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The Effect of High School Courses on EarningsAuthor(s): Heather Rose and Julian R. BettsSource: The Review of Economics and Statistics, Vol. 86, No. 2 (May, 2004), pp. 497-513Published by: The MIT PressStable URL: http://www.jstor.org/stable/3211643 .

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THE EFFECT OF HIGH SCHOOL COURSES ON EARNINGSHeather Rose and Julian R. Betts*

Abstract-We estimatethe effect that six types of high school mathcourseshaveon students' arningsnearlya decade aftergraduation.Weuse High SchoolandBeyond transcript atato differentiate oursesat amoredetailed evel than nprevious esearch.Thisenablesus to show thatmore-advancedourseshave largereffects than ess-advanced nes. Wealso provideevidence that mathcoursescan helpclose the earningsgapbetween students rom low-incomeand middle-income amilies.Finally,by incorporatingther academicsubjects,we demonstrate ow specificcourse combinations an explain the earningspremiumrelated to anadditional earof school.

I. IntroductionDUCATIONhas been at the forefrontof the nation'sconcerns ordecades.Falling est scoresthroughouthe1960s and 1970s promptedgovernmentofficials to pre-scribea new curriculum.n 1983,the NationalCommissionon Excellence in Educationadvisedthat all high schoolstudentsshould follow a morerigorouscurriculum.' incethen, statepolicymakershave adoptednew graduation e-quirements ndcurriculum tandardso satisfythe commis-sion's recommendations.

Althoughmanyobserversbelieve that an enhancedcur-riculum s the vehicle to improvededucationaloutcomes,little researchhas been done to understand ts long-termeffects.Altonji 1995)marksone of theprimary ttempts yan economistto systematically stablisha directlink be-tween curriculum nd wages. His work, which examineshigh school graduates rom 1972, producesthe puzzlingresult that the curriculum as an extremelyweak effect onwages. Studying graduates rom the late 1970s and early1980s,LevineandZimmerman1995)findsomewhat tron-ger results from some of their model specifications,butconclude thatany potentialeffects of the mathcurriculumare restricted o certainsubgroupsof the population menwith low education evels and highly educatedwomen).Because the notion that the curriculumdoes not matterraisesseriousquestionsabout heeffectivenessof theAmer-ican public school system, it is essential to investigatefurther.Therearealso moregeneral easonswhyit is importantounderstandhe effects of the high schoolcurriculum. irst,

Received for publicationOctober22, 2001. Revision acceptedforpublication une20, 2003.* PublicPolicy Instituteof California; nd PublicPolicy InstituteofCalifornia ndUniversityof California, anDiego, respectively.We would like to thankJeff Owingsand RobertAtandaat NCESforproviding s withthemathandsciencecourseclassifications. articipantsat the annualmeetingsof the American EconomicsAssociation,theAssociation or PublicPolicyAnalysisandManagement, nd numerousEconomicsDepartmenteminars,as well as Dan Hamermesh nd tworeferees,provideduseful nsights.Wewould also like to thank he PublicPolicyInstitute f Californiaor research upportor thisproject.Thiscurriculum,ubbed he "NewBasics,"consistedof fouryearsofEnglish, hreeyearsof math, hreeyearsof science,threeyearsof socialstudies,two yearsof foreign anguage forcollege-bound tudents),andsix monthsof computer cience.TheReviewof Economics and Statistics,May 2004, 86(2): 497-513

if thehighschool curriculum as little influenceon studentoutcomes, hen interventionmaybe necessaryat an earlierstage. Second, with the recent eliminationof affirmativeactionin some states,minorityaccess to highereducationmaysuffer.As the returns o a collegeeducation ontinue orise, such limited access would aggravatencomeequalityamongethnicgroups.Carryingorward he literaturehatAltonjiinitiated,weestimate the effect that specific high school math courses(vocationalmath,pre-algebra, lgebra/geometry,ntermedi-ate algebra,advancedalgebra,andcalculus)haveon earn-ings nearlyten yearsaftergraduationor a cohortof stu-dents who werehighschoolsophomoresn 1980.2We alsodeterminewhether variedmathcurriculumanexplain heearningsgap betweenstudentsof differentethnicities,so-cioeconomicstatuses,and genders.Ourstudydiffers dra-matically romprevious tudies n thatwe use verydetailedtranscriptdata to analyze the effects of specific mathcourses rather han ust the total numberof math courses.Ourprincipal atasource s HighSchoolandBeyond HSB).The paper proceedsas follows. Section II presentsatheoretical iscussionof thelinkbetweenmathematicsur-riculumandwagesand reviews theexisting empirical iter-ature.SectionIIIdescribes he econometricmodel that weuse to estimatethe effects of curriculum n earningsandprovidesan in-depthdescriptionof our data. Section IVpresentsthe resultsfrom our earningsmodels as well asseveral robustness checks. In section V, we investigatewhether he curriculum anexplainethnic,socioeconomic,andgender-basedarningsgaps.Section VI concludes.

II. How Might Curriculum Affect Earnings?A Review of Theory and EvidenceA. TheHumanCapitaland SignalingModels

Human apital heory mpliesthata curriculumas valuebecause t imparts kills thatmakestudentsmoreproductiveand betterrewardedn the labor market.This mechanismcan work in several ways. Students who take more-advancedmathclasses earnskills thatmayapplydirectly ocertainobs. They mayalso learn ogic andreasoning killsthat indirectlymake them more productive.In addition,advancedmathmay also teach studentshow to learn. Fi-nally,evenif ajob only requiresbasic mathskills,a student2Researchby Murnane,Willett,andLevy (1995) andby GroggerandEide (1995) shows thatbetween the 1970s and the 1980s the relativeimportancef math estscores n determiningarnings rewsubstantiallyand thatmathachievements a betterpredictor f adultearningshanareother ypesof testscorescommonlyavailable.We thereforeocusmainlyon the mathcurriculum,lthoughwe broaden hisanalysis o include hecurriculumn otherfields. Anotherpractical eason o focus on math sthat he contentof mathcourses s muchmorecomparablecrossschoolsthan s the contentof courses n othersubjects see Porter t al., 1993).

? 2004 by the President and Fellows of HarvardCollege and the Massachusetts nstituteof Technology

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THE REVIEW OF ECONOMICS AND STATISTICSwho has taken advanced math has had an additional chanceto master those skills.3In contrast to the human capital model, the signalingmodel (Spence, 1973) suggests that math courses do notcause the student to be more productive.Rather,the innatelymore productive, that is, "more able," students choose toobtain the specific levels of education thatprovide signals toemployers.In the case of the curriculum, the signaling model isapplicable at several levels. Students who take a morerigorous curriculumprovide a signal of ability to colleges.College attendance in turn provides a signal of ability toemployers.4 It is less clear how taking more high schoolcourses could act as a signal for students who do not attendcollege. Perhaps employers of high school graduateslook athigh school transcripts-an assumption not generally sup-portedby the research of Bishop (1989). Nonetheless, moreable students may signal that they have taken certaincourses duringjob interviews.The signaling-human-capital debate matters for policy. Ifa student gains no productivity by taking a specific mathcourse but merely buys a signal of ability, then requiringallstudents to take that course would not raise labor marketproductivity or aggregate wages. Further, such a policychange could lead to inefficiencies in the labor market,because a standardized curriculum would make it moredifficult for employers to identify the most productivestudents. In contrast, human capital theory contends thatadditional math courses could perhaps make all workersmore productive, so there is a causal relation betweencurriculum and wages. Given the stark difference betweenthe implications of the two theories, our analyses involvenumerous robustness checks.B. Previous Research

The economics literaturehas been slow to incorporatethehigh school curriculum into wage models, with the excep-tions of Altonji (1995) and Levine and Zimmerman(1995).5Altonji asks: Does an extra year of education serve merelyas a screening device, or do the courses that make up that3 Gamoran1998) mentions hesepathsand cites other,corroboratingstudiesas well.4It is possiblethatemployersdo not use educational ackgrounds asignal of ability,but that the studentpossesses some characteristic,unobservableo the researcher,hat causes him or her to takea more-advanced urriculum nd o earnhigherwages.Such a patternwould eadtoendogeneity ias.This s closelyrelated othesignalingmodel,becauseit recognizesthe possibilitythat differences n returns rom differentcourses could be caused by selection effects that are the result ofunderlyingability.We thank DeborahReed and Kim Rueben for thisinsight.5Gamoran1998)provides n excellentreviewof other tudies hathaveundertakenimilargoals.Mostof these studiesarequitedatedand notinthe economics iterature.Many ocus on the effectsof tracking ather hanspecific highschool courses.Others hat do look at coursesrestrict heirsamplesto studentswho obtain no postsecondaryducation. n unpub-lished work, Ackerman 2000) also addresses the issue of the mathcurriculum ut does not divide up coursesin as detailed a manneraswe do.

year possess some intrinsic value? Using the National Lon-gitudinal Survey of the High School Class of 1972 (NLS72),he models the log wage of each person as a function ofcredits completed in eight different subjects during grades10-12, standardbackground variables, and years of post-secondary education.6 Because the eight curriculum vari-ables are highly correlated, he conducts the same analysisusing combinations of courses by subject instead of enteringthe individual courses separately.He uses three methods to estimate the effects of thecurriculum:OLS, OLS with high school fixed effects, and amodel in which he uses a school's average numberof creditsearned per student within each subject as an instrument foreach student's number of credits earned in that subject. Allthree approaches lead to similar results. Altonji's overallconclusion is that "the effect of a year equivalent of coursesis much smaller than the value of one year in high school."In otherwords, the whole is greaterthan the sum of its parts.Even before controlling for background characteristics,theIV estimates suggest that each additional year of science,math, English, social studies, and foreign language com-bined leads to a minuscule 0.3% increase in wages. He findsstronger curriculum effects if he excludes the negativeeffects of English and social studies. An additional year ofmath, science, and foreign language increases earnings by3.1%.7 Because an additional year of school is estimated toincrease wages by 7%, Altonji's results lend supportto theview that high school serves as a screening device ratherthan as a mechanism for human capital formation.On the other hand,Altonji's results could be not so mucha refutation of humancapital theory as a sign that schoolingincreases human capital in ways quite distinct from thecurriculum. For instance, schooling may improve student'scritical thinking and punctuality. See Bowles, Gintis, andOsborne (2001) for a discussion of these ideas.Levine and Zimmermanfocus on the effect that math andscience courses have on wages. They use data from twomain sources: the National Longitudinal Survey of Youth(NLSY) and HSB's 1980 senior cohort. Levine and Zim-merman focus on students who graduatedin the late 1970sthrough the early 1980s and estimate separate models formen and women. Like Altonji, they use the number ofcredits earned in math and science courses (separately) astheir curriculum measures in the HSB data.Levine and Zimmerman find that the number of scienceclasses has very little effect on wages for either males orfemales. However, their OLS results indicate that an addi-tional semester of math increases male wages on average by3% and female wages on average by approximately 2%.

6 The eight subjectsarescience,math,English,social studies,foreignlanguage, ndustrial rts,commercial ourses,and fine arts. One creditrefers o an additional ear'sworthof thecourse.7 OLS estimatesareslightly arger, ndOLSestimateswithhighschoolfixed effectsaresubstantiallyarger.OLS estimateswithout ixedeffectspredict hat he effectof an additional earof mathematics n earningss1.8%,but thatdisappears nce abilitycontrolsareadded.

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HIGH SCHOOL COURSES AND EARNINGSTABLE .-REGRESSORSNCLUDEDNMAINMODELS

Math curriculum Math creditsearnedin each of the following six mathcategories:vocationalmath,pre-algebra,algebra/geometry,intermediatealgebra,advancedalgebra,and calculus.Demographic nformation Ethnicity, gender, age in 1991, and maritalstatus in 1991.Family characteristics Parental ncome, parentaleducation,parentalnativity,and the numberof siblings.School characteristics Student-teacher atio,books per pupil, length of the school year, school enrollment,percentageof disadvantagedstudents,percentageof teacherswith a master'sdegree, district'saveragespending per pupil, teachersalary,whether teachers are unionized,and the public school's type (regular,alternative,CubanHispanic,or otherHispanic), geographicregion (nine U.S. regions), andurbanicity rural,urban,or suburban).Highest degree High school dropout,high school diploma, some postsecondaryeducation(but no degree), a certificate,anassociate's degree, and a bachelor's degree or higher.

Note: Specific categoriesand means of the above variablesare available from the authorson request.

Further,they find that the math effects are limited to menwho have only a high school degree and to women whohave completed some college or have earned a collegedegree. For female college graduates,an additionalsemesterof math during high school leads to a 5.4% increase inwages. The effect for men with only a high school diplomais 3.1%. When Levine and Zimmerman use instrumentalvariables with Altonji's instrument,the math effects disap-pear. The variation in results across subgroups may be theresult of the small sample sizes within each group. Further-more, they are looking at wages only approximately6 yearsafter high school graduation,so males may not have settledinto careers indicative of their curriculum and educationalattainment.C. Contributionsof ThisPaper

A key factor that distinguishes our work from the twoearlier contributions is our detailed analysis of the types ofmath courses taken. A second distinguishing factor is ourfocus on the role, if any, that the high school curriculumplays in creating the well-known wage gaps between work-ers of different races, ethnicities, and genders.Like Levine and Zimmerman, we use the HSB data set.Unlike Levine and Zimmerman, we use the sophomorecohort of that data set, most of whose members graduatedfrom high school in 1982, rather than the senior cohort thatgraduatedin 1980. This alternativesample provides severaladvantages. First, our data reflect earnings 10 years aftergraduation, rather than only 6 years as with Levine andZimmerman's data. The effects of curriculum on earningscould look quite different for workers in their late twentiesthan for a sample of 24-year-olds who may not yet havesettled into careers. Even students who obtained amplepostsecondary education have relevant earnings data in oursample. Second, the transcript data for the 1982 HSBseniors are much more detailed than the course informationfor the 1980 HSB seniors. Third, both Levine and Zimmer-man and Altonji study a cohort of seniors, thus excludinghigh school dropouts. Because we begin with a tenth-gradecohort, we are able to include some dropoutsin our models.Fourth,whereasAltonji examines earnings in the 1970s andin 1986, and Levine and Zimmerman examine earnings in1986, we follow the students into the early 1990s. This

update may be important, given the dramaticincrease in thereturns to education in the United States between the late1970s and the mid-1990s.III. Earnings Model and Data

A. Estimatingthe Effectsof Curriculumon EarningsWe construct the following linear model of the log of1991 annual earnings for student i at school s:In earni, = a + I3oCurricis 3lDemois+ 32Fami,

+ P3Schis+ 34HiDegis+ ?is, (1)where Currici, denotes the curriculum (a vector of thecredits earned in each of six math course categories);Demois refers to demographicinformation;Famsi andSchisare family and school characteristics,respectively; HiDegisrepresentsa series of dummy variables indicating the high-est degree the student has earnedby 1992; and eis is an i.i.d.error term.8 The specific regressors included are listed intable 1. Each element in the vector of coefficients, 3o,describes the effect of an additional credit in the corre-sponding math course on the log of earnings. Because weinclude the school variables upon which the HSB surveywas stratified,we do not weight the regressions.Insofar as educational attainment could itself be an en-dogenous function of the high school curriculum, we alsoestimate reduced-form models that exclude educational at-tainment. We elaborate on the specific models we estimateafterdescribing the data. In section IV, we discuss the issueof omittedability extensively andpresent several alternativespecifications, including an instrumentalvariables approachsimilar to that used by Altonji (1995) and a model thatincludes school fixed effects.

8 In our initial analyses, we assume the errorterm is independent acrossstudents. However, because some shocks may affect all students at aparticular school in the same way, we also estimated random-effectsmodels in which the error term also contains a school-specific component.The estimated curriculum coefficients and standard errors were nearlyidentical to those estimated by OLS (the coefficients differed by 0.0002 atmost, and the standard errors by even less, depending on the specificmodel specification), so we report the OLS estimates for simplicity.

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THE REVIEW OF ECONOMICSAND STATISTICSB. Data Description

The principalsourceof datafor this studyis the HSBsophomore ohort:1980-1992data.Thislongitudinal tudysurveyedover30,000 highschoolsophomoresn 1980 andfollowedup approximately 5,000of them in 1982, 1984,1986, and 1992. This is an excellent source of data forseveralreasons.It providesextremelydetailedhigh schooltranscriptnformation,ncludingeverycourse takenby thestudent, he term t was taken,the gradereceived,and thenumber of credits earned. It also provides a wealth ofpersonalandfamilycharacteristicsnd ncludeshighschooldropoutsn the transcript ndfollow-upsurveys.9We use thelog of annual arningsn 1991as ourprimarydependent ariable.Thereare two primary hortcomings fthesedata.Theearningsdataaremissingforapproximately20%of thepublicschoolsample, husreducing he numberof usable observations.These data are missing primarilybecause of the lack of participationn the finalfollow-up.Secondly, heearningsdatameasureannualearnings atherthan an hourly wage, which is a muchbetter measureofactualproductivity.10hus any apparent urriculum ffectmay operate hrough wo channels:aneffecton wagesandan effect on employmentstatus and hours worked. It isimpossibleto disentanglethese two effects entirely.Wetherefore restrict the range of earningsthat we model,eliminating hosewho earned ess than$2,000 (to excludethose most likely working part-time)and those few whoearnedmore than$75,000.11We constructeddata on mathematics urricula rom therestricted ighschooltranscript ata.Inthis dataset, everyhighschoolmathcoursea student ookis classified nto oneof 42 categoriesusing the standardClassification f Sec-ondarySchool Courses(CSSC).We aggregated hese 42classes into six broader ategoriesbased on a classificationsystem providedby the National Center for EducationStatistics(NCES). In increasingorder of rigorthese are:vocationalmath,pre-algebra, lgebra/geometry,ntermedi-ate algebra,advancedalgebra,andcalculus. TableAl de-scribes the specific math courses includedin each cate-gory.'2The number f creditsa student arnedn each classis alsoavailable,wherea typicalone-year ourse s assigned1 credit and a half-yearcourse is assigned 0.5 credits(technically, hese credits areCarnegieunits).Combiningthese two variablesyields our primarymeasureof the

9Respondentswho missed a year were still included in subsequentfollow-ups f possible.Even studentswho were selected nto thebase-yearsurveybutmissed t were included n the follow-ups f possible.10The surveydid gatherextremelydetailedwage data until 1986,butstoppedafter hat." Grogger(1996) and Groggerand Eide (1995) make similar datarestrictions.n a subsequent ection,we discuss how the resultschangewhen we relax this incomerestrictionand when we use a version ofmonthlyearningsas the dependent ariable.12 Althoughwe describemathherefor simplicity,we do analyzeotheracademic ubjects.TableA2 shows the classification ystemthatwe usefor science courses.

curriculum:he numberof credits earnedby student ineach of the six mathcoursecategories.'3Students or whomearningsdata or curriculum ataaremissingareexcluded rom hisanalysis.We alsorestrict ursample o studentswho attended ublicschools andexcludestudentswho changedschoolsduringhigh school.In addi-tion,we exclude studentswho were enrolled n postsecond-aryeducation tanytimeduring heyear1991or for whomenrollment ataaremissing,because heirearningsmaynottruly reflect their humancapitalformation,or their finalsignal.'4Tables A3 and A4 list the number of missingobservations or the primary ariablesusedin the analysis.We treatedquestionabledata values as missing(for ex-ample, student-teacher atios of 0.17 and of 2000). Forvariablesother than the dependent ariableandthe curric-ulum measures,we set missing values equal to 0 andincludeda dummyvariablendicatingwhether he variablewasmissing.Inapproximately5 cases,we imputedvaluesfor earningsor considered hem to missing when the re-porteddata seemed mplausible.Forexample,we assumedincomesthat umpedfrom$20,000in 1990to $200,000in1991 and then back to $20,000 in 1992 were dataentryerrorsand we corrected hem appropriatelyin the abovecase, set to $20,000). We did not change largejumps inearnings hatcoincidedwiththecompletionof a bachelor'sdegree.15C. DescriptiveStatistics

Because HSB used a stratified ationalprobability am-ple of schools in whichschools with a highpercentageofHispanic tudentswereoversampled,hesummarytatisticsmust be weightedto make meaningfulprojections o thepopulationas a whole.'6 In table A5, we presentbothweightedandunweightedmeansandstandard eviationsof

13 In theunrestricted ersionof thedata,onlythe totalnumber f mathclasses that a student took is available.Thus, no measureof coursedifficulty s available.Also problematics that the precalculatedoursecounts n thetranscriptatagiveeach course akena countof 1.So, if onestudent akes a one-yearalgebracourse and another tudent akes twoone-semester lgebracourses,they will have coursecounts of 1 and 2,respectively.nessence,thetwo studentshavetaken he samecourse,buttheirtally is misleading.This could lead to measurementrrorbias inmodels that use theunrestricted ersionof the data(ortheprecalculatedcourse counts n the restricted ersion),whichwouldbias the estimatedeffect of math oward0.14 School attendancedata are nonexistent or August of 1991, so inpractice he restriction ppliesto those enrolled,or missingenrollmentdata,during heremaining leven monthsof the year.15Although he last follow-up ookplacein the springof 1992,we didnot use the annualearningsdata from that year, because they seeminaccurate.Whereas he averageannualearnings teadily ncrease rom1982through1991 n anexpected ashion, heyfall to approximatelyalfof theirexpectedvalue in 1992,as if somerespondentsaveyear-to-dateearningsnformation. venafterdiscussionswith he HSBpersonnelromtheDepartmentf Education,we could not find a clear cause.Althoughthe 1991 earningsreportsare self-reported nd retrospective, hey arelikelyto be accurate ecause he dataweregatheredn 1992(andnear axtime for 1991income).16 Although hattypeof school was oversampled,withinthe school 36studentswere randomly elected. The ethniccompositionof the over-sampledschools still leads to a higherthan nationallyrepresentative

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HIGH SCHOOLCOURSESAND EARNINGSTABLE.-THE EFFECTSFSPECIFICATHCOURSESNLOGEARNINGS:LS, IV,ANDFIXED-EFFECTSSTIMATES

(1) (2) (3) (4) (5) (6) (7) (8)Vocational 0.001 -0.024** -0.027** -0.029** -0.084** -0.086** -0.019 -0.023*(0.011) (0.011) (0.010) (0.011) (0.030) (0.030) (0.012) (0.013)Pre-algebra 0.067** 0.023 0.007 0.005 0.015 0.013 0.006 0.004(0.014) (0.014) (0.014) (0.014) (0.034) (0.034) (0.017) (0.017)Algebra/geometry 0.080** 0.061** 0.031** 0.029** 0.090** 0.083** 0.029** 0.027**(0.010) (0.010) (0.010) (0.010) (0.035) (0.035) (0.012) (0.012)Intermediatealgebra 0.109** 0.078** 0.032** 0.022 -0.107 -0.100 0.054** 0.042**(0.017) (0.016) (0.016) (0.017) (0.068) (0.067) (0.019) (0.019)Advancedalgebra 0.134** 0.088** 0.042** 0.029** -0.077 -0.082 0.054** 0.039**(0.014) (0.014) (0.014) (0.015) (0.050) (0.050) (0.017) (0.017)Calculus 0.195** 0.120** 0.065** 0.047 -0.132 -0.140 0.077** 0.058(0.033) (0.032) (0.032) (0.032) (0.167) (0.167) (0.036) (0.036)Totalmath redits 0.106** 0.069** 0.027** 0.019** -0.009 -0.010 0.036** 0.027**(0.006) (0.007) 0.007 (0.007) (0.024) (0.024) (0.008) (0.008)Math GPA 0.036** 0.063** 0.039**(0.009) (0.015) (0.009)Other controls:Demographicnformation No Yes Yes Yes Yes Yes Yes YesFamily haracteristics No Yes Yes Yes Yes Yes Yes YesSchoolcharacteristics No Yes Yes Yes Yes Yes No NoHighest ducationegree No No Yes Yes Yes Yes Yes YesEstimationmethod OLS OLS OLS OLS IV IV FE FER2 0.069 0.172 0.199 0.201 0.187 0.192 0.316 0.319Number f obs. 5,919 5,919 5,919 5,896 5,864 5,841 5,919 5,896

** Significantat the 5%level; * significantat the 10% evel. Standard rrorsarein parentheses.All models include an intercept.Addingdummyvariables orcollege majorchangesthe coefficientsonly minimally.In the first-stageregressionsof each IV-estimatedmodel, the P-values for the F-test of the hypothesisthat the coefficients on the six school-average nstrumentsareequal to 0 are 0.0001.

theprimary ariablesusedin ouranalysis.Wepresent hesedescriptive statistics for the 11,724 students in publicschoolsand,becausesome crucialdataaremissing,for thesubsampleof observationsused to estimatethe earningsmodels (the regressionsample).The means and standarddeviations n theregression amplearestrikingly imilar othose obtainedwhen using the full set of potentialpublicschool observations.17hissimilarity ffers someassurancethatsampleattrition ndmissingvalues have not distortedoursample.

IV. Earnings Model Results:Does Math Curriculum Affect Earnings?A. Basic Log-EarningsModels

Table 2 presents the coefficients and standarderrors fromthe model in equation (1) as well as from two more parsi-proportionof Hispanics in the sample. Ourregressions do not use weights,opting nstead o includecontrols or the variables sed to stratify choolsin the HSB sample.17Weexaminedmeandifferencesor all regressors,ncluding hose notshown n tableA5. Thebiggestmeandifference ccurs n thepercentageof samplememberswho are male. Thispercentages 4.5 pointshigher nthe usableregression ample, ndicating hat we lose a disproportionatenumber f females.Thisis notsurprising:n average,morefemales willbe out of the labor force and thereforemissing earningsdata in theappropriate ange. As an additional est of whetherthe correlationsbetween the curriculum variables and other regressors in our regressionsubsample are different than in the excluded data, we ran regressions ofeach curriculum variable on the other conditioning variables and tested forvariations n coefficients between the full sampleand the regressionsample.We found ittle evidenceof any changes n covariations etweencurriculum nd otherconditioning ariables.

moniousmodels. The coefficientscan be interpreteds thepercentage hangein earningsassociatedwith an increaseof 1 credit,that is, 1 year,for each of the specificmathcourses.18 hepredicted ffectsof takinghighschool mathvaryacrossmodels,butthefinalconclusionappears obust:Mathmatters.19All of the mainmodels in this tabledisaggregatemathcoursesby type.However,under he six disaggregatedmathcourses,we providea rowshowingtheresultsof otherwiseidenticalmodels that controlonly for the total numberofmathcourses aken.Although heseaverage ffects areoftenstatistically ignificant, hey mask some fairly largevaria-tions n the effect of differentypesof mathcourses.Forthisreason,our discussion of table 2 will focus on the moredetailedmodels thatdisaggregatemathcoursesby type.Column1 contains heresults romthesimplified ersionof the modelin equation 1) that does not controlfor anystudentcharacteristics,ummarizinghe variation n meanearnings among workerswith differentnumbersof math

18These are approximate percentage changes. The regression coeffi-cients represent a first-orderapproximationto the proportionalincrease inearnings from a 1-unit increase in a regressor. The exact percentagechange is given by (eP - 1) X 100%, where P is the regressioncoefficient.19These models are unweightedregressions.Althoughthe sampleisstratified,DuMoucheland Duncan 1983) arguethat the preferredsti-mation echniques not to weightbutrather o includecontrols orall thevariablesuponwhichthe samplewas stratified,which is the course wetakehere.Wereplicatedhe mainmodels n thispaperusingtheweightswe used to reportsample means in tableA5, and found similarresults. Onesubstantialhangewas that hecalculuscoefficientn column3 becomesinsignificant t the 5%level.

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THE REVIEW OF ECONOMICSAND STATISTICScourses. The math coefficients are quite large and vary bythe level of the course. An additional year of calculus ispredicted to increase earnings by approximately 19.5%,whereas an additionalyear of algebra/geometryis predictedto increase earnings by approximately 8.0%. Vocationalmath courses, however, seem to have almost no effect onearnings.

Obviously, this first model is simplistic in that it does nottake account of many other observable variables that areknown to affect wages. As column 2 shows, adding demo-graphic, family, and school characteristicscauses the effectof math courses at or above the algebra/geometry level todrop by 24% to 38%; the lower-level math effects drop byeven more. This pattern suggests that a portion of thecurriculum effects from the previous model should be at-tributedto these other factors.20Nonetheless, all the curric-ulum coefficients, except that of pre-algebra, are still quitelarge and statistically significant at the 5% level. An addi-tional credit in algebra/geometry is predicted to increaseearnings by 6.1%, but advanced algebra is associated withan 8.8% gain. In this model, vocational math has a signif-icant negative coefficient, indicating that taking additionalvocational math courses leads to lower earnings.This resultmight seem to suggest that signaling, rather than humancapital formation, is at work. Though this may be, the resultis consistent with either signaling or humancapital theories.There are virtually no students in the sample who take nomath at all. Because the model contains a constant term,each coefficient is identifiedby variationsin the correspond-ing variable from the sample average. Thus, in our model,the negative sign does not imply that taking an extravocational math course actually lowers earnings relative toa student who takes no math courses. Rather,the negativecoefficient means that taking an additional vocational mathcourse lowers earningsrelative to the studentwho has takenthe average curriculum, which includes only 0.69 year ofvocational math courses. This could indicate that vocationalmath is a negative ability signal. It could also indicate thatthe minority of students who take one or more years ofvocational math have paid the opportunity cost of takingmore advanced math courses that would have helped themdevelop human capital needed in the labor market.To further illuminate the path along which these curric-ulum effects work, we control for the ultimate educationalattainmentof the student. We add to the previous model aseries of dummy variables indicating the student's highesteducational degree attainedby 1992 and present the resultsin column 3. With these controls, the math curriculumcoefficients drop by approximately one-half. The signalinginterpretationof this drop is that approximatelyone-half ofthe overall effect of high school math reflects the way inwhich math courses enable more productive students toattend college and therefore signal their ability to their

20 See table 1 fora list of the specificdemographic,amily,and school

employers. The human capital interpretation is that highschool math courses increase a student's efficiency, thusincreasing his or her chances of attending college, and inthis way increase the student's productivity further.In thehuman capital interpretation,column 2 continues to showthe overall effects of curriculum, whereas the results incolumn 3 show the effect that works directly rather thanindirectly through education. The striking curriculum ef-fects that remain in column 3 after controlling for educa-tional attainmentsuggest that theremay be a direct effect ofmath curriculum on labor market productivity that worksindependentlyof the final degree attained.In this model, thevocational math coefficient is still negative and significant,the coefficient on pre-algebra credits is no longer signifi-cant, but the high-level math coefficients remain signifi-cant.21A course in algebra/geometryis estimated to increaseearnings by 3.1%, and a calculus course appearsto increaseearnings by 6.5%.22,23,24

21 Todeterminehe extent o which henegative ignon vocationalmathis being drivenby studentswho takeonly vocationalmathcourses andnothinghigher,we reestimated he model in column 3 but included adummyvariablendicatingwhether he studenthadtakenonlyvocationalmath.The coefficienton this indicators -0.065 and s significant t5%.Themagnitude f the vocationalmathcredits oefficientbecomesslightlyless negativeat -0.019, but s nowonlysignificant t 10%.This ndicatesthat,on average,studentswho takeonly vocationalmathearn ess thanthose who take vocationalmath and some highermath.It also indicatesthat even those studentswho take some vocationalmathbut also takesome highermath (approximately5% of the studentswho take onevocationalmathcoursefall into this category)still earnless than theaveragestudentwho does not take any vocationalmath. Because theaverage tudentdoes not take an entirecreditof vocationalmath, tudentswho do takeone creditaretaking t at the expenseof a moreadvancedcourse.Thus,there s someopportunityost to takingvocationalmath.22The calculus coefficient s very largerelative o most others n themodel. One effect that s almostas large s comingfroma familywith anincomegreater han$25,000 rather hancomingfrom a familywith amid-level ncome $20,000 o $25,000).Furthermore,hecalculus ffect salmostgreatenough o offset thenegative ffectof coming roma familywithextremelyow income(less than$7,000)relative o comingfrom afamilywith mid-level ncome. The calculuseffect also counterbalancesthe effect of havinga motherwithless thana high schooldegreeratherthanhavinga motherwith a high school degree.In contrast, tandardmeasuresof school quality such as the student-teacheratio are notstatistically ignificant.Not even reducing he percentageof disadvan-tagedstudents t a schoolby 25 percentage ointsoutweighs he effect oftakinga calculuscourse.23To allay concernsthat excluding observationswith earningsnotbetween$2,000 and $75,000 was drivingourresults,we estimated hecolumn 3 model but set all nonmissing arningsvaluesless than$2,000equal to $2,000 (approximately0% of these earningswere $0). Thisimputedearningsvalue can be thoughtof as earnings hat individualsforgo by remainingat home, or it may representa low-valueof thehouseholdworkfor those not working. n thiscase, the resultsare alsoquitesimilar o thosein of column3 in table2. As a second solution oelicitproductivityather hanvariations elated o labor orceattachment,we modeled helog of monthly arnings calculated s annual arningsn1991dividedby the number f months hat herespondentwasemployedduring hatyear).Ateachstage,theresultingmathcoefficientswereveryclose to those from the originalmodel usingannualearnings.Becauseusingthemonthly arningsmeasuremeant osing 150more observationsresultingrommissingemployment ata,we chose to use annual arningsthroughouthispaper.24Anothermportantssue is whether hereturnso takingmathcoursesare nonlinear.We reestimatedmodel 3 afteraddingthe squareof thevariablesused.

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number f credits aken n each mathsubject.None of thesquarederms

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HIGH SCHOOL COURSES AND EARNINGSAnother mechanism throughwhich the curriculum couldaffect earnings is by channeling students into majors, or bykeeping the door open to majors and occupations that aremore highly rewarded in the labor market. We estimated,but do not show, models that also controls for the student's

college major and occupation (with nine and thirteencate-gories, respectively). The purpose of these models is tounderstandthe channels through which high school curric-ulum increases wages. As expected, in models that controlfor students' college major, the curriculum coefficients allfall, but not enough to indicate that the bulk of the remain-ing curriculum effect operates though the college-majorchannel. Even with these additional controls, many of themath effects are still statistically significant.25 Separatemodels that controlled for students' occupation were quitesimilar. Vocational math, algebra/geometry, and advancedalgebra remain significant at 5%, while calculus and inter-mediate algebra become insignificant.26To understand better the degree to which educationalattainment, college major, and occupation can account forthe observed impact of math courses on earnings, we cal-culated the predictedimpact of taking an average numberofcourses in each category (from the final column of appendixtable A5) before and after allowing for educational attain-ment (table 2, models 2 and 3, respectively), and in aversion of model 3 that also added controls for collegemajor and occupation. We found that 64% of the impact ofmath courses appears to work through educational attain-ment, and an additional 18% works through students' sub-sequent occupation and college major.This leaves 18% ofthe curriculum effect that apparently works through othermechanisms.

In sum, it appears that the effects of the curriculumoperate much more through educational attainment thanthroughthe choice of majoror occupation. The results fromthis section indicate that,even afterallowing for a multitudeof factors, a more rigorous curriculum is associated withhigher earnings, indicating that the math curriculum maydirectly affect labor market productivity.were close to being significant.Althoughwe suspectthatdiminishingreturns houldset in at somepoint,thesmallnumber f courses aken neachsubject, s shown nappendixableA5,prevents s fromdeterminingat whatpointsuchnonlinearities egin.25Thealgebra/geometryoefficient s 0.027, whereas hatof advancedalgebras largerat 0.034. Calculus till hasthelargest ffect at5.7%,butit is statistically ignificant nly at the 10% evel. Wethought hattheremightbe importantnteractions etweeneducational ttainment ndma-jor.However,he curriculumffects didnotchange ubstantially henweadded hese interaction erms.Indeed,none of the interactions f curric-ulum andhighest-degree ummieswerestatistically ignificant, uggest-ing thatthe impactof takingadditional ourses s widespread.26Thecoefficientson the mathvariables re also slightlysmalleroncewe control for occupation,at -0.02 (vocationalmath), 0.005 (pre-algebra),0.025 (algebra/geometry),.026 (intermediatelgebra),0.038(advancedalgebra),and 0.050 (calculus).We also tried models thatsimultaneouslyontrolled or occupation ndcollege major.Thegeneralpatternwas a furtherslight reduction n the math coefficients,withvocationalmath,algebra/geometry,ndadvanced lgebra emaining ig-nificantat 5%.

B. OmittedAbilityTwo factors that are impossible to include fully in anyschooling-earnings study are ability and motivation.Theorysuggests that these traits are positively related both tostudents' level of education and to their subsequentwages.27Thus, if these characteristics are omitted from an earningsmodel, the coefficients on the schooling variables (in ourcase, the curriculumvariables) will be biased upwardto theextent that these characteristics are positively correlatedwith curriculumand earnings. This could be a particularlylarge problem when we count the number of courses of aspecific type, rather than when we aggregate all mathcourses into one category.We adopt two main strategies to deal with this issue. Ourprimarystrategy is to add ability and motivation controls inthe form of the student's mathematics grade point average(GPA). We also use an instrumental variables approachsimilar to thatused by Altonji (1995) to eliminate the partofcurriculum that is related to the student's own ability and

motivation.Controlling for Ability and Motivation: The student'smath GPA provides a potentially good measure of abilityand motivation in that it represents how well studentsunderstandand apply themselves given a particularcurric-ulum. But GPA may in part measure factors quite distinctfrom human capital, such as punctuality,neatness, and theinvolvement of parents in the student's schoolwork. Con-sidering the difficulty in distinguishing one effect from theother, we refer to the ensemble of ability and motivationsimply as "ability."The model with math GPA appears in column 4 of table2. The algebra/geometrycoefficient is still significant at the5% level and approximately as large as before, with apredicted effect of 2.9%. Similarly, the advanced algebracoefficient remains significantat the 5% level, but does dropsomewhat in magnitude. The calculus coefficient is nolonger significant with math GPA in the model. This latterresult is certainly consistent with the idea that some of themost advanced courses may reflect ability in partrather hanthe creation of human capital.28

27 Intheory, negative elation ouldarisebetweenabilityandeducationif more able students ound t optimal o leave school earlierbecauseofthe high opportunityosts of schooling n the form of forgoneearnings.See Griliches 1977).28 Weexperimented ith otherpotential bilitycontrols,and theresultswere fairlyconsistentregardlessof the controlwe used. We hopedtoincludea pre-high-schoolest score to control or pre-high-schoolmathability andmoregenerallypriorachievement).Unfortunately,heearliesttest score dataavailable n HSB are from a seriesof tests administeredduringspringsemesterof the student'ssophomoreyear.Becausethisscore s likelyto be affectedby thecoursesstudentsakeduringgrades9and10, it does notprovideanadequatemeasure f pre-high-schoolmathaptitude. tmayactuallyovercontrolorability, ausinga downward iason thecurriculum oefficients.Nonetheless,we didestimatea modelthatincluded he student'smathematicsest score andthe resultsarecompa-rable o the case withGPAcontrols. n this model,thealgebra/geometrycoefficient s 0.025 andsignificant t the 5%level;theadvanced lgebra

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THE REVIEWOF ECONOMICS ND STATISTICSWe also reestimatedmodel 4 afteraddingcontrolsforcollegemajorandoccupation, othseparately ndtogether.The results mirrorour discussion of these extensionstomodel 3: there s evidence thatcollege majorandoccupa-tion explainsome but not all of the impactof high schoolmathcourseson earnings.The most striking hangescamewhenwe addedcontrols or bothmajorandoccupation,n

which case vocationalmath remainedsignificantat 5%,algebra/geometry as significantat almost5%,andinter-mediatealgebrawas significantat approximatelyhe 10%level. In a model not shown,where we repeatmodel4 butwithouteducationalattainment,we find thatthe estimatedimpactof mathcoursesrisessubstantially,imilarly o whatwe show in model 2.Werecalculated ur earlierdecomposition f the sourcesof the math effects, but this time using the models thatconditiononmathGPA.Theresultssuggest hat68%of theeffect worksthroughstudents'educationalattainment ndan additional19% worksthroughstudents'college majorand occupation.The unexplainedportion,approximately13%,appears o workthroughothermechanisms.Instrumental Variables Estimation: In another attemptto curbomittedabilitybias,we followAltonji's eadandusea school's averagemathcreditsearned n each of the sixmathcategoriesas instruments or the student'sown mathcreditsearned n those categories.The intuition s that wewant to purgethe portionof the curriculum ffect that isrelated to ability.We use the school's average curriculum topredict hestudent's ctualcurriculum,ndanydeviationofthe student'sactualcurriculum romthe predicted evel isassumed o be causedby variations n ability, husleaving

thepredictedvalueindependent f ability.Therefore,f weuse this predicted urriculumevel in our modelinsteadofthe actual evel, we will be estimating he effect of curric-ulumalone rather han the effect of a mix of curriculum,ability,and motivation.However,note that if parentsofhighlymotivated tudentsall flock to the sameschool,theinstrumentwill notfully eliminateabilitybias. (Wecontrolfor this possibility, houghrathermperfectly,by includingdummies for census region and for suburbanand ruralschools.) We return o this issue after discussingthe IVresults.coefficient s slightlysmallerat0.027 andsignificant t the 10% evel. Incontrast o the modelwithGPA,controllingor testscoreyieldsa calculuscoefficient that is significantat the 10% level and slightly largerinmagnitudeat 0.055. The mathcoefficientsmay change across modelspecificationsn partbecauseof the fallingsamplesizes thatresult rommissingdata in some of the controls(13%of the regression ample smissingtest scoredata).As an additionalway to take accountof studentmotivationandparentalnfluence,we controlled or a set of attitudinalvariablesndicatingheacademicnclination f students ndparentssuchas whether heparents loselymonitor hestudent's choolwork,whethertheparents nowwhere heirchildren re atalltimes,whetherhe studentintends o go to college,theamount f television he studentwatches,andhowmuch imethe student pendsreadingoutsideof class).Adding hesevariables,rather han GPA,causes even smallerchangesin the mathcoefficients rom thecase of no abilitycontrols.

We estimateour earningsmodel using two-stageleastsquaresandpresent he results n columns5 and 6 of table2.29 Column5 shows the IV results with no additionalabilitycontrols,and column6 includesGPA.The results nthe two IV specifications restrikingly imilar.30 ocationalmath creditshave a statistically ignificantnegativeeffecton earningsof around8%. Creditsearned n the algebra/geometrycategoryare significantat the 5% level in bothspecifications ndareof similarmagnitude tapproximately8% to 9%. This is a rather argeincreasefrom the OLSestimates.It appears hat the effect of higher-levelmathcourseshas been condensed nto the algebra/geometryat-egory.It is importanto stress hatalthoughhehigher-levelmath coefficientsnow have negative signs, they are notsignificantlydifferent rom0.31

High School Fixed Effects: As another robustnesscheck,we use OLSto estimateanearningsmodel withhighschool fixed effects both with and withoutGPA(see col-umns 7 and 8). Whereas he IV estimatesshould net outabilityeffectswithineachschool,the fixed effectsestimatesshould control for variations n abilities across schools.WithoutGPA n the model,half of the curriculum oeffi-cientsarehigher hanfor the comparablemodel in column3. Thepre-algebrandalgebra/geometryoefficients emainpracticallyunchanged,and the coefficienton vocationalmathis no longersignificant.The results with mathGPAaddedin additionto the fixed effects are similarto, butsomewhatstronger han,the correspondingmodel in col-umn4 withGPAbut withouthigh school fixedeffects.32

29Weexclude hestudent's wncurriculum hencalculatingheschoolaveragecurriculumor that student. n our second-stage egression,weexclude students who come from schools where the school averagecurriculum ascalculatedusingfewer than ourobservations,ausingusto excludeapproximately% of the students.The resultschange onlyminimallyf we changethe requirementor the numberof observationsforcomputingheaverage rom eachschool. Thenumber f studentsperschoolranges rom1 to 36, witha medianof approximately2. Wetriedanalternativepecificationwherewe estimated he first-stage egressionsusing the largestpossible sampleof students, ncluding hose studentswhomwe excluded romthe second-stage egressionbecauseof missingearningsdata.However, he resultschangedonly minimally.30 Infact,thefollowingresultsalso hold nother Vmodelspecificationsthat nclude ontrols or math est scoreandmodels hat ncludebothmathGPAand math est score.31 Given that ew students ookthehigh-levelmathcourses, hequalityof the instrumentmay be reducedfor that course level, which wouldexplainthe lack of precisionn estimatinghesecoefficients.32F-teststhat hehighschooldummiesare ointly equalto 0 producedP-values of 0.0001 withoutGPA n the modeland0.00014 withGPA nthe model.However,ourothermodels thatconditionupon high schoolcharacteristicsppearo capturemuchof thisvariation,withP-valuesforthe F-tests of 0.02 regardlessof whetherwe include GPA.The schoolcharacteristicshat were significantat the 5% level were manyof thedummies ndicating he stratificationssed to sampleHSB schools,andregiondummies.None of the measuresof schoolresourcesweresignif-icant; hepercentage f studentswho weredisadvantaged as the demo-graphic haracteristiclosest to being significant t the 5%level.

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HIGH SCHOOL COURSES AND EARNINGSC. AdditionalHigh School Subjects

Although our research focuses on the effects of mathe-matics curriculum, we also incorporatecourses in English,science, and foreign language into our model, using detailedcurriculum categories.33We classified the number of En-glish credits earned into four levels: below grade level,average grade level, above grade level, and English litera-ture courses. We measured the science curriculum as thenumber of credits earned in six science course categories(see table A2 for the classification system). We classified theforeign language curriculum into two variables: one indi-cating that the student took only one or two courses, and theother that the student took three or four courses.We estimate models containing all four subjects usingboth OLS and IV methods and present the results in table 3.For comparative purposes, we include models that do anddo not condition on math GPA. However, we focus on themodels in columns 2 and 4 that condition on math GPA.Wenote that the other subjects may also serve as ability/motivation controls. All models include controls for demo-graphic, family, and school characteristics as well as thehighest educational degree attainedby the student.Including the credits earned in other subjects (column 2)causes the math coefficients to drop by approximately30%to 40% from the base level case, depending on the mathcourse (except for the case of vocational math). It appearsthat taking an average or above-level English course isassociated with increases in earnings roughly similar to thepredicted gains from taking a math class at the algebra/geometry level or higher. The above-level English creditsare predicted to have a larger effect on earnings than areaverage-level English credits. None of the science coeffi-cients are statistically significant except for primaryphys-ics, which is predicted to have a negative effect on earnings(most likely for the same reasons that vocational mathdoes). Taking three or four foreign language courses alsohas a significant positive effect. At 5.6%, its coefficientseems large comparedto those of other subjects. However itrepresents the effect of three to four credits, whereas thepredictedeffects of the other subjects representthe effect ofonly one additional credit.We repeatthe analysis using the IV technique.The resultsfrom adding the additional curriculummeasures are remark-ably similar to the IV results in table 2, column 6, in thatthesole math variable that is significant at 5% is algebra/geometry. The IV models are less supportive of the notionthatforeign language and science are associated with higherearnings than are the OLS models.

33These curriculummeasures display collinearity with math. The num-ber of math credits earned has a correlation of 0.54, 0.36, and 0.38 withscience, English, and foreign language credits, respectively. We alsoestimated models that included social science credits, but the main resultswere not altered. We decided to leave them out to reduce collinearityproblems.

TABLE 3.-THE EFFECTS OF SPECIFIC MATH, ENGLISH, SCIENCE, AND FOREIGNLANGUAGE COURSES ON LOG EARNINGS: OLS AND IV ESTIMATES

OLS IV(1) (2) (3) (4)

VocationalPre-algebraAlgebra/geometryIntermediate lgebraAdvancedalgebraCalculusBelow-level EnglishAverageEnglishEnglish literature oursesAbove-level EnglishBasic biologyGeneralbiologyPrimaryphysicsSecondaryphysicsChemistry1, physics 1Chemistry2, physics 2,AP BiologyForeignlanguage(1-2)Foreignlanguage(3-4)

-0.030**(0.011)0.004(0.014)0.020*(0.011)0.019(0.017)0.030**

(0.015)0.043(0.033)0.004(0.013)0.015**(0.008)0.015*(0.009)0.026**

(0.013)-0.008(0.019)-0.015(0.013)-0.023**(0.012)0.005(0.034)0.020(0.014)0.020(0.020)0.025(0.017)0.054**(0.026)

GPA-mathR2 0.200Number of observations 5,735

-0.032**(0.011)0.002(0.014)0.019*(0.011)0.010(0.017)0.018(0.016)0.028(0.033)0.005(0.013)0.015**(0.008)0.015*(0.009)0.025*(0.013)

-0.009(0.019)-0.014(0.013)-0.024**(0.012)0.005(0.034)0.015(0.014)0.020(0.020)0.028(0.017)0.056**

(0.026)0.036**(0.009)0.2035,718

-0.075* -0.075*(0.039) (0.040)0.030 0.029(0.045) (0.045)0.097** 0.093**(0.044) (0.045)-0.129 -0.134(0.082) (0.082)-0.093 -0.101*(0.058) (0.059)-0.162 -0.187(0.171) (0.173)0.019 0.020(0.033) (0.033)0.025 0.024(0.024) (0.024)0.034 0.035(0.029) (0.029)0.071** 0.076**(0.036) (0.036)

-0.080* -0.084*(0.046) (0.046)-0.069* -0.070*(0.040) (0.040)-0.060* -0.059*(0.031) (0.031)0.143 0.149(0.100) (0.100)-0.004 -0.012(0.060) (0.060)0.028 0.045(0.073) (0.071)-0.024 0.000(0.104) (0.103)0.129 0.138(0.143) (0.142)0.067**

(0.020)0.186 0.1915,681 5,664

** Significantat the 5% level; * significantat the 10% evel. Standard rrorsare in parentheses.Allmodels control for demographic, amily, school, and highest-degreecharacteristics.See table 1 for acomplete list. Each model contains an intercept.For the first-stageregressionsin each IV model, theP-values for the F-testof thehypothesis hat hecoefficients on the instruments reequalto 0 are0.0001.

Ourresults indicate thatmathematicscourses have a largeeffect on earnings, regardlessof whether we also control forother types of courses taken. In fact, the IV estimates implythatthe returns to taking a one-unit algebra/geometrycourseare statistically significant and large in magnitude-over9%. This is higher than the average returnsto an additionalyear of schooling (often cited as 7%). Other math courses,as in the simpler IV model, become insignificant.In contrast to the OLS estimated model, the effect of theabove-average English credits in the IV estimated model istripled,but that of foreign language is insignificant.Perhapsaccumulatingcredits in foreign language is a sign of abilityor motivation, which the IV method eliminates. Finally, inthe IV estimated model, the low-level science courses are

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THE REVIEW OF ECONOMICSAND STATISTICSstill predictedto have negative, and now even larger,weaklysignificant effects.Unlike some of the earlierliterature,we find that the sumof the parts(thatis, the effect of high school courses) can beas large as the whole (thatis, the effect of an additionalyearof high school, often cited as a 7% increase in earnings),contingent upon the student taking the right courses. In thecase of students who take the most demanding courses,curriculum predicts earnings gains of more than 7% peryear. This can be seen best by considering some simplethought experiments.To compare our estimated effects of a year's worth ofcurriculumwith the 7% effect of a year's worth of school-ing, table 4 shows OLS estimates of potential combinationsof high school courses. The first row shows that studentswho drop out in tenth grade experience a 12% earningsdeficit compared to those who stay in school (calculated asthe effect of having less than a high school degree in theTable2, column 4 model). This resonates with the estimated7% benefit per year that school provides. The remainingrows in the table compare the earnings gain for a studentwho takes the stated set of courses with that of an otherwiseidentical student who does not take the courses. In eachcase, the set of courses is meant to approximate what atypical student might take by staying in school one yearlonger. For students who do not drop out, we present threehypothetical course loads (low, medium, and highly aca-demic combinations) that they could take during their elev-enth and twelfth grades. The returnsto curriculumdependcritically on the type of courses taken. A low-level curric-ulum taken in either year has a predicted effect on earningsof approximately 2%, compared to a 5%-6% returnfor amedium-level curriculum.An additionalyear of a high-levelcurriculumcarries a predicted earnings premium more like7% to 9%.34We conclude that on average, the returnsto one year ofhigh school can be largely explained by the courses, espe-cially in math and English, that students take.

D. Comparisonwith PreviousResearchSo far,our unique contribution to this branch of literatureis to classify the numberof math courses that students takeaccording to the academic level of the course. To highlightthe difference that classifying courses by their type makes,we reestimate the previous set of models using the aggre-gate credits earned in a particular subject rather than the

34 Throughout this exercise, we assume that all other background char-acteristics are held constant and that the only difference between thestudentswe arecomparings theircurriculum.n otherwords, he effectswithin each academicyear (such as the twelfth grade)are measuredrelative o a hypotheticaltudentwho staysin school thatacademicyearbutdoes not takeanymath,English, cience,orforeign anguage ourses.The more interestingcomparisonsare between students who take ahigh-levelcurriculumnd those who takea low-level curriculum.

TABLE4.-THE PREDICTEDARNINGS FFECTOFHYPOTHETICALOURSECOMBINATIONSURINGGRADES11 AND 12

School Year Predictedand Level HypotheticalCurriculum Effect10 Dropout No more subjects -0.122**(0.036)11 Low No math,averageEnglish, secondary physics, 0.021no foreign language (0.035)11 Med Intermediate lgebra, averageEnglish, 0.054**chemistry 1, foreign language(thirdyear) (0.022)11 High Advancedalgebra,advancedEnglish, 0.072**chemistry1, foreign language (thirdyear) (0.021)12 Low Same as grade 11 low 0.021(0.035)12 Med Advancedalgebra,English literature,physics 0.062**1, foreign language(fourthyear) (0.019)12 High Calculus,advancedEnglish,chemistry2, 0.086**foreign language (fourthyear) (0.037)** Significantat the 5% level.Standard errors are in parentheses. Except for the effect of droppingout (which is simply thecoefficient on the dropoutdummyvariable n column4 of table 2), the predictedeffects are computedby summing he individualeffects of thehypotheticalclass list from column 2 of table 3. In otherwords,the effects withineach academicyear (suchas grade 12) are measuredrelativeto a hypotheticalstudentwho stays in school that academicyearbut does not takeanymath,English,science,or foreignlanguagecourses.The standard rrors are computed by taking the squareroot of the varianceof the sum of thecoefficientsfrom the hypotheticalclass list. To computethe effects more easily, we estimatea slightlydifferentspecificationof the column 2 model in table 3 in which we enter thetotal numberof foreignlanguage credits rather than the two dummy variables. The coefficients on the other subjects arepracticallyunchanged.That of foreignlanguagecredits becomes 0.014.

detailed credit counts.35 We also present a specificationusing aggregate credits that matches Altonji's (1995) spec-ification as closely as possible. We present the outcomesfrom the aggregate models in table 5.Notably, the results from our models with aggregatecourse counts in the four subjects closely approximate theresults in Altonji (1995).36 Thus our method of classifyingthe curriculum by level seems to explain some of the"curriculumpuzzle."37We also find that some of our otherhypotheses concerningAltonji's results are incorrect or onlypartially correct.Columns 1 and 2 of table 5 repeat the models fromcolumns 1 and 2 of table 3 but use aggregate credits insteadof detailed course counts. Both models control for thedemographic, family, school, and educational attainmentcharacteristics that have been used throughoutthis paper.Inmodel 1, the math coefficient is only marginally significant,whereas in this model's table 3 counterpart,several of thedisaggregated math coefficients are significant at the 5%

35Rather than relying on the precalculated course counts provided inHSB, we calculated the total number of credits earned directly from thetranscriptdata.36 This applies to models estimated by both OLS and IV methods. Tofurther approximate Altonji's results, we estimated these models butexcluded high school dropouts. The results changed minimally, with thepredicted effects differing by 0.002 at the most. We had hypothesized thatour results differed from Altonji's because we used a more recent cohortand included high school dropouts in our analysis. Now it seems clear thatthe differences stem mostly from our more detailed classification ofcurricula.37This term was coined by Altonji for describing the small estimatedeffects of the curriculum.

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HIGHSCHOOLCOURSESAND EARNINGS 507TABLE 5.-THE EFFECTS OF AGGREGATE MATH,ENGLISH, SCIENCE, AND FOREIGN LANGUAGE COURSESON LOGEARNINGS: OLS ANDIV ESTIMATES

OLS IV(1) (2) (3) (4) (5) (6) (7) (8)

MathEnglishScienceForeignlanguageControls:

Demographic nformationParentalSESSchool region/typeSchool resourcesHighest educationaldegreeTest scores (1982)GPADropoutsincludedin model

0.014*(0.008)0.011(0.007)0.005(0.008)0.025**(0.007)

YesYesYesYesYesNoNoYes

0.008(0.008)0.013*(0.007)0.003(0.008)0.024**(0.007)

YesYesYesYesYesNoYesYes

0.009(0.008)0.016**(0.008)-0.001(0.008)0.025**(0.007)

YesYesYesNoYesNoYesNo

0.005(0.009)0.017**(0.008)-0.008(0.008)0.021**(0.008)

YesYesYesNoYesYesNoNo

-0.029(0.033)0.030(0.023)-0.025(0.026)-0.034(0.028)

YesYesYesYesYesNoYesYes

-0.034(0.034)-0.030(0.023)-0.026(0.026)0.036(0.028)

YesYesYesYesYesNoYesYes

-0.040(0.034)0.030(0.022)-0.030(0.025)0.053**(0.026)

YesYesYesNoYesNoYesNo

-0.025(0.034)0.042*(0.023)-0.045*(0.027)0.010(0.030)

YesYesYesNoYesYesNoNoR2 0.193 0.197 0.182 0.182 0.189 0.193 0.178 0.179Numberof obs. 5,738 5,718 5,404 4,834 5,681 5,664 5,356 4,790

** Significantat the 5%level; * significantat the 10% evel. Standard rrorsare in parentheses.For the first-stageregressions n each IV model, the P-values for the F-test of the hypothesisthat the coefficientson the instrumentsareequal to 0 are 0.0001. Models 1 and 2 use the same demographic, amily,and school characteristicsound in table2. The differencebetweenmodels 1 and 2 is that model 2 includes GPA.Models 3 and4 use our data to mimicAltonji's(1995) table2, model 7. These models excludehigh school dropouts. n these models, the demographicdata ncludeethnicity,gender,andage. Age is ourbest proxyforAltonji'scontrol or the numberof months n the labor orce. The parentalSEScategory ncludesparental ducation,parentalncome,and whether he parent s a U.S. native.Wedo not have a comparablevariableto Altonji'scontrolfor parental nvolvement. We also includeschool regionandtype, as Altonjidoes, but we do not control for city size and college proximity.These replicationsexclude the respondent'smaritalstatus, he numberof siblings,and a host of highschool characteristics, ll of which are included n models 1and 2. Thedifference between models 3 and4 is thatmodel 3 controls orabilityusingGPA ourpreferredspecification),whereas model 4 controls for abilityusing the s tudent's senior yeartest scores in math,reading,and vocabulary ourclosest approximationo Altonji's specification).The progressionof models inthis tablehighlightshow our results can be compared o Altonji'swhen we use the total numberof credits earned n the differentsubjects.Models 5 through8 repeatthis progressionusing IV estimates nsteadof OLS estimates.Comparing esults rom thistableto those in table3 also highlightshow usingthe total numberof credits s not as informative s usingdetailedcreditcounts. Models 1 and 2 in this tablecorrespondsto models 1and2 in table 3. The noncurriculum ontrolsarethe same in bothmodels, but this table uses the total numberof credits n a particular ubject,whereas table 3 uses detailed credit counts in each subject.Similarly,models 5 and 6 in this table corresponds o models 3 and 4 in table 3, respectively.

level. Model 2 in table 5 adds GPA to model 1. Theaggregatemath coefficient is no longer significant.TotalEnglishcreditsbecomemarginally ignificant.Column3 takesthe firststep towardapproximating l-tonji's table 2, model 7. The main changes are that weremove the school resourcesthat are not included n Al-tonji'smodel,and we also excludehighschooldropouts sAltonji does.38Neither of these differencesbetween Al-tonji'smodel and our own seems to mattermuch,whetherthese changesare madejointly,as shown in the table,orindividually.At this point, the majordifference between Altonji'smodel and our replication s thatwe use math GPAas acontrol orability,whereasAltonjiusestest scores. Column4 of table 5 takes the finalsteptowardreplicatingAltonji'smodel. It makes the same restrictionsas the column 3model,but t includes enioryeartestscores nsteadof GPA.In this replication,aggregatemath credits are not signifi-cant.Englishand foreignlanguagecredits are significant,but the effects are modest. The main differencebetweenthesefindingsandthose of Altonji s thatEnglishcredits nour model are significant.Altonjireports hat one yearofmath,science, and foreignlanguageis associatedwith again in earningsof approximately .5%.Our table5, col-umn4, gives an estimateof 1.9%.But when we addin a

38See the notes to table 5 for more details of how columns 3 and 4 differfrom columns 1 and 2 in a bid to mimic the specification used by Altonjias closely as possible.

yearof English,our estimate umpsto 3.6%,comparedo0.6% according o Altonji.Still, overall the results seemhighlysimilar o Altonji's n that we do not come close to"explaining" 7%increase n earnings romattending nemoreyearof school.Disaggregationof coursestakenis the most importantinnovationwe make,but the use of GPA rather han testscoresis a secondary easonfor why ourresultsare some-what more optimisticthanAltonji's.Althoughthe mathvariable s stillnotsignificantn eithermodel3 or4, it doesfall by half when we include test scores rather hanGPA.Overall,we interprethis as a sign thatour decisionnot touse high school test scores as a control,becausethey areendogenous,makesa substantivedifference.It is also notable hatthe time framesdiffersignificantlybetween oursamplesandAltonji's--ourearningsobserva-tions are from 1991,comparedwith 1977through1986inAltonji(1995). Because the returns o education ncreasedmarkedlybetween the late 1970s and the early 1990s, wehadspeculated hatperhapsmathcurriculummattersmoretoday than it did in the past. Ourresults do not providestrongevidencethat his is thecase,except perhaps or ourfinding hat n ourspecification losest toAltonji's,Englishcoursesmattermuch more thanhe found.Theremaining olumns n table 5 repeat he sameseriesof specifications ut use the IV estimator.Perhapshemostnotable indinghere is that the coefficienton mathcoursestaken s neversignificant nd s alwaysnegative.Ourearlier

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THEREVIEWOF ECONOMICS ND STATISTICSIV models thatdisaggregate uggestthat n fact some mathcourses do indeed matter.Overall,we concludethat the mainreasonfor the diver-gence between our results and those of Altonji is ourdisaggregationof courses by type; a secondaryreasonappears o be our decision not to conditionon high schooltest scores because they are an endogenousfunction ofcourses taken.The findingthat coursetype mattershas many implica-tions for curriculum eform. nparticular,merely ncreasingthe numberof math coursesrequiredof studentsmay notachieve the desiredeffect. It will be importanto focus onthetypeof coursesstudents rerequiredo take as well.39 nparticular, ur results suggest that algebraand geometrycourses should be a fundamentalpartof any curriculumreform.

V. An Analysis of Earnings Gaps among Ethnic,Socioeconomic, and Gender GroupsThis sectionexamineswhetherdifferencesn highschoolcurriculum ontribute o the well-knowngaps in earningsamongworkersof different aces andethnicities.Similarly,we test whethergaps in earningsrelated to a person'sparentalbackground r the person's gender n partreflectvariationsn high schoolcourses.In the early 1980s, math coursecompletionrates variedconsiderablyby ethnicity.Nearly9%of Hispanicstudentsand 10% of black studentscompletedmathcreditsin ad-vancedalgebraor calculus,compared o ratesof 22%and43% for white andAsianstudents, espectively.40he samedisparities mergewhen we examinethe numberof creditsearnedrather hanthe highestcoursecompleted.Hispanic,black,andNative Americanstudents ended to earn morecredits n vocationalmathand fewercreditsat or abovethealgebra/geometryevel thanAsianand white students.Similarly, students from the lowest-income families(thosewithparentswho earned ess than$7,000 annually)were concentrated n the lower-level math courses, with46%failing to progressbeyondvocationalmath. For stu-dents frommiddle-income amilies(thoseearning$20,000to $25,000),only 19% ailed to advancebeyondthat evel.Whereas24%of middle-incometudents ookcoursesat orabove the advancedalgebra evel, only 8% of the lowest-incomestudentsdid.How much of the earnings gap between members ofdifferentethnicgroupsor parental ncome groupscan beattributed o these variations n mathematics-course-takingbehavior?We firstestimatea model of earnings hatonlyincludes ethnicity variables as explanatory actors, with

39Whengraduationequirementsre ncreased,here s therisk of morestudentsdroppingout. See Costrell 1994) andBetts (1998) for a theo-reticalanalysis,and Lillard 1998) for an empiricalanalysis.40Thesefiguresare basedon every publicschool observationor whichwe have ethnicityand math data. The same course-takingrends areevidentfor the weightedregression ampleas well.

white studentsas the omittedgroup.The resultsappear ncolumn1 of table 6. Consistentwith commonperception,this simple model shows that Hispanicsand blacks earnsignificantly ess than whites on average-approximately5.2% and 10% ess, respectively.41To establisha baselineearningsgap for students romdifferentparental ncome levels, we carryout a similarprocedure-estimatinganearningsmodelthatonlycontainsparentalncome levels as explanatoryactors.Wemeasurethe differencesin average earningsrelative to studentswhoseparentswere in the middle-income ategory, hat s,familiesthatearnedbetween$20,000and$25,000a year n1980.42In this model (shown in column 2 of table 6),students n the lowest parental-incomeategory(less than$7,000) earn approximately 0% less than students rommiddle-income families, whereas those in the highestparental-incomeroupearn 10% o 11%more.Next, we estimate a model that conditionson both pa-rental ncome andethnicitywhile takingaccountof demo-graphic,family, and school characteristics.The resultingearningsgaps are presented n column3 of table 6. Thenoncurriculumactorsthat we addin this thirdmodel canexplainalmostall of the ethnicearningsdifferentials nd alarge portionof the socioeconomicearningsgaps. In thismorerealistic model of earnings, he Hispanicand blackearningsgaps disappear ntirely.Asianstudents till expe-rience an earningspremium elativeto white students,butthe effect is statisticallyweak. Native Americanstudentsstill experiencean earningsdeficit. Whichfactors are re-sponsible orthe closure n theHispanicandblackearningsgaps?Entered nto the model on its own, eitherparentalincome or parental ducationcan explainnearlyall of theHispanicgap and approximatelyhalf of the black gap.Together, he two measures of parentalbackground anaccount for the entire earningsgap between whites andeitherof theseminoritygroups.As column3 of table 6 also demonstrates,he earningsgaps related to parental-incomeroupsdiminish substan-tiallyaftercontrollingor theremainingdemographic,am-ily, and school factors,yet they are still present.Studentsfrom the lowest-income amilies earnapproximately 7%less thanthose frommiddle-incomeamilies,andstudentsfrom the highest-incomeamilies now earnapproximately6% more.Column3 also suggests that there is a gender gap inearnings,withmalesearning27%more thanfemales.Next,we addthemathcurriculumo themodel n column3 to see whether t canexplain heethnic, SES, andgenderdifferences.The resultsappearn column4. Adding he six

41 These earningsdeficits are smaller than those reported n otherliterature,because of the HSB samplingscheme. The HSB data setincludesonly thosepeoplewho are still in school in the secondhalf oftheirsophomore ear n highschool.Thus, t excludesstudentswho dropout of school at an earlyage, as well as immigrantswho had no U.S.education.42The incomecategoriesn this sectionareexpressedn 1980 dollars.

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HIGH SCHOOLCOURSESAND EARNINGSTABLE6.-EARNINGS GAPS BASED ON ETHNICITYNDPARENTALNCOMEBEFOREANDAFTERCURRICULUMS ADDEDTO THEMODEL)

(1) (2) (3) (4) (5) (6)Hispanic -0.052** 0.010 0.036* 0.026 0.043**(0.019) (0.021) (0.021) 0.021 (0.021)Black -0.100** -0.010 -0.0002 0.004 0.008(0.024) (0.025) (0.0249) (0.025) (0.025)Asian 0.092** 0.072* 0.023 0.033 0.010(0.043) (0.044) (0.043) (0.043) (0.043)Native American -0.229** -0.102** -0.068 -0.088* -0.064(0.054) (0.052) (0.051) (0.052) (0.051)

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THE REVIEWOF ECONOMICS ND STATISTICSof the studentswho camefrom the lowest-income amilieswereHispanic,20% wereblack,and 34% were white.

VI. ConclusionThe mainmessageof thisstudy s thatmathmatters.Themathcourses thatstudents akein highschool arestrongly

related o students' arnings round10years ater, venaftertakingaccountof demographic,amily,and school charac-teristics,as well as the student'shighesteducational egreeattained, ollege major,andoccupation.Another mportantmessage is that not all math courses are equal. Moreadvancedmathcourseshave a larger ffect on earningshanless advancedones. Ourresultssuggestthat a curriculumthat ncludesalgebraandgeometry s systematicallyelatedto higherearnings or graduates decade aftergraduation.As we have stressed hroughouthepaper, t is notentirelyclear whether he linkbetweenmathandearnings s causalormerelyreflectsunobserved ariationsn student bilityormotivation. But it is noteworthy hat math continues tomattereven after controllingfor proxies of ability andmotivation,such as math GPA and mathtest scores, andafterusinginstrumentalariablemethods.The IV estimatessuggest hatalgebra/geometryreditshave thelargesteffecton earnings,whereas he remaining ourseshave insignifi-cant effects. Indeed,throughouthis batteryof robustnesstests,creditsearned n the algebra/geometryategorymostreliablyremaina statistically ignificantpredictor f earn-ings.Furthermore,oththe OLS andIVresultspersistwhenwe includeEnglish,science,andforeign anguagecurricu-lum measures n the model, althoughsome of these othertypesof courses(forexample,above-levelEnglish) appearto influenceearningsas well.Cangaps in curriculummeasuresexplaingaps in earn-ings amongracial and socioeconomicgroupsor the gaprelated o gender? nansweringhisquestion, t is importantfirst to take account of variations n family background.Virtuallyall of the earningsgap betweenwhitesandmostminoritygroupscan be accountedfor by differences infamilybackground nd,to a far lesserextent,schoolchar-acteristics,withoutany need to controlfor curriculum.ncontrast, he earningsgap relatedto variations n parentalincome levels or in gendercannot be fully explained byfamily and school characteristics.We found no evidencethatmathcourses akencanexplain hegenderpay gap.Butthe math curriculum an explain nearly one-quarter f thegap between studentswith parental ncome in the lowestand middlegroups.This latter inding s important ecauseit suggests a tool-namely the math curriculum-for in-creasing hedegreeof equity n students' arningsopportu-nities later n life.Of course, it is difficult to know how in practicetoimplement his deceptivelysimple policy prescriptionorenrichingthe math curriculum.Why do low-incomestu-dentsfail to takemorehighschool math f it is true hat hiseffort wouldsubstantially oost theirearnings ater n life?

We suspectthatpartof the answer s thatyoung studentshave rathermperfectknowledgeof thelabormarket eturnsto education, et alone to specific courses. For instance,Betts (1996) surveyed undergraduatest an elite publicuniversityand findsthatthoughon averageundergraduateshavea reasonably ood knowledgeof the returns o educa-tion in various ields,the beliefs of individual tudentsareoftenmassivelywrong.It stands o reason hathighschoolstudentsfrom low-income families, who lack the samewindows into the higher educationsystem, have a lessaccurate nderstandingf the returnso education verallorto takingcourses in individualsubjects.A second reasonwhy students rom low-income families may not want toenroll in the most demandinghigh school courses is thattheyhavea ratherhighdiscountrate.Indeed, he idea thatyoung people discounttheirfuture ncometoo highlycanexplain why we have compulsoryattendance aws. Theexcessive discountingof future income is likely to beparticularlyommonamongthe less affluent.For evidencethatpeople ivingin povertyhavehigherdiscount ates hanaverage, ee Lawrance1991).A thirdreasonwhy studentsliving in povertymaynot take"enough" igh schoolmathcourses could well be that by the time they reach highschool, their accumulated ducationaldeficit makesit dif-ficult for them to take further ourses at grade evel.Better nformation bout he realitiesof the labormarket,combinedwithhigherstandardsor all students,mightdomuchto solve the firsttwo problems.The standardsmove-ment that swept the United States duringthe 1990s hasalready ed to muchclearer,andin generalhigher,require-ments orhighschoolgraduationn moststates, hroughhetighteningof courserequirements nd,in manycases, thecreationof high school exit exams. The thirdissue, thatstudentsivingin povertymaybe farbehindgrade evel bythe startof high school, is farmoreproblematic. t wouldsuggest that setting higher course requirementsn highschool could backfireunless at the same time educationpolicymakers losely examined he deficiencies n studentperformancet lowergradesand intervene arly enough nstudents'careers to minimize these deficiencies.Clearly,suchinterventionsouldprove costly,andwe cannotspec-ulate on the cost-benefitratioof such interventions.Still,our results do provide some concrete evidence that thebenefits of a richercurriculum rereal andmeaningfulnsize; it is the cost side of the equation hatis less clear.Ourresults emanate rom the detailedmanner n whichwe measure urriculum, nd this is a majorcontributionfthisstudy. f we simplyanalyze he effect of aggregatemathcreditsearned,we find that t is anaverageof specificmathcourseeffects.Whenaggregate redits n othersubjectsarealso included, he aggregatematheffect is only marginallysignificantand the effects of Englishand science subjectsdisappear ntirely.Furthermore,he aggregatenumberofmathcreditsa studentearnscannotexplainas much of theearningsgapas the credits n individual ourses can.

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HIGH SCHOOL COURSES AND EARNINGSA perennial problem facing researchers working on theeconomics of education concerns the human-capital-signaling debate. Does education, or in our case the curric-ulum, increase earnings by increasing humancapital (thatis,skills) or simply by signaling preexisting student ability?This issue is of pivotal importance for policymakers. If theonly role that math courses play is to provide more able

students with an opportunityto signal this fact to the labormarketby surpassingother students, then a policy requiringa more enriched curriculum for all students will not makestudents intrinsically more productive.Although our data cannot provide unequivocal results onhow curriculum affects earnings, our preferred earningsmodels that condition on math GPAsuggest that 68% of theeffect works through students' educational attainment andan additional 19% works through students' college majorand occupation. The unexplained portion, approximately13%, appears to work through other mechanisms.Furthermore,our controls for student ability (math GPAand test score) suggest that signaling of ability and motiva-tion is unlikely to be the only way in which curriculummatters. Unlike some earlier work, we find evidence thatcourses taken duringhigh school can indeed explain most ofthe economic returnsto a year of schooling. In this sense, aswell, our results suggest that education does more thansignal ability.As public attention continues to focus on suchissues as school spending and class size, this study showsthatit is crucial to remain focused on the heart of the matter:what students actually learn in school.

Griliches,Zvi, "Estimatinghe Returns o Schooling:SomeEconometricProblems,"Econometrica5:1 (1977), 1-22.Grogger,Jeff, "SchoolExpendituresndPost-SchoolingEarnings:Evi-dence fromHighSchool andBeyond," hisREVIEW,8:4 (1996),628-637.Grogger, eff,and EricEide,"Changesn CollegeSkills andthe Rise inthe College Wage Premium," Journal of Human Resources 30:2(1995), 280-310.Ingels,StevenJ., KathrynL. Dowd,John R. Taylor,VirginiaH. Bartot,MartinR. Frankel,and Paul A. Pulliam,NationalLongitudinalStudy of 1988-Second Follow-up: Transcript Component DataFile User'sManual,NCES 94-377 (Washington,DC: NationalCenter orEducationStatistics,1995).Lawrance,EmilyC., "Poverty nd he Rateof TimePreference: videncefrom Panel Data," Journal of Political Economy 99 (February1991),54-77.Levine,PhillipB., and David J. Zimmerman,TheBenefitof AdditionalHigh-SchoolMath and Science Classes for Young Men andWomen,"Journal of Business and Economic Statistics 13:2 (1995),137-149.Lillard,Dean R., "Accountingor Substitution etweenCredentialsnEstimatesof the Returns o GED and High School Diplomas,"CornellUniversity, npublishedmanuscript,thica,NY (1998).Murnane,RichardJ., John B. Willett,and FrankLevy, "TheGrowingImportance f CognitiveSkills in WageDetermination,"his RE-VIEW,77:2 (1995), 251-266.Porter,A. C., M. W. Kirst,E. J. Osthoff,J. S. Smithson,and S. A.Schneider, Reform Up Close: An Analysis of High School Mathe-matics and Science Classrooms, Consortium for Policy Researchin EducationFinal Report(Madison:Universityof Wisconsin-Madison,WisconsinCenter orEducationResearch,1993).Spence,Michael,"JobMarket ignalling,"Quarterlyournalof Econom-ics 87:3 (1973), 355-374.

APPENDIXData

REFERENCESAckerman,Deena,"Do The Math:HighSchool Mathematics lassesand

the LifetimeEarningsof Men,"Department f Economics,Uni-versityof Wisconsin-Madison ndUniversityof Vermont,manu-script 2000).Altonji,JosephG.,"TheEffectsof HighSchool CurriculumnEducationand Labor Market Outcomes," Journal of Human Resources 30:3(1995),409-438.Betts,JulianR., "What o StudentsKnowaboutWages?Evidence romaSurvey of Undergraduates," Journal of Human Resources 31:1(1996), 27-56."TheImpactof Educational tandards n the Level and Distri-bution of Earnings," American Economic Review 88:1 (1988),266-275.Bishop,HohnH., "Why heApathy nAmericanHighSchools?"Educa-tional Researcher 18:42 (1989), 6-10.Bowles, Samuel,HerbertGintis,andMelissaOsborne, TheDeterminantsof Earnings:A BehaviouralApproach,"Journal of EconomicLiterature, 9:4 (2001), 1137-1176.Costrell,RobertM., "ASimpleModel of Educational tandards,"mer-ican Economic Review 84:4 (1994), 956-971.DuMouchel,WilliamH., and GregJ. Duncan,"UsingSampleSurveyWeights n MultipleRegressionAnalysesof StratifiedSamples,"Journal of the American Statistical Association 78:383 (1983),535-542.Gamoran,Adam, "The Impactof Academic Course Work on LaborMarketOutcomes for Youth Who Do Not Attend College:AResearchReview," n Adam Gamoranand HaroldHimmelfarb(Eds.), The Quality of Vocational Education: Background Paperfrom the 1994 National Assessment of Vocational Education(Washington, C: National nstitute n Postsecondary ducation,Libraries, ndLifelongLearning,Office of EducationalResearchandImprovement, .S. Departmentf Education,1998).

1. Math Test ScoreThemath est score hatwe includedwasbasedona math est nwhichstudentshad 21 minutes o answer38 questions.Thequestions equiredthemto compare wo quantities nddeterminewhetherone was greater,whetherheywereequal,or whether herelationshipwas indeterminablebasedon thegivendata.Weused theHSB-computedtemresponse heory(IRT)scoresfromthistest as ourmeasureof math est score.45

2. Grade PointAverageand Number of CreditsEarnedWecomputedhe student'smathGPAon a scaleof 0 to 4.3. Wetooka weightedaverageof the student's radepointsfor eachcourse,wherethe weightswere the numbers f credits hat the studentearned or theclasses. These credits were either0.25, 0.33, 0.5, or 1, dependingonwhether he courselengthwas a quarter,rimester, emester,or (morecommonly) year-long ourse.Weconvertedettergrades ogradepoints.An A received4 points,a B received3 points,a C received2 points,anda D received 1 point.We added0.3 pointsfor a plus and deducted0.3pointsfor a minus.Forexample,we counteda B+ as 3.3 points.If a student aileda course,butsubsequentlyetook t andpassed t, weincluded the letter grade and credit information rom the successful

45 IRT s a "method f estimating chievementevel by consideringhepattern f right,wrong,andomitted esponses nall itemsadministeredoan individualstudent. Ratherthan merely countingright and wrongresponses, he IRTprocedure lsoconsiders haracteristicsf each of thetest items,suchas theirdifficultyand the likelihood hatthey couldbeguessed correctlyby low-ability ndividuals. RTscoresare less likelythan implenumber-rightormula cores obedistorted ycorrect uesseson difficult tems if a student'sresponsevectoralso contains ncorrectanswers o easierquestions." ee Ingelset al. (1995,p. M-4).

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THE REVIEW OF ECONOMICSAND STATISTICScompletion of the course in the student's GPA, and ignored the informa-tion from the failed attempt.We believed that it is the final level of successin a given course that i