

Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance

reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature

attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut

schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence

spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso

discreteeventswithtimingduemoretolegalprocessesthantopotentially

endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem

attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof

spendingonoutcomesThebarriertothishasbeentheabsenceofnationally

comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby

examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing

ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan

5

andPayne2002)orbyexamininglessproximateoutcomeslikeeventual

educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand

PersicoforthcomingCandelariaandShores2015)

Weprovidethefirstevidencefromnationallyrepresentativedataregarding

theimpactofschoolfinancereformsonstudentachievementWerelyonrarely

usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also

knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage

studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool

districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof

theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform

Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms

Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative

spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy

frameworkwefindthatfinancereformsleadtosharpimmediateandsustained

increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns

ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally

positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent

reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms

havepositiveeffectsontotalrevenuesforatleastadozenyears

Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem

theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold

5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere

6

incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth

quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore

progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)

followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly

aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity

ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand

persistorevengrowoveratleastthenextdecade

Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe

relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome

intheschooldistrictUsingoureventstudyframeworkwefindthatthe

ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income

districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform

indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused

productivelyThe(local)averageeffectofanextra$1000inper-pupilannual

spendingistoraisestudenttestscorestenyearslaterby018standarddeviations

Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending

intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms

correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies

thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool

6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 4: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

4

judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso

therewaslessscopetoleveldowninresponsetoanadverseruling

Althoughattentionhasshiftedinrecentyearstoaccountabilityandother

processreformsasmoreimportantleversforeducationalopportunityfinance

policychangesremainquiteimportantwithatleast20schoolfinancereformcases

decidedsince2000Severalauthorshaveexaminedindividualadequacy-based

reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans

(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa

grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle

knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending

Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance

reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature

attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut

schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence

spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso

discreteeventswithtimingduemoretolegalprocessesthantopotentially

endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem

attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof

spendingonoutcomesThebarriertothishasbeentheabsenceofnationally

comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby

examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing

ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan

5

andPayne2002)orbyexamininglessproximateoutcomeslikeeventual

educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand

PersicoforthcomingCandelariaandShores2015)

Weprovidethefirstevidencefromnationallyrepresentativedataregarding

theimpactofschoolfinancereformsonstudentachievementWerelyonrarely

usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also

knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage

studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool

districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof

theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform

Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms

Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative

spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy

frameworkwefindthatfinancereformsleadtosharpimmediateandsustained

increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns

ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally

positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent

reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms

havepositiveeffectsontotalrevenuesforatleastadozenyears

Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem

theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold

5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere

6

incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth

quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore

progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)

followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly

aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity

ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand

persistorevengrowoveratleastthenextdecade

Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe

relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome

intheschooldistrictUsingoureventstudyframeworkwefindthatthe

ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income

districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform

indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused

productivelyThe(local)averageeffectofanextra$1000inper-pupilannual

spendingistoraisestudenttestscorestenyearslaterby018standarddeviations

Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending

intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms

correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies

thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool

6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 5: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

5

andPayne2002)orbyexamininglessproximateoutcomeslikeeventual

educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand

PersicoforthcomingCandelariaandShores2015)

Weprovidethefirstevidencefromnationallyrepresentativedataregarding

theimpactofschoolfinancereformsonstudentachievementWerelyonrarely

usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also

knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage

studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool

districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof

theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform

Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms

Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative

spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy

frameworkwefindthatfinancereformsleadtosharpimmediateandsustained

increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns

ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally

positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent

reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms

havepositiveeffectsontotalrevenuesforatleastadozenyears

Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem

theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold

5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere

6

incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth

quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore

progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)

followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly

aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity

ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand

persistorevengrowoveratleastthenextdecade

Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe

relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome

intheschooldistrictUsingoureventstudyframeworkwefindthatthe

ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income

districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform

indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused

productivelyThe(local)averageeffectofanextra$1000inper-pupilannual

spendingistoraisestudenttestscorestenyearslaterby018standarddeviations

Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending

intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms

correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies

thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool

6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

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3

1

12

2 5

7

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11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

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WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

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NDOKOR

PA

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TNTX

UT VT

VA

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NM

OH

minus1

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02

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1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

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20

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40

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60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 6: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

6

incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth

quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore

progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)

followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly

aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity

ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand

persistorevengrowoveratleastthenextdecade

Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe

relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome

intheschooldistrictUsingoureventstudyframeworkwefindthatthe

ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income

districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform

indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused

productivelyThe(local)averageeffectofanextra$1000inper-pupilannual

spendingistoraisestudenttestscorestenyearslaterby018standarddeviations

Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending

intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms

correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies

thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool

6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 7: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

7

districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits

consideredarethoseoperatingthroughsubsequentearnings

Inafinalanalysisweconsidertheimpactoffinancereformsonoverall

educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-

incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno

discernableeffectofreformsoneithergapThereasonisthatlow-incomeand

minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow

meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur

estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-

incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe

averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom

zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective

atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district

resourceandachievementgapswillbeneededtoaddresstheoverallgap

I Schoolfinancereforms7

Americanpublicschoolshavetraditionallybeenlocallymanagedand

financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir

taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources

availabletoachildrsquosschooldependedimportantlyonwhereheorshelives

IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda

novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966

7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 8: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

8

Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual

ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood

schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance

systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts

TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent

SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike

theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts

inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother

statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential

rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka

varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto

ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith

similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese

second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch

studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card

andPayne2002MurrayEvansandSchwab1998)

Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance

reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe

stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired

thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave

anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)

Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg

9411US1

10790SW2d186

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

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00

10

00

02

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1 S

lop

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

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FLGAID

IL

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KSKY

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RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
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Page 9: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

9

ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto

competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin

thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially

inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher

spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-

schooldisadvantagesoflow-incomestudents11

TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct

of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand

curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts

andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures

perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)

Since1990manyotherstatecourtshavefoundadequacyrequirementsin

theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod

manyofthemadequacybasedWediscussourtabulationofpost-1990finance

reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII

Aswithearlierequity-basedreformstherehasbeennosingledefinitionof

adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted

Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms

willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan

didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt

ordermightpermitlevelingdowntoastingybutequalfundingformulaastate

cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto

11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

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1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

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Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

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Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

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Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

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Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

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NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

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Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

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NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

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Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

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NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

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Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 10: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

10

haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income

districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves

Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher

spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto

smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)

Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand

theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa

frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson

bothspendinglevels(SectionIV)andstudenttestscores(SectionV)

II Analyticapproach

WedevelopouranalyticapproachinthreepartsFirstweintroduceournew

post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof

schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss

ourmethodologyforrelatingreformeventstosubsequentoutcomes

A Characterizingevents

Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme

courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders

changesinthefundingformulaMuchofthepriorschoolfinancereformliterature

hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal

(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)

supplementingthemwithourownresearchintocasehistoriesWefocusonevents

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

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3

1

12

2 5

7

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11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

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SDTN

TXUT

VT

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WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

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02

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1 S

lop

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

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CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

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NDOKOR

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NM

OH

minus1

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

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60

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20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 11: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

11

in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP

panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12

Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat

weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto

thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash

nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior

workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery

singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision

isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe

initialdecisionandliftsthestay

NotallmajorschoolfinancereformeventsresultedfromcourtordersIn

someimportantcases(egCaliforniaColorado)legislaturesreformedfinance

systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin

threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative

reformsthatchangeschoolfinancesystemsinoureventlist

AsshowninFigure1weidentifyatotalof68eventsin27statesbetween

1990and201351arecourtordersand40arelegislativeactionsin9of

casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA

completelistofoureventsalongwithacomparisontothoseusedinotherstudies

ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance

12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 12: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

12

reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe

geographicdistributionofeventsusingshadingtorepresentthedateofthefirst

post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare

geographicallydispersedthoughrareinthedeepSouthandupperMidwest

B Measuringschoolfinancesystemsandstudentoutcomes

Nextweturntothemeasurementoftheindependentvariablesofinterest

beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe

distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine

thestandarddeviationofspendingperpupilandothersummariesoftheunivariate

distributionButthisapproachdoesnotaccountfortherelationshipofspendingto

areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe

equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof

resourcesavailabletothelowest-incomedistrictswepreferameasurethat

correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand

relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto

theadequacyandequityofthefundingsystemrespectively

Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily

incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance

14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

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3

1

12

2 5

7

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11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

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WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

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NDOKOR

PA

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TNTX

UT VT

VA

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NM

OH

minus1

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02

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1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

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20

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40

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60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 13: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

13

equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor

fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily

incomedistributionButwhiletheextremesofthedistributionarecertainlyof

particularinterestinequitydiscussionsonemightalsobeinterestedinthe

distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize

therelationshipbetweenspendingandincomeacrosstheentireincome

distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe

bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts

inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear

(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist

HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe

meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains

controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A

morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-

incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative

coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat

revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate

Whenweturntoourexaminationofstudentoutcomesweuseparallel

measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat

districtsinthebottomquintileofthefamilyincomedistributionthegapbetween

disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

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1990-1993

1994-1997

1998-2001

2002-2005

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2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

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10 1025 105 1075 11 1125

1990

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15000

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Sta

te a

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pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

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COCT

DE

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ID

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IN

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KS KYLA

ME

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45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

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45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

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(a) Log income gradients

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1990 1995 2000 2005 2010Fiscal year

State aid

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(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

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02

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ha

ng

e in

Sta

te A

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minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

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minus5 0 5 10 15 20

(a) Q1

minus1

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(b) Q5

minus1

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(c) Q1 - Q5

minus1

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minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

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ha

ng

e in

To

tal R

eve

nu

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minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

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(b) Q5

minus1

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(c) Q1 - Q5

minus1

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minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 14: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

14

thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma

regressionofmeantestscoresondistrictfamilyincome18Eachisestimated

separatelyforeachavailablestate-year-subject-gradecombination

C OhioCaseStudy

Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform

eventswepresentOhioasacasestudyFigure3showstherelationshipbetween

districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis

isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe

verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin

1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater

lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas

wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990

bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid

thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis

negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch

morenegativein2011thanin1990In1990each10increaseinmeanhousehold

incomewasassociatedwithabout$144lessinstateaidperpupilthe

correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic

increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw

increasesbuttheirgainsweremuchsmaller

18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 15: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

15

Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin

1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot

anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes

(moreprogressivedistributions)in2011thanin1990

Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues

perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers

withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger

andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal

taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates

Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween

1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat

extentwerethechangesduetointentionalreformsToanswerthisweneedto

relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest

casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional

resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex

interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand

legislativechangesovermanyyearsandspendingchangesgradually

OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes

ontheDeRolphvStatecasein199720002001and2002The1997ruling

declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand

specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda

ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt

determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained

16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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  • all tables figures
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16

inadequateThesameyearthelegislaturerevisedthesystemandasubsequent

rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied

constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith

newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot

beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving

judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000

Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-

incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe

figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach

gradientbetween1997and2002followingaperiodofstabilitybefore1997There

islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave

interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend

tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005

thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle

signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo

setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar

timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween

districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome

distributionThismirrorstheslopetrendswiththeexpectedverticalflip

D Eventstudymethodology

Tomodeltherelationshipbetweenschoolfinancereformeventsand

measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur

strategyisbasedontheideathatstateswithouteventsinaparticularyearforma

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 17: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

17

usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor

fixeddifferencesbetweenthestatesandforcommontimeeffects

Weestimateparametricandnon-parametricmodelsThenon-parametric

modelspecifiestheoutcomeforstatesinyeartas

(2) = + + 1 = lowast + +

HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor

nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe

effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)

Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat

kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent

relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross

stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19

Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif

eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue

Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor

outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample

whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin

Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event

dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe

areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat

ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

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1990-1993

1994-1997

1998-2001

2002-2005

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2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

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10 1025 105 1075 11 1125

1990

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Sta

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(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

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COCT

DE

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IN

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KS KYLA

ME

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45 degree line Linear fit (unweighted)

(a) State revenue per pupil

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45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

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(a) Log income gradients

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1990 1995 2000 2005 2010Fiscal year

State aid

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(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

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ng

e in

Sta

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minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

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minus5 0 5 10 15 20

(a) Q1

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(b) Q5

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(c) Q1 - Q5

minus1

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(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

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ha

ng

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To

tal R

eve

nu

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minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

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(b) Q5

minus1

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(c) Q1 - Q5

minus1

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minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 18: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

18

eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour

relianceonaneventstudyframework

Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent

ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric

specificationbutwefocusourattentiononamoreparametricspecificationthat

replacestherelativetimeeffectsin(2)withthreeparametricterms

(3) = + + minus lowast $ + 1 gt lowast $ +

minus lowast 1 gt lowast $ +

Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile

βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear

trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe

eventandcontinuesafterwardandisinterpretedasapotentialconfound

analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself

AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe

parametricandnon-parametricestimatesindicatethatthethree-coefficient

structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents

thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes

delayedayearorspreadoutovertwotothreeyearsfollowingtheevent

Acomplicationwefaceinimplementingtheeventstudyframeworkisthat

statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral

eventsinastateseparately20Specificallysupposethatstateshaseventnumbern

20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3

19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
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19

(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling

themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates

withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)

Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand

eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof

eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and

(3)withstate-eventandyearfixedeffects

Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe

interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe

reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot

holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg

courtrulings)beforethefinancereformisactuallyimplementedThusgradual

increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance

formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral

yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant

empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour

designatedeventsandpersistwithoutgrowingthereafter

Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing

thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin

meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe

expectadifferenttimepatternofeffectshereBecausestudentoutcomesare

cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas

21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

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CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

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TNTX

UT VT

VA

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WV

WIWY

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OH

minus1

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00

50

00

10

00

02

01

1 S

lop

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 20: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

20

largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward

weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe

βphaseincoefficientoralternatelythroughgradualgrowthintheβrs

III Data

OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof

schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool

financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common

CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)

andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles

householdincomedistributionsfromthe1990Censusandstudentachievement

outcomesinreadingandmathin4thand8thgradefromtheNAEP

TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof

NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal

educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-

95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom

theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-

94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual

censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel

forschoolracialcompositionfreelunchshareandpupil-teacherratios

22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 21: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

21

Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool

DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof

theirstatersquos(unweighted)distribution

Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP

microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce

representativesamplesforeachparticipatingstateThisbeganin1990with8th

grademathand42statesparticipatingandhasbeenadministeredroughlyevery

twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003

therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery

odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof

assessmentsthenumberofparticipatingstatesandthenumberofstudents

assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha

representativesampleofabout2500studentsin100schoolsperstate

TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand

gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe

firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean

andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-

subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean

scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur

eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells

23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative

Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink

fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict

namestocheckandsupplementthecrosswalk

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

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3

1

12

2 5

7

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11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

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WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

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NDOKOR

PA

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TNTX

UT VT

VA

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NM

OH

minus1

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02

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1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

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20

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40

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60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 22: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

22

Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-

2011Table2bpresentssummarystatisticsforthestate-yearpanel

IV ResultsSchoolFinance

Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers

fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe

non-parametriceventstudyspecification(2)takingtheincomegradientofstate

revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe

yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas

2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears

followingtheeventThegradientcontinuestodeclinethereafterreachinga

minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding

somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe

graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin

years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value

lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022

Figure6alsoshowstheparametricspecification(3)asadashedlineNot

surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically

insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda

slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis

three-parametermodelfitsthenon-parametricpatternquitewell

Columns1-3ofTable3presentestimatesfromvariousversionsofthe

parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 23: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

23

thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe

phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis

showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=

βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe

trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance

Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe

thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump

coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient

ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor

about5ofmeantotalrevenuesperpupilinoursample

Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand

fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)

andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate

revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill

substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa

resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime

Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts

beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent

EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe

trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe

focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat

staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe

increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 24: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

24

zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean

logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa

largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3

Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals

orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance

Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan

averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents

thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance

reformsarealmostcertainlylargerthanthosethatweestimate

Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal

taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges

thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto

modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels

forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable

3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin

thetotalrevenuegradientThoughnoindividualcoefficientisstatistically

significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall

post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe

gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin

thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)

Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal

revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically

significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

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1

ʹ

2

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3

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12

2 5

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11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

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ND

OK

OR

PA

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SDTN

TXUT

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AKNVWY

OH

minus1

00

00

minus5

00

00

50

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02

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1 S

lop

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

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CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

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NDOKOR

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

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13

$ p

er

pu

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1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

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60

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20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

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23

minus5 0 5 10 15 20

(b) Q5

minus1

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minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 25: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

25

districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout

twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults

AsdiscussedinSectionIacentralconcernintheschoolfinancereform

literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin

totaleducationalspendingToassessthisweexamineaveragestaterevenueand

totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand

Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent

withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal

revenuesissmalleraround$550butequallysharpandalsohighlysignificant

Takentogetheroureventstudymodelsindicatelargeincreasesinthe

progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby

increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income

districtsorinoverallmeansTheincomegradientandquintilemeananalysesare

broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage

totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe

approximately$1000averageabsoluteincreasethattheyseefollowinganevent

representsabitunder10oftheirtotalrevenuestherelativeincreasecompared

tohigherincomedistrictsisabouthalfaslarge

Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable

specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s

perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate

25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 26: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

26

theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor

theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour

slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata

muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin

partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial

oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid

V ResultsStudentOutcomes

Theaboveresultsestablishthatreformeventsareassociatedwithsharp

immediateincreasesintheprogressivityofschoolfinancewithabsoluteand

relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis

productivewemightexpecttoseeimpactsonstudentoutcomes

Figure10presentsparametricandnon-parametriceventstudyestimatesof

theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog

meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe

financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear

changeinthetrendfollowingreformeventsThenonparametricestimatesindicate

asmoothnearlylineardeclineinthetestscoregradientfollowinganevent

indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly

thepatternonewouldexpectastestscoresarecumulativeoutcomesthat

presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades

sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 27: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

27

ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno

indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent

whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe

post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso

wecannotruleoutthissortofslowing26

EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin

SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate

panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-

eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-

eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno

evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso

wefocusonthemodelswithjustaphase-ineffectinColumns1and4These

indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera

reformeventforatotaldeclineovertenyearsof009

Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap

inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis

noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise

linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten

yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno

changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap

26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 28: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

28

inlogmeanincomesisabout06sothe0007coefficientinTable7isquite

consistentwiththe0009coefficientinthetestscoreslopemodelinTable6

Thedivergenttimepatternsofimpactsonresourcesandonstudent

outcomescombinedwiththecumulativenatureofthelatterpreventsasimple

instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof

theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare

relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn

SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten

yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten

yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool

resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation

thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects

Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger

estimatesoftheachievementeffectperdollarifweusedestimatesformorethan

tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful

newprogramsafterfundingincreases)orsmallereffectswithashorterwindow

Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby

gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn

5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th

thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27

27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 29: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

29

VI Mechanisms

Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial

increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough

absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter

thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute

achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe

mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved

studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios

teacherandstudentcharacteristicsandsubcategoriesofspending

Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto

enrollmentorthecompositionofthestudentbodyarelikelytocontributeto

improvementsintestscoresWeestimatethesametypeofevent-studyanalysis

showninTables3-4butfocusingondistrictdemographiccompositionResultsare

showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe

shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients

withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second

panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely

tobethemechanismfortheriseinachievement28

OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-

teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint

estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-

incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 30: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

30

Table10showsparallelresultsforcomponentsofspendingTotal

expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance

reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe

quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional

componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto

accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof

impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither

oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit

implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell

StangeandMcFarlin2015andNeilsonandZimmerman2014)

Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof

schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual

allocationsareclosetooptimalItispossiblethattheachievementeffectswould

havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway

Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto

involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe

additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash

ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30

29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 31: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

31

VII EffectsonAchievementGaps

Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed

overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-

incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures

thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational

systematdeliveringequitableadequateservicestodisadvantagedstudents

(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya

smallportionofincomeorotherinequalityisbetweendistrictschangesinthe

distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto

meaningfullyclosethesegaps

Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent

subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean

(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions

Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin

meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch

designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas

thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina

statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek

RivkinandTaylor(1996)

Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus

respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon

achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof

magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 32: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

32

AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand

freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto

attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge

Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein

firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas

largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative

resourcestowhichthetypicalminorityorlow-incomestudentisexposed

Toassessthismorecarefullyweassignedeachstudentthemeanrevenues

forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-

whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported

inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues

intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe

averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas

moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould

stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo

averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto

havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe

concludethatwithin-districtchangeswouldbenecessarytohaveameaningful

impactontheaveragelow-incomeorminoritystudent

VIII Conclusion

Afterschooldesegregationschoolfinancereformisperhapsthemost

importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 33: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

33

whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen

wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave

ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent

achievementOurstudypresentsnewevidenceoneachofthesequestions

Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy

eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot

accomplishthisbylevelingdownschoolfundingbutratherbyincreasing

spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough

wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough

localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending

inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent

achievementwefindthatthisspendingwasproductiveReformsalsoledto

increasesintheabsoluteandrelativeachievementofstudentsinlow-income

districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who

examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial

positiveimpactsonavarietyoflong-runoutcomes

Toputourresultsintocontextconsidertheimpliedeffectofanaverage-

sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean

relativetoadistrictatthemeanAccordingtoourestimatesthereformraised

relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect

thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again

immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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Page 34: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

34

wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe

reformeventthatifanythingcontinuedtogrowthereafter

Thecost-effectivenessofthesereformscanbeassessedbycomparingthe

financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects

areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer

discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa

presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard

deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin

adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect

estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof

$4815perpupilimplyingabenefit-to-costratioofnearly14

ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue

effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese

comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile

countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe

benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof

earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest

scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos

(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult

outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus

althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto

indicatethatthespendingenabledbyfinancereformswascost-effectiveeven

withoutaccountingforbeneficialdistributionaleffects

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 35: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

35

Ourresultsthusshowthatmoneycananddoesmatterineducationand

complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom

Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics

(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin

districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas

tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan

evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts

ButthereisanimportantcaveattothisconclusionAswediscussinSection

VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income

districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind

thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income

schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps

betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps

viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin

schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy

References

BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson

edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress

BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent

AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 36: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

36

CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation

andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40

CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA

directassessmentQuarterlyJournalofEconomics107(1)151-200

CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool

spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82

CascioEUGordonNampReberS(2013)Localresponsestofederalgrants

evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159

CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe

IntroductionofTitleIAmericanEconomicReview103(3)423-427

CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility

investmentsEvidencefromadynamicregressiondiscontinuitydesign

QuarterlyJournalofEconomics125(1)215-261

ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance

reforminMichiganEconomicsofEducationReview28(1)90-98

ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)

HowDoesYourKindergartenClassroomAffectYourEarningsEvidence

fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660

ClarkMA(2003)Educationreformredistributionandstudentachievement

EvidencefromtheKentuckyEducationReformActUnpublishedworking

paperMathematicaPolicyResearchPrincetonNJ

ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF

DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684

CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress

CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole

inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge

CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The

changingdistributionofeducationfinance1972ndash1997Socialinequality433-465

CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating

ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 37: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

37

DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73

FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress

GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269

HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98

HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland

HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress

HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627

HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172

HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231

HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript

JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics

KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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Page 38: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

38

KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge

KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532

KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63

KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress

LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge

MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September

MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812

NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120

PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839

PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474

ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation

SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044

WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 39: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figures

Figure 1 Timing of school finance events

02

46

8E

ven

ts p

er

yea

r

1990 2000 2010Year

Statute amp court

Statute

Court

Notes When multiple events occur in a state in a given year they are combined into a single event for thischart

39

Figure 2 Geographic distribution of post-1989 school finance events

3

2

͵

23

1

3

3

2

1

ʹ

2

5

3

3

4

3

1

12

2 5

7

2

11

1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

2006-2009

2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
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Page 40: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 2 Geographic distribution of post-1989 school finance events

3

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1

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1 No Event

1990-1993

1994-1997

1998-2001

2002-2005

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2010-2013

Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period

40

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

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20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

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10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

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GA

ID

IL

IN

IA

KS KYLA

ME

MD

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45 degree line Linear fit (unweighted)

(a) State revenue per pupil

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FLGAID

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IN

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KSKY

LA

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MDMAMI

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minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

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20

00

40

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20

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$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

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20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

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ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

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minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

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01

00

02

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0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 41: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 3 State aid vs district income Ohio 1990 and 2011

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

1990

05000

10000

15000

20000

25000

10 1025 105 1075 11 1125

2011

Sta

te a

id p

er

pupil

(2013$)

ln(district avg HH income 1990)

Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution

41

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 42: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011

AL

AZAR

CA

COCT

DE

FL

GA

ID

IL

IN

IA

KS KYLA

ME

MD

MA

MI

MN

MSMOMT

NENH

NJ

NM

NY

NC

ND

OK

OR

PA

RI

SC

SDTN

TXUT

VT

VA

WA

WVWI

AKNVWY

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(a) State revenue per pupil

ALAZ

AR

CA

CO

CT

DE

FLGAID

IL

IN

IA

KSKY

LA

ME

MDMAMI

MNMS

MO

MT

NE

NV

NH

NJ

NY

NC

NDOKOR

PA

RI

SC

SD

TNTX

UT VT

VA

WA

WV

WIWY

AK

NM

OH

minus1

00

00

minus5

00

00

50

00

10

00

02

01

1 S

lop

e

minus10000 minus5000 0 5000 100001990 Slope

45 degree line Linear fit (unweighted)

(b) Total revenue per pupil

Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit

42

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 43: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 5 Summaries of school finance in Ohio 1990-2011

minus6

00

0minus

40

00

minus2

00

00

20

00

40

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(a) Log income gradients

minus2

00

00

20

00

40

00

60

00

20

13

$ p

er

pu

pil

1990 1995 2000 2005 2010Fiscal year

State aid

Total revenue

(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income

Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform

43

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 44: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

Sta

te A

id S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3

44

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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  • all tables figures
Page 45: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4

45

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 46: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope

minus2

00

0minus

10

00

01

00

02

00

0C

ha

ng

e in

To

tal R

eve

nu

e S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6

46

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 47: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile

minus1

01

23

minus5 0 5 10 15 20

(a) Q1

minus1

01

23

minus5 0 5 10 15 20

(b) Q5

minus1

01

23

minus5 0 5 10 15 20

(c) Q1 - Q5

minus1

01

23

minus5 0 5 10 15 20

(d) Overall

Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4

47

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 48: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 10 Event study estimates of ecrarrects of reform events on test score slope

minus3

minus2

minus1

01

Ch

an

ge

in T

est

Sco

re S

lop

e

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3

48

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 49: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores

minus1

01

23

Ch

an

ge

in M

ea

n T

est

Sco

res

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate Parametric Estimate

Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6

49

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 50: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Tables

Table 1 NAEP Testing Years

Year Subject(s) Grade(s) Number of States Number of StudentsTested

1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250

Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules

50

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 51: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 2 Summary statistics

(a) District-Year Panel

mean sd N

Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207

(b) State-Year Panel

mean sd N

State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100

51

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 52: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)

Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)

Trend -2400 -1663(2772) (3990)

Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438

Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level

52

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 53: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile

(a) State Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 10227 7728 5102 5281 5175 2457

(2799) (2494) (3286) (2559) (2105) (1193)

Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)

Trend 5573 1244 4475(3627) (3251) (2804)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091

(b) Total Revenue

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event 8380 6747 3075 4178 5344 2577

(2368) (2098) (2209) (1931) (1795) (1230)

Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)

Trend 3883 -1968 5962

(3971) (2570) (3092)

Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119

Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level

53

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 54: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil

(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev

Post Event 7623 7601 6911 5446 5624 5686

(2977) (2771) (2401) (2215) (2126) (1894)

Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)

Trend 2477 -2256(3133) (2972)

Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014

Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level

54

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 55: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 6 Event study estimates for test score slopes

(1) (2) (3) (4) (5) (6)

Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711

(000313) (000324) (000369) (000357) (000367) (000419)

Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)

Trend -000168 -000253(000365) (000388)

Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X

Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level

55

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 56: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 7 Event studies for mean subgroup scores

(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5

Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698

(000264) (000375) (000176) (000191) (000256) (000253)

Post Event -000538 -000400 -000485(00151) (00151) (00121)

Trend 000417 000382 0000740(000459) (000228) (000295)

Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263

Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel

56

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 57: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 8 Event studies for test score slopes by subject and grade

Test Score Slope Q1-Q5 Mean

Pooled -000882 000734

(000313) (000256)

By Subject Math -00106 000803

(000340) (000304)Reading -000653 000577

(000383) (000244)

By Grade4th -00106 000780

(000396) (000286)8th -000724 000728

(000341) (000295)

Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level

57

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 58: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 9 Mechanisms Teacher and student variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesShare blackhispanic -000175 -000164 00000824 0728

(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480

(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990

(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415

(0137) (0134) (00338)

Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718

(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796

(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588

(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832

(0137) (0103) (00182)

Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined

58

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 59: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 10 Mechanisms Revenue and expenditure variables

Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)

SlopesTotal revenue per pupil -3212 -2937 1154 0438

(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339

(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896

(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325

(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397

(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909

(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975

(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264

(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465

(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517

(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584

(1022) (9224) (1205)

Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119

(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910

(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548

(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795

(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128

(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726

(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673

(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117

(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522

(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666

(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501

(7299) (6279) (2310)

Notes See notes to table 9

59

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 60: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table 11 Event studies for mean subgroup scores

Post Event Yrs Elapsed

Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)

By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)

By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)

Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum

of the inverse subgroup sample sizes (egq

1Na

+ 1Nb

for subgroups a and b) For this reason the estimated

test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup

60

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 61: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Appendix

Overview of Appendix Results

Sample construction

Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event

Number of events

During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state

Heterogeneity by grade

It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time

Change in district incomes

One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the

61

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 62: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events

Robustness alternative specifications

Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates

In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results

Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant

Income race analysis

Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion

62

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 63: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Appendix Figures

Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo

020

40

60

o

f S

tate

minusE

vents

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(a) State-year-event sample for finance analysis

020

40

60

80

100

o

f S

tminusG

rminusS

ubminus

Ev

Cells

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(b) State-year-event-subject-grade sample for test score analysis

Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis

63

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures
Page 64: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Figure A2 Event study of number of events to date

minus1

01

23

4C

hange in

num

ber

of eve

nts

so far

minus5 0 5 10 15 20Years Since Event

Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications

Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)

minus3

minus2

minus1

01

Change in

Test

Sco

re S

lope

minus5 0 5 10 15 20Years Since Event

NonminusParametric Estimate (G4) Parametric Estimate (G4)

NonminusParametric Estimate (G8) Parametric Estimate (G8)

Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores

64

Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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Appendix Tables

HanushekampLindseth(through2005)

JacksonJohnsonampPerisco(through2010)

CorcoranampEvans(results

through2006)

MurrayEvansampSchwab(through1996)

CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994

19971998

1994Equity

1994199719982007

_ 1994

Arkansas 199420022005

19952007

2002Equity

199420022005

20022005

1994

California _ 19982004

Equity 2004 _ _

Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995

2010_ 1995

Idaho 19932005

1994 _ 19982005

_ _

Indiana 2011 _ _ _ _Kansas 2005 1992

20052005

Equity2005 2005 _

Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993

2005Equity 1993 _ _

Montana 2005 19932007

2005Equity

199320052008

2005 1993

NewHampshire 199319972002

19992008

1997 19931997199920022006

19971998199920002002

1993

NewJersey 1990199419982000

1990199619972008

2002Equity

199019911994

1990199419971998

199019911994

NewMexico 1999 2001 Equity 1998 _ _NewYork 2003

20062007 2003 2003

20062003 _

TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through

2013)

65

NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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NorthCarolina 199720042012

2012 2004 19972004

2004 _

NorthDakota _ 2007 _ _ _ _Ohio 1997

20002002

2000 _ 199720002002

1997200020012002

_

Tennessee 199319952002

1992 Equity 199319952002

199319952002

19931995

Texas 19911992

1993 Equity 199119922004

199119922005

19911992

Vermont 1997 2003 1997Equity

1997 1997 _

Washington 2010 2013 _ 19912007

_ _

WestVirginia 19952000

_ 1995 _ 1994

Wyoming 1995 19972001

1995Equity

19952001

1995 1995

Noyeargivenplantiffvictory

Table A2 Dicrarrerence in log mean district income 1990-2011

(1) (2) (3)

Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)

log(Dist avg HH income) -00863 -00519 -0114

(00263) (00397) (00320)

log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)

Observations 12527 12527 15576Event States X XAll States X

Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level

66

Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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Table A3 Alternative ways of handling event sample

(a) First event in each state

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -4608 -1949 4270 6101

(2546) (3950) (3086) (2388)

Post Event Yrs Elapsed -000810 000461

(000332) (000269)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) Court events only

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)

Post Event Yrs Elapsed -000885 000789

(000478) (000360)

Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) Reweight states w multiple events by 1n

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -5639 -3177 5590 6946

(2444) (3451) (2631) (2029)

Post Event Yrs Elapsed -000771 000487

(000362) (000266)

Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(d) Number of events to date

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)

Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

67

Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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Table A4 Alternative income measures

(a) 2010 district income

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3844 -2221 4100 3947

(1683) (2205) (2095) (1461)

Post Event Yrs Elapsed -000977 000844

(000286) (000207)

Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(b) 1990 housing values

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event -3318 -2141 5590 6946

(1386) (2094) (2631) (2029)

Post Event Yrs Elapsed -000717 000871

(000201) (000248)

Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

(c) 1990 share lt 185 poverty line

Slopes Q1-Q5 Means

St Rev Tot Rev NAEP St Rev Tot Rev NAEP

Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)

Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)

Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X

Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details

68

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

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Page 69: School Finance Reform and the Distribution of Student ...jrothst/workingpapers/LRS_schoolfinance_120215.pdfstudent achievement and of disparities between high- and low-income school

Table A5 Fraction in each district income quintile

Q1 Q2 Q3 Q4 Q5

Black 0238 0242 0225 0171 0124

BlackHispanic 0237 0232 0243 0171 0117

White 0196 0189 0182 0203 0230

Freereduced-price lunch 0312 0219 0201 0158 0110

Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one

Table A6 Event studies for per pupil revenue gaps

St Rev Tot Rev

BlackWhite Free Lunch BlackWhite Free Lunch

Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)

Observations 1810 1624 1810 1624

Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level

69

  • draft_20151130-jrcuts-clean
  • all tables figures

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