DoIndividuals“StrategicallyDivorce”ToMaximizeMaritalSettlements?
JamesFanSID20352777
UsingdatatakenfromtheAlamedaCountydistrict,Itestthehypothesisthatindividualsplantheirdivorcefilingsaroundthe10‐yearmarkwhereeconomicallypaymentscanlastalifetime.Ifirstobservegraphicevidencewithindistributionsforthistheoryof“strategicdivorce”,thenuseKolmogorov‐SmirnovTeststoverifytheirdistributionaldifferences.Ithenconducttimeseriesregressionstocheckforthestatisticalsignificanceatthe10‐yearmark,lastlyconstructinghazardratesaftereachyearupuntil20.Iconcludethatthereissignificanceatthe10‐yearmarkbutneithergenderexhibitsaparticularbehaviornorasawholethatwouldindicatetheexistenceof“strategicdivorce”.
1
1 Introduction
Astheknowledgesurroundingdivorceanditsprocessbecomesclearer,the
economicssurroundingdivorcelawplaysalargerrolealso.Californiamaritallaw
countsamarriagelasting10yearsorlongerasalong‐termmarriage.Inthesecases
thespouseearninglessincomehastherighttoalimonypaymentsandsupportto
maintaintheirstandardoflivingforaslongastheyneedorforaslongasthepaying
spouseiscapableofpaying.Thetheoryof“strategicdivorce”,orindividualsfiling
unilaterallyfordivorcetoeitherextractoravoidalargesettlement,becomesan
importanteconomicthreat.
Thereisnoliteraturecurrentlypublishedexploringtheincidenceofthis
theory,howevertheconceptssurroundingtheeconomicsofdivorcehavebeen
coveredinparticularbyStevenson(2007).BetseyStevensonhascovereddivorce
lawaswellastheeconomicssurroundingmarriageextensively,andinher2007
work“TheImpactofDivorceLawsonMarriage‐SpecificCapital”shetracksthe
courseofdivorcelawchangesinthe1970sand1980sasamajorinfluenceon
householdbehavior.Stevensonfindsasignificantdecreaseininvestmentmarried
couplesspendtowardsmarriagespecificcapitalsuchasspousaleducation,children,
andhouseholdspecialization,whileinvestmentinhomeownershipitselfvaries
basedonlocalpropertylaws.Herpaperfocusesonthehousehold’sdecisionmaking
pertainingtosecuringindividualsagainstadissolutionthough,andnottheactual
motivationstowardsusingunilateraldivorceasameansoffinancialgain.
2
Thispaperexaminesthestatisticssurroundingdivorceratesinvarying
windowscenteredatthe10‐yearmark,wherefollowingthatmilestone,marriage
dissolutionsettlementsmayresultinlifetimesupport.Inthispaper,varying
questionswillbeconsideredtofindevidenceoforagainstthetheoryof“strategic
divorce”.Thepaperfirstexaminesgraphicalrepresentationsoftherawdataacross
demographicsaswellaswithinvaryingtimesegments.Thepaperthenapplies
statisticalinferenceteststocomparethedistributionsacrossgroupsandcheckfor
statisticallysignificantvariations.Usinganyevidenceof“strategicdivorce”present
hereIusetimeseriesteststotestthedataforotherevidenceofsignificantchanges
inthecumulativedivorcefilingobservationsaround10years.Finally,Iestimate
hazardratesandthelikelihoodsofdivorceovertimeandasaproductofthe
numberofkidsfromthecurrentmarriage.
Thepaperisstructuredasfollows:thesecondsectionwillpresentpertinent
literatureonthetopicandotheracademicinsight.Thethirdsectionwilldescribe
thestatisticalandeconometricmethodologyused,aswellashypothesizingwhat
shouldbeexpectedfromthedatacollected.Thefourthsectionwillanalyzethe
empiricalresults.Afinalsectionwillconcludethepaperanddiscussextensionsand
applications.
2 LiteratureReview
Asaforementioned,literatureontheactual10‐yearmarkasaneventof
interestdoesnotexistineconomicwriting.InStevenson’s2007work,“Divorce‐Law
Changes,HouseholdBargaining,andMarriedWomen’sLaborSupplyRevisited”she
observesvaryinghouseholdcapitalvaluesasdecisionstakentohavedifferent
3
implicationsforthemarriageasoneunitandthevaluethespouseputsinwerethe
marriagetobedissolved.Thedevelopmentofunilateraldivorceasthekeyevent
Stevensonusesinthispaperallowshertoexaminehowmarriedcoupleswill
actuallyinvestlessincapitalsuchaschildrenortheotherspouse’smarket‐based
skills,asthoseconsumptiongainsarenon‐rivalwhenthemarriagestandsbut
wherethehouseholdtodissolvethereturnsontheinvestmentmayfallsignificantly.
AsavaluablehistoricalreferencepointformyresearchStevenson’sfindingsthatas
investmentlevelsfellforjointcapital,reasoningforthisbecomesmoresignificant
whenexamininganevenmoreextremeconceptsuchas“strategicdivorce”.
Stevensonpositsthattheknowledgethateachspouseislesslikelytoreapthe
benefitsofmarriage‐specificcapitalreducedtheincentivetoinvestjointly.
Stevensoncontinuestoexploretheeffectsofdivorcelawchangesonfemale
laborforceinanother2007work,“Divorce‐LawChanges,HouseholdBargaining,
andMarriedWomen’sLaborSupplyRevisited”.Buildingonherpreviouswork
Stevensonfindsthatwhileinvestmentinjointcapitallargelydecreasedasaresultof
70‐80slawchanges,theincidenceofunilateraldivorceledtoariseinmarriedand
unmarriedwomen’slaborforceparticipation.AnumberofStevenson’spapers
becomerelevantinmyworkaswell,particularlyherexaminationofthemarital
shifttowardslessjointinvestment,andafemalemovementtowardshoningmore
individualskillsaswell.Wherestereotypicallymenhaveinthepastbeenthe
breadwinnersforhouseholds,Stevenson’sfindingsofferinterestinginsightsinto
whetherthisideastillholdsaroundthe10‐yearmarkbasedongendercomposition.
4
Friedberg(1998)examinestheactualchangeindivorceratesfollowingthe
introductionofunilateraldivorceasanoption.SynthesizingworkdonebyH.
ElizabethPeters(1992)andDouglasW.Allen(1992)whichcoveredacrosssection
ofwomenobservedin1979,Friedbergfindsthatdivorceratewouldhavebeen
about6%lowerin1988ifnotypeofunilateraldivorcehadbeenadoptedinstates
thatswitchedtoitafter1968.Friedbergsuggeststhatthemovetowardsunilateral
divorceaccountedfor17%oftheincreaseindivorceratesbetween1968and1988
witheffectsondivorcebehaviornotbeingashockbutratherpermanent.
Wolfers(2003)alsoexaminestheeffectofunilateraldivorcelawsondivorce
rates,findingthatwhilethedivorcelawchangescausedanoticeableriseindivorce
ratesforaboutadecade,thatchangewassubstantiallyreversedoverthenext
decade.Wolfers(2003)notesthattheseradicalchangesofferlittleexplanationfor
theriseinthegeneraldivorcerateoverthepasthalfcentury.Thepaperfinally
concludesthattheresultsarelikelysuggestiveofspousesbargainingwithin
marriagesaseachpartner’sdivorcethreatisnowapossibility.
Rasul(2005)presentsaninterestingquestiontoexplorewithmydatasetas
well,examiningtheeffectsofunilateraldivorcelawsondivorceratespertainingto
thosealreadymarriedatthetimeoftheirintroduction.WhileRasul(2005)confirms
mostexistingliteraturethatthelargerdivorcerateshavebeenraisedasaresultof
unilateraldivorce,thefindingsofhispaperalsosuggestthatthechangetounilateral
divorcecancausethosemarriedtobebettermatchedthanthosemarried
previouslyundermutualconsentdivorcelaws.Iapplytheconceptspresentedby
Wolfers(2003),Friedberg(1998),andRasul(2005)regardingoveralldivorcerates
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tocheckforchangesindivorceratesbetweentheoverallsampleandthetime
framesofinterestaroundthe10‐yearmark.
Thedirectlypertinentlegalhistoryformingthebasisforthispaper’s
questioncanbefoundasfarbackasMarvinv.Marvinin1976.Thecaseestablished
theframeworkbywhichmarriagelawyerswouldhavetounderstandtherightsof
unmarriedcohabitants,statingthatinthecaseofnomaritalcontractexisting,the
commonlawruleappliedmeaningeachindividualwouldtakebackfromthe
relationshipwhattheyhadbroughttoit.Marvinv.Marvin’sprecedentledeventually
tothe1986case,MarriageofBukatywhichestablishedthatpriorcohabitationand
evenapriormarriagemaynotbefactoredintheawardingofspousalsupport.
Similarly,theevenmoresignificantcaseMarriageofPrietschandCalhounin1986
producedarulingthatifasupportedspouse’sincomeandneedshadnotchanged
sincethepriororderthanitwouldnotbeappropriatetoterminatetheorder.
ThefirstcodedirectlyrelevanttothispaperisCaliforniaFamilyCodeSection
4336.ThecodestatesthatpostJanuary1,1988long‐termmarriagesaresubjectto
thecourtretainingjurisdictionindefinitelyincasesofdissolutionandanychanges
inthespousalsupportstructure,includingtermination.Thesectionthencontinues
tostatethatamarriageof10yearsorlongerwillbetermedalong‐termmarriage
unlessprovenotherwisebasedonfactorssuchastheseparationdate,etc.Thiskey
lawestablishedthedefinitionforalong‐termmarriageinCaliforniaaswellashow
thejudgescanmaketheirrulingsregardingdissolution.Thesecondlawfollows,as
CaliforniaFamilyCodeSection4337.Continuingonlong‐termmarriages,thecode
statesthatunlessotherwiseagreeduponbythepartiesinquestion,theobligationof
6
onepartytopaysupporttotheotheronlyterminatesupondeathofeitherpartyor
theotherparty’sremarriage.
3 Statistical/EconometricMethodology
Thepaper’sprimaryfocusistoanalyzesignificantstatisticalquestions
surroundingdistributionsofthelargedissolutionfilingscollectionaswellasthe10‐
yearmarkofinterest.Inparticular,thispaperfocusesontheincidenceofdivorce
ratesaround10‐yearsandthedemographicssurroundingtheprobabilityofdivorce
asahazardrate.
ExtensivelymentionedbyStevenson(2007,2007),Wolfers(2003),Rasul
(2005),andFriedberg(1998)istheuseoftheeconomicprincipleoftheCoase
Theoremwhenlookingatdivorcerates.Theconceptsuggestedbylargeamountsof
empiricalliteraturethatfocusedonthechangesindivorceratestaketheCoase
Theoremtobeanullhypothesis,thatachangeintheallocationoftherightto
divorceshouldhavenoeffectonratesofbothmarriageanddivorce.Inthecontext
ofthispaper,Iconsidertheconceptthatanystatisticalchangeindivorceratemay
notbesignificant.ByusingKolmogorov‐Smirnovtestsonvaryingslicesofthedata,I
lookforstatisticallysignificantvariationsindistributions.
Initially,Ipresentthestatisticsinhistogramandkerneldensityplotformas
wellasvarioustablestooffergraphicalrepresentationsandalookatwhatshapes
thedistributiontakesovertimeaswellasinshorttimeframes.Afterexaminingthe
statisticsinrawform,IuseKolmogorov‐Smirnovtestsasthecomparisonsofthe
distributionsoncescaledshouldaccountforthenon‐parametricnatureofmydata.
TheabilityoftheKolmogorov‐Smirnovtesttotakedistributionfreeobservations
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andbestestimatethedifferencesinempiricaldistributionsbetweentheadjusted
bandsoftimeofferstheconvenienceoftestinganytwodistributionswithinthe
overallsample.
Followingthis,Iusecollapsethedatasettoatimeseriessetcomposedof
divorcefilingsobservedevery146days.Thetimeframeselectedheremadeforan
evenmeasureuponthe10‐yearmarkaswellasperevery2years.Abasictime
seriesregressionisthenruntocheckforthestatisticalsignificanceofthe10‐year
markitselfinthenumberofobservationseithersideof10yearsper146‐day
period.
Lastly,Iestimatehazardratesandtheratesofchangefromoneyeartothe
nextfordivorce.Thehazardratesarecalculatedusingprobabilitydensityfunctions
usingmyobservationalpool,andahypothesized,fixeddistributionfunctionor
survivalfunction.Thehazardratesofferinsightsintowhattimeperiodsindividuals
areatgreatestrisktofilefordivorcewithspecialinterestsurroundingthe10‐year
mark.
ThispaperusesmarriagedissolutionsfiledwiththeReneC.Davidson
CourthouselocatedinOakland,CaliforniaintheAlamedaDistrict.Thedataavailable
wasfromaregisterofactionscomputersystemwithintheCourthouse’selectronic
files,meaningtheycouldonlybeaccessedon‐site.Thepapertakesdissolution
filingsfromallfourseasonalperiodsintheyearof2007withobservationsfrom
January,February,June,July,andOctober.Theyear2007wasselectedasitisan
approximatelyevendistance20yearsawayfromanumberofthepivotallate1980’s
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eventsdiscussedinsection2,particularlythepassingoftheofFamilyCode4336as
wellasthe1987casesthatprecededtheneedforsuchacode.
Thedatacollectedincludesthepetitionergender,whetherthefinaljudgment
ofdivorcewaspassed(althoughthe10‐yearstipulationappliesthedateoffillingfor
dissolutionasvalidfor10‐years),whetherthecouplehadchildrenfromthecurrent
relationship,thenumberofchildrenfromthecurrentrelationship,andthetime
frommarriagetofilling,andseparationlengthifany.
3.1 Hypothesis
The“strategicdivorce”hypothesispositedbythispaperspecificallysuggests
thattherearestatisticallysignificantbimodalclustersaroundthe10‐yearmarkof
marriageswheredissolutionshavebeenfiled.Withthefamilycodes
aforementionedinsection2andtheknowledgewithindivorcelawofspousal
supportpaymentsthatcanlastalifetimeonceamarriagebecomes“long‐term”I
hypothesizethatthereshouldbeevidencesupporting“strategicdivorce”.Basedon
gendersplitincomedatatakenfromtheUnitedStatescensus,whereincomegaps
havebeensignificantandconsistentsincetheinceptionofthecensusbythis
parameter,Ianticipateastatisticallysignificantdifferenceinthetwodistributions
bygenderaroundthe10‐yearmarkandingeneral.
Thedifficultyofpredictingwhenindividualsbegintheprocessofconsidering
divorcebeforetheybecomeawareofthe10‐yearmarkisavariablebeyondthe
scopeoftestablecontrol.Essentially,the“strategicdivorce”theoryattemptsto
capturethenotionthatpeoplewilleitherdivorceasapremeditatedprotection
againsttheirspousecollectinglonglastingpaymentsorviceversa,butifthe
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sentimentthistheoryattemptstocapturehasnoopportunitytopresentitselfthe
datamaynotreflectaccuratelythecountofdissolutionsthatactuallywereor
shouldhavebeeninfluencedby“strategicdivorce”.Ifaprimaryearningspouse
findsoutjustpastthe10‐yearmarkabouttheexistenceoffamilycodesthatthere
wastheopportunitytofilefordivorcebeforelonglastingspousalsupportmaybe
awarded,heorshemaysimplyarbitrarilyfileanytimeorevenrightafterthe10‐
yearmark.Thiswouldindeedsupportthe“strategicdivorce”hypothesis,butinthe
contextofthispaper’sfurtherintenttofinddemographicspecificitiesofwhoacts
whenandbasedonwhatfactors,anyspeculationsmaybebiased.
Similarly,akeyquestiontoconsiderthatcannotbeaccountedforwasthe
incomeearnedbythepetitionersinquestionaswellasanypotentialpropertytobe
divided.TheReneC.Davidsoncourthousepapersformarriagedissolutiondidnot
stipulatethisinformationbeprovidedonthedissolutionfilingitself.Additionally,
theregisterofactionsasturnedinbythefilersandpetitionersthemselves
frequentlyfailedtodocumenttheirincomeorinothercasesputapproximations.An
extracomponentwasthatunlikethedissolutionrecordsthemselves,which
containedthelengthofmarriageandpetitionerandrespondentname,thecourt
documentsspecifyingtheincomeandpropertysettlementswereinvaryingcases
lockedfromviewatthepublicaccessworkstation.
4.1 StatisticalDistributions
Thedatacollectedtotaled559observations,butingendersplitcases,only
534observationswereusableduetomissinginformation.Ingendersensitivecases,
thegenderreferredtothroughoutthepaperalwaysreferstothegenderofthe
10
petitionerfilingfordivorce.Referringtothetotaldatasamplefirst,thetabulated
databygenderandsplitbetweenpre‐10andpost‐10yeardivorcesshowsthatthe
numberoffemalesfilingfordivorcefromthesampleof534observationsisnearly
oneandahalftimesthenumberofmales.
[ReferenceFigure1]
Otherwise,nothingparticularlydescriptiveaboutthedifferencebetween
pre‐10andpost‐10yearmarriagesforthetwogendersisreadilyvisiblefromthe
rawcounts,howeverthestatisticaldifferencesbetweenthetwogender
distributionswillstillbetestedaswillthepre‐10andpost‐10distributions.
Examiningasliceofdatawithin2‐yearrangesbelowandabovethe10‐year
markindicatesnearlydoubletheamountoffemalesversusmaleswithinthe4‐year
band.
[ReferenceFigure2]
Thesubsamplesizeofmenwithinthis4‐yearrangeisonly37though,
makingtheinferencesdrawnformensomewhatdifficulttoplaceaccurately.
Fromvisuallyreferencingthehistogramandkerneldensityplotsofthedata
withinthis4‐yearperiod,whilethelargerweightofobservationsappearstobepre‐
10years,thereisnotabimodaldistributioneithersideof10yearsthatmightverify
thestrongestformofthe“strategicdivorce”theory.
[ReferenceGraphs1.1‐1.2]
Totestforthepossibilitythatsuchatheorymaybeinverselyrelatedper
gender,adensityplotisprovidedsplitbygenders.
[ReferenceGraph1.3]
11
Thedistributionsseemvisiblydifferentnow,whiletheplotforwomen
appearssomewhatrandomwithanearlynormallookingdistribution,themen’splot
appearssignificantlypositivelyskewed.Forlackofdescriptiveness,histogramsare
notusedinthissection.Understandingthatthekerneldensityplotwillnotcapture
theactualobservationsrightatcertainmarkers,thedensityplotallowsfor
convenient,directoverlappingoftwodistributionsandtheirtrends.
Extendingthesubsamplesizeto3‐yearrangestwoways,centeredat10
years(atotalofa6yearselection)revealsakerneldensityplotbothfarmore
skewedrightthantheoverallsamplefromthe4‐yearband.
[ReferenceGraph1.4]
Thedistributionnolongerappearsrandomized,whilethelarger6‐yearband
rangewillbecomparedtootheroverlappingandadjacentdistributionswiththe
Kolmogorov‐Smirnovtestsinsubsection4.2.Again,graphicvisualsareprovided
basedongenderaswelltocheckforevidenceofmorespecifiedpartsofthe
“strategicdivorce”hypothesis.
[ReferenceGraph1.5]
Bothsetsofdistributionsviatheirkerneldensityplotsareskewedrightthis
time,notjustthemales.Thedegreetowhichthemaledensityplotisskewed
howeverdoesseemmoreextremethanforfemalesbutagain,theextenttowhich
thetwodistributionsarethesamewillbetestedlater.Visually,itappearsboth
gendersfilemostlybeforethe10‐yearmarkwhenlookingatan8‐yearbandof
observationscenteredat10.Forvisualconveniencetheoveralldensitiesofmale
andfemalepetitionersisalsoprovided:
12
[ReferenceGraph1.6]
Ingeneralthegraphsforfemalepetitionersindicatetherearenorealpeaks
indivorceclustersuntilthe6‐yearmark.Theclusterisroughlyaroundthe2100
dayspoint,approximately6years.Ahigh‐densitysetofobservationsaroundthis
pointmaybestatisticallysignificantandduetosomeactualparameter,however
withinthecontextofthe“strategicdivorce”theory,wouldhavelittlesignificance.
Thedistributionformalepetitionersseesthemostsignificantclusteraroundapoint
justbefore2100daysbutanotheronethatcanbevisiblearoundthe3000days
mark,justunder8¼yearsintoamarriage.Thisobservationmaybeofgreater
significancetowards“strategicdivorce”andwillbeinterpretedindepthin
subsection3.2.Ultimatelyfromavisualglanceattherawstatistics,itappearsthe
observationlevelsfortheoverallsampleaswellasgendersplitspeakaround6
yearsinsteadofcloserto10.
4.2 KolmogorovSmirnovTests
UsingKolmogorov‐Smirnovtests,Imeasurethestatisticalvariationsin
distributionsacrosssectionsofdissolutionfilingperiodsrangingfrom4‐yeartime
framesto8years.TheKolmogorov‐Smirnovtestoftheavailablestatisticaltestsis
thestrongestoptiontowardscomparingdistributionalequalities.WheretheKuiper
TestalsousesthelargestmagnitudediscrepanciesD+andD‐betweentwo
cumulativedistributionfunctions,theteststatisticsumsthetwo,makingitmore
sensitivetothetailsofthedistribution.Basedonthedistributionofthesetof
observationsasexaminedinsection3,95%oftheobservationsformalesand
femalesfallwithinanapproximate7.9‐10.7yearand7.4‐9.5yearrange
13
respectively.AdditionaltestsconsideredsuchastheAnderson‐DarlingTestare
moresuitedtotestingfordeparturesfromnormality.TheCramer‐vonMisesTestis
analternativetotheKolmogorov‐SmirnovTestandstronglyconsideredbutfor
functionalandhypothesistestingsimilaritiestotheKolmogorov‐SmirnovTestwas
notused.
Thefirstsegmentofinterestasvisuallypresentedinsubsection4.1,isthe6‐
yearbandcenteredatthe10‐yearmark.Takingtheslicefrom7‐13yearsfirstand
comparingtothe1‐7slice,the“strategicdivorce”theorywouldsuggestthatthetwo
groupsarestatisticallydifferentdistributions.Thetestresultsfiguresarepresented
asfollows:
€
1:H0 :F(x) ≤G(x) vs. H1 :F(x) >G(x)2 :H0 :F(x) ≥G(x) vs. H1 :F(x) <G(x)Combined K − S :H0 :F(x) =G(x) vs. H1 :F(x) ≠G(x)
TheDvalueistheKolmogorov‐Smirnovteststatistic,whenplotted,the
maximumverticaldistancebetweenthetwoempiricaldistributionsbeing
compared.Thenotationalformforwhattheteststatisticsrepresentisasfollows:
€
1:D1+ = sup
x(S1(x) − S2(x))
2 :D1− = sup
x(S2(x) − S1(x))
Combined K − S :D1 = supxS1(x) − S2(x)
Thefirsttestof7‐13and1‐7yearbandsareasfollows:
[ReferenceFigure3]
Thep‐valueat0withamaximumDmagnitudeof1(thehighestpossible)
suggeststhatthetwodistributionsaredifferentata1%level.The13‐19yearrange
testresultsareasfollows:
14
[ReferenceFigure4]
Thep‐valueisagain0withafairlyhighmaximummagnitudeDbetweenthe
twodifferencesof.7413.Wewouldclearlynotexpectthedistributionstobethe
sameacrossthesethreetimeframes;infactevidenceofstatisticallydifferent
distributionswouldbeanticipated.Thesignificanceatthe1%levelthatthese
distributionsaredifferenthoweverisstillstrongevidenceofsomethingparticularly
significantabouthowthedistributionschangeoncethesignificantslicecenteredat
10yearsisreached.
ThenextgroupofKolmogorov‐Smirnovtestsarefocusedon2yearadjacent
slices.Forthedatatosupportthe“strategicdivorce”theory,thetestsshouldreturn
highp‐valuesforthefirstslicestested,earlyoninthemarriagetermlengthswith
thep‐valuesexpectedtodecreaseuntilapointofpotentiallystatisticalsignificance
atthe8‐10and10‐12comparisonwherethetwodistributionsshouldbehighly
dissimilar.Beginningfromthestartofthesample,thecomparisonsforthe0‐2and
2‐4yearmarriagetermsareasfollows:
[ReferenceFigure5]
Thep‐valueismoderatelyhigh;toohighforthenullhypothesisofthetwo
distributionsbeingstatisticallythesametoberejected.Wethusfailtorejectthe
hypothesisthatthedistributionsfrom0‐2and2‐4yearsarestatisticallydrawnfrom
thesameempiricaldistribution;inessencethearestatisticallythesame.Thep‐
valueandteststatisticarebothlowerthananideallevelfortheveryfirstbandtobe
testedfrom0‐2and2‐4.Wewouldhaveexpectedstrongerevidencethatthetwo
distributionswouldbestatisticallythesame,butwithvaryinglevelsofnoisetobe
15
somewhatexpectedintheearlybandsofmarriagedissolutions,thefollowingtests
maycloserfollowthepatternhypothesized.Theresultsforthe2‐4and4‐6year
bandcomparisonsareasfollows:
[ReferenceFigure6]
Theresultsforthe2‐4and4‐6yeartimeframesarenearlyexactlyas
anticipated,withthemoresignificantp‐valuedroppingveryslightly.Thereshould
beincreasingevidencethatthetwodistributionsarenotthesame,butthep‐valueis
stilltoohightorejectthenullthatthedistributionsweredrawnfromthesame
empiricaldistribution.Theteststatistichasfallenabitasthenumberofdegreesof
freedomhaschanged.Themoreimportantvalueagainisthatthep‐valuehasfallen
aswell.Thefollowingtestwasconductedoverthe4‐6and6‐8yearbands,withthe
correspondingresults:
[ReferenceFigure7]
Thep‐valueisincrediblyandunexpectedlylowforthistest.Werejectthe
nullhypothesisthenthatthesedistributionshavebeendrawnfromthesame
empiricaldistributionat5%.Thep‐valuehasdroppedfromtheprevioustestof2‐4
and4‐6yearbandsbutagain,perhapsfarmorethanwemighthaveexpectedtosee.
Ifresultsbestsupportingthe“strategicdivorce”aretofollow,thep‐valuewill
continuetodecrease,whiletheteststatisticshouldrise.Theevidencethoughatthis
stageisalreadyverystrongthatthedistributionofdivorcefilingsingeneralis
beginningtorapidlychangeinshape.Whilethisdoesnotsupportastrongcaseof
“strategicdivorce”theresultsfromthistestdofollowwhatwasvisuallyseenin
subsection4.1,thatthemostsignificantpeakbeforeachangeinshapewasatthe6‐
16
yearmarkinsteadof10.Followingthistest,theresultsofa6‐8and8‐10yearband
comparisonare:
[ReferenceFigure8]
Theresultsherearecompletelyunexpected,withthehighestobservedp‐
valueyet,aswellasthelowestteststatistic.Withsuchstrongevidencewefailto
rejectthenullthatthesetwodistributionsareactuallydrawnfromthesame
empiricaldistribution.
Again,thisinferenceisthefirstofthefourtestsconductedthusfartoprovide
evidenceagainst“strategicdivorce”,suggestingthatthemovementofthe
dissolutionfilingsisbeginningtofollowanapproximatelymarkabletrendas
opposedtostatisticallysignificantshifts.Thetestforthe8‐10and10‐12bandsthat
maybethemostcriticaltoexamineisthenperformedwiththefollowingresults:
[ReferenceFigure9]
Theresultsareagainintheoppositedirectionfromwhatwashypothesized.
Wherethep‐valuewasexpectedtosteadilydroptowardshighlysignificant
evidenceagainstthenulltosuggesttheincidenceof“strategicdivorce”,the
distributionsarestatisticallydrawnfromthesameempiricaldistribution.
Thecolossalp‐valueindicatesthatatthemostcriticaltestjunctureof8‐10
and10‐12yearrangesforevidenceof“strategicdivorce”thebandseithersideare
statisticallylikelytobethesame.Havingacolossalp‐valueheresuggeststhatthe
two2keyframeseithersideof10yearsdonothavequitethebimodalclustering
expectedrightaround10years.Theconceptthatthe10‐yearmarkisastatistically
significanteventaffectingthenumberofdissolutionsobservedistestedusinga
17
collapsedtimeseriesregressioninsubsection4.3.Atthispointtheideathatthetwo
distributionsarestatisticallydrawnfromdifferentdistributionsdoesnothold.The
10‐12and12‐14yearframesaretestedwithresultsasfollows:
[ReferenceFigure10]
Thep‐valueissmallerbutstillfartoolargetorejectthenullatanyimportant
levelofsignificance.Giventhatthe10‐12yearbandshowedageneraldownward
trendindissolutionfilingsobserved,the“strategicdivorce”hypothesiswouldbe
supportedbydownwardmovementinthe12‐14bandaswell.Suchasimilartrend
wouldbecapturedbythetwodistributionsbeingdrawnfromthesameempirical
distributionfunction.The“strategicdivorce”theoryisnotnecessarilyprovenor
disprovenbydistributionalsimilaritiesbetweentheseadjacentbands,howeverin
thecaseofthecriticalpointat10years,evenforthe8‐10and10‐12rangesshowing
similardistributions,ifthe6‐8yearsand8‐10yearsaswellasthistestshowedhigh
p‐values,wemightstillseeevidenceof“strategicdivorce”,simplynotinthebimodal
shapeexpected.Essentiallyforthosetwotestsboundedateithertheupperorlower
limitbythe10‐yearmark,mayindicatestatisticallysimilardistributionsthatrise
aroundthe10‐yearmarkandfallafterwards.Kolmogorov‐Smirnovtestswouldfind
thattheseindividualtestsusehighlysimilardistributionsbutnotnecessarilythe
factthatthereisakeytrendwithinthe4yearpre‐10andpost‐10observationrates
indissolutionfilings.TotestthisasthelastKolmogorov‐Smirnovdistribution
comparisonofthetotalsample,the6‐10and10‐14bandsaretestedwiththe
followingresults:
[ReferenceFigure11]
18
Thep‐valueof0meansata1%levelofsignificancethetwo4yearrangesare
indeedstatisticallydrawnfromdifferentempiricaldistributionfunctions.
AggregatingtheKolmogorov‐Smirnovtestsdonefor6yearbandswithonecritical
onecenteredat10,testsdonefor2yearadjacentbands,andthelasttestdirectly
comparing4yeardistributionseithersideof10years,afewobservationscanbe
maderegardingwhatproofthereappearsfororagainst“strategicdivorce”evident
inthesampledobservations.
The6yearbandtestsprovidedtheunderlyingfoundationforthereeven
beingacriticalpointcenteredbetween7and13years.Thenotionbehindthose
testswasthattheincidenceofanypeakorclusterofhighfrequencydissolutions
wastobefoundinthatrange.The2‐yearbandtestsweretotryandprovea
somewhatambitiouslinearitytrendindistributionslicesthatshouldhaveclimbed
steadilyuntilthe10‐yearmarkwhereaverylowp‐valuewouldhaveprovidedfairly
strongevidenceofsomeformofsharpstatisticaldiscontinuityordiscontinuities
withinthe8‐12yearframe.Thefactthattherewasinsteadstrongevidencethatthe
twobandscomparedwithinthe8‐12yearframewerestatisticallydrawnfromthe
samedistributionfunctionledtothe4‐yearbandtest.Basedonthegraphical
representationspresentedthroughoutsubsection4.1andevenfromthe8‐12year
frame,the4‐yearbandtestwasperformedtotestaweaker“strategicdivorce”
hypothesis,thatwhiletheremaynotbestrongbimodalevidencethe10‐yearmark
isstillstatisticallysignificant.Thetwodistributionsbeingdirectlysplitbythe10‐
yearmarkwereshownindeedata1%leveltobedrawnfromdifferentempirical
19
distributionssuggestingthatthesubsequentpaneldatatestmayprovidemore
conclusiveevidencesupportingorrefuting“strategicdivorce”.
Theoverallsamplethusdoesnotprovidestrongevidenceofdistributional
differencescenteredat10years.Theotherdistributionalquestionofinterest
pertainstothegendersplitswithtestsfirstrunfortheoverallgenderdistributions,
then2‐yearsplitsbeforeandafter10years,then4yearsbeforeandafter.The
resultsfortheoverallsampleareasfollows:
[ReferenceFigure12]
Thefairlylargep‐valueat.486suggeststhatthemaleandfemale
distributionsforthecollectivesamplesetarestatisticallydrawnfromthesame
empiricaldistribution.Beingthatthereare534observationsinplayherethatmay
notbeunexpected.Thetestssurroundingthecriticalpointat10yearsmayprovide
moreevidenceofonegender’stendencytofileatacertainpointoranother.The
resultsforthe8‐10yearframeareasfollows:
[ReferenceFigure13]
Thedistributionsagainshowafairlyhighp‐valueat.269indicatingthatfor
this2‐yearbandbefore10yearsneithergendersignificantlyfilesfordivorcesata
higherrate.Thisagainsupportswhatthevisualevidencefromsubsection4.1
suggested.Thetestfor10‐12yearsyieldsthefollowingresults:
[ReferenceFigure14]
Thep‐valueisincrediblyhighforthethirdstraighttest,at.872.Theevidence
isverystrongagainthattherearenostatisticallysignificantdeviationsbetweenthe
maleandfemaledistributions.Again,thevisualrepresentationsfromsubsection4.1
20
showedverylittlevariationbetweenthetwogendersthroughthis8‐12yearperiod
withthestatisticalsimilaritiesbetweenthetwodistributionsnowproven.Thelast
twotestsrunforthetwogenderdistributionscoverthelargerrangeof6‐10and
then10‐14years,whereevidencefromthelargersamplesuggestedthattherewasa
statisticallysignificantdifferencebetweenthosetwodistributions.Theresultsfor
the6‐10yearrangeformaleandfemalepetitionersisasfollows:
[ReferenceFigure15]
Againthep‐valueisverylargeat.744,withteststatisticmaximumsthatdo
notcomeclosetothedifferencesobservedwherethedistributionswouldbe
statisticallydifferent.Thefinaltestforthe10‐14yearrangeisrunwiththe
followingresults:
[ReferenceFigure16]
Optimistically,thisisthefifthstraighttestofthetwogendersthathas
suggestedneithersidefilesfordivorcesignificantlymorethantheotherduringthe
timeframesofinterest.Compoundingthevisualevidencefromsubsection4.1and
thelargep‐valuesfordistributionsobservedheresuggeststhatforthetimeseries
regressionthecollapseddataneednotaccountforgenderdifferences.
4.3 TimeSeriesRegression
Totesttheevenweakerhypothesisfrom“strategicdivorce”thatthe10‐year
markisastatisticallysignificantevent,Iuseabasictimeseriesregression.Icollapse
thedatasoitisatime‐seriesdataset–whereeachobservationisatimeperiod
insteadofadivorce.Thecollapseddatasetreorderedintoatimeseriessetisthen
bunchedinto146‐dayclustersofobservationstocapturethevelocityorrateat
21
whichdissolutionsarefiled.Thefirsttestisrunforthe6‐14yearbandwiththe
followingresults:
[ReferenceFigure17]
Thewaythedataisbunched,thecoefficientonthepost‐10yearevent
variablesuggeststhatper146‐daygroupobservedafterthe10‐yearmark,thereare
1.1778lessmarriagesobservedthanbeforethatsamemark.Thehighp‐valueat
.718aswellasaconfidenceintervaloftheestimatethatrangesfrom(‐7.977,5.621)
suggestthecoefficientislikelytobestatisticallyzero.Theadditionaltimetrend
variablehasap‐valueof.101meaningevenata10%significancelevel,thereis
almostnoeffectonthedataovertime.Anothertestisthenrunfortheoverall
samplewiththefollowingresults:
[ReferenceFigure18]
Theregressionthistimewithoutthe6‐14yeartimeconstraintreturnsap‐
valueof.001forthecoefficientonthepost‐10dummy.Thecoefficientis
significantlynegativethistimeat‐7.879,whichsuggeststhatafterthe10‐yearmark,
within146daygroupingstheaveragenumberofdivorcesfiledhasfallenbynearly
8fromwhattheobservationlevelswereatbefore10years.Theestimateis
significantat1%andprovidessomeevidencethatoverthetotalsamplesizethereis
astatisticallysignificantshiftatthe10‐yearmark.
Intermsofevidenceof“strategicdivorce”thetimeseriestestcontrolsforthe
growthovertimeofdivorcefilingssothesignificanceofthepost‐10variableis
meaningful.Proofhereofthatmarkbeingstatisticallysignificantexistsbutsuggests
onlytheweakestformofthe“strategicdivorce”hypothesis.
22
4.4 HazardRate
Thefinalapplicationtakenwiththesampledobservationsinvolves
calculatingahazardrateformarriagesbasedoneachpassingyear.Usingamodified
formulafromthetraditionalhazardrateformulathehazardrateformarriagesuses
anassumedstandardsetofmarriagesfromtime0andobserveddatainplaceofthe
probabilitydensityfunctionandthesurvivalfunction.Theformulaisasfollows:
€
Divt = probability of being divorced after time tMarrt = probability of being married after time tNt = instantaneous number of divorces in time tTt = remaining number of divorces by time t
Pr(Div1 | Marr0) =N1
(T1 − N0)
Pr(Div2 | Marr1) =N2
(T2 − N1)(1−D1)
Pr(Divt | Marrt−x ) =Nt
(Tt − Nt−x )((1−Dt−x ) × (1−Dt−x−1) ×…(1−D1))
Basedonthisformulawhichcontinuallyaccountsforthesurvivingratioof
marriages,thehazardratescalculatedareasfollows:
[ReferenceTable1]
Thehazardratesclimbtowards10years,butactuallypeakat7yearsandnot
at10.Thisfindingisactuallyexactlyinlinewiththegraphicalrepresentations
showninsubsection4.1.Thehazardratereachespeaksat7yearsand16years,
whilethenumberofdivorcesobservedpeaksinyears6and7.Again,thisismostly
inaccordancetowhatwasexpectedfromthestatisticaldistributions,wherepeaks
inobservationclustersdidnotsurround10years.
23
Thehazardrateprovidesaninformativelookatthelikelihoodofdivorce
followingacertainyearconditionalonhavingsurvivedtheyearsprior,basedonthe
instantaneouslychangingpopulationoftotalmarriagesfromtime0.Astheyears
progress,thedecreasingratioofpopulationofsurvivingmarriagesgenerallyfollows
adecreasingquantityofdivorcesobserved.Thatthebandofhazardratesnever
exceedsapeakof7.78%andaminimumof2%(withthevalleyappearinginyear1)
suggestsoptimisticallythattheremaybenoevidenceof“strategicdivorce”.The
hazardratesfrom8‐14yearsinparticularnevervarybeyonda1%rangewhichis
againpositiveevidencethatindividualsarenotmorepronetodivorcewithinthose
ranges.Theobservationlevelsofdivorcefilingsgenerallydropsduringthattime
frameaswellasfallingpastthe14‐yeartimeaswell.
Ingeneralthelowvarianceoftheobservedhazardratesandabsenceofany
realtrendwithinthe20‐yeartermcalculatedprovidesnoevidencewhatsoeverof
“strategicdivorce”.
5. Conclusions
Thecentralquestionof“strategicdivorce”intheinstanceofmarriages
observedinAlamedaCountyintheyear2007isaddressedfirstbytakinggraphical
representationsandstatisticalorderingsofthedataforvisualevidenceofany
skewnessorpeaksinthedistributionsbasedaround10years.Thelargestpeakfor
theoverallsamplewasactuallydetectedaroundthe2100daysorapproximately
the6yearmark.Uponsplittingthedistributionbygendertherewaslittlevisual
evidencethatthetwodistributionsweresignificantlydivergent,whilebothsubsets
ofobservationsfollowedtheoverallsample’sshapewithapeakaround6years.The
24
overallandindividualgenderplotsallshowedprecipitousdropsindivorce
observationsjustfollowing10yearshowever,aswellasacontinuingdownward
trendinobservations.
Usingthevisualrepresentationsindicatingthemostevidenceinfavorof
“strategicdivorce”,Kolmogorov‐Smirnovtestsareusedtocheckforthe
distributionalequalitiesofkeysegmentsofthedata.Forastrongcaseof“strategic
divorce”,itishypothesizedthatobserving2yearbandsbeginningfrom0‐2and2‐4
upthroughandjustpastthe10‐yearmark,thep‐valuesshouldsteadilyfalltowards
10yearsandthenriseagain.Suchfindingswouldindicatethatwheretheearly
movementofthesetofobservationsisconsistentandtheincidenceofdivorce
filingsshouldbeincreasing,around10yearsthereshouldbeasignificantshiftin
thedistributionofobserveddivorces.Thefindingsinsteadsuggestedthatatthe
mostcriticalpointof10years,distributions2yearsaboveandbelowthismarkare
statisticallydrawnfromthesameempiricaldistributionorthattheyarefunctionally
notdifferent.Thetestofthesetwobandsat8‐10and10‐12yearsshowedan
incrediblylargep‐value,confirmingwhatwasobservedfromthegraphical
representations.Thestrongestevidenceofdistributionsbeingstatisticallydifferent
wasthetestofthe4‐6and6‐8mark,againobservedfromthedensityplotsand
histogramsashavingapeakat6years.
Extendingtoasingulartestofdistributions4yearsbelowandabovethis10‐
yearmark,therewassignificantevidencethatthe6‐10and10‐14bandswere
distributionalverydifferent.Withthisstrongevidenceofdistributionaldifferences,
atimeseriesregressionwasrunforthis6‐14rangeandthelargersample,usingthe
25
10‐yearmarkasaneventdummy.Thetimeseriesregressionreturnedacoefficient
withtheexpectednegativesignbutwithap‐valuesuggestingitwasstillstatistically
zero.Atimeseriesregressionrunfortheentireobservationsetsuggestedthatat
the1%levelthepost‐10markwasastatisticallysignificantevent.
Thelastapplicationwasincalculatinghazardratestotryanddetermine
whencoupleswereathighestriskfordivorcingaswellastheconditional
probabilitylevelchangesfromyeartoyear.Thehighesthazardratescalculated
followedthe6th,7th,and16thyears,withthehighestobserveddivorcefilings
followingyears6and7.
Fromthegraphicalrepresentationspresentedinsubsection4.1throughthe
distributionalcomparisonsfromsubsection4.2tothedirecttimeserieseventtests
fromsubsection4.3andlastlythroughthehazardratescalculatedinsubsection4.4,
atbestonlyaweakcaseof“strategicdivorce”canbefound.Thelargestpeakas
showninallsubsectionsisactuallyat6years.Thefindingsoptimisticallysuggest
thatnotonly“strategicdivorce”likelynotpresent,inparticular,thereisno
differencecross‐genderindivorcefilingtimes.
Cruciallyhowever,itmustbeacknowledgedthatthedataset’simperfections
maynotlenditselftostrongerinferences.Thevalueofsuchdatapointsasthe
numberofkidswithinmarriagesdidnotproveusefulinhelpingjudgetheincidence
ofdivorceorsuggestanythinginterestingaroundthe10‐yearmark.Additionallyas
notedearlier,datathatcouldhaveprovenincrediblydescriptivepertainingto
maritalincome,sharedproperty,orwhatchildsupportpaymentswereset.Thedata
setalsoasawholedidnotfeatureaproportionallylargesampleofobservations
26
particularlyclosetothe10‐yearmark,meaningmosttestsofinterestdonefocused
atthatpointusedanywherefrom99‐253observations.Lastly,althoughoveralarge
enoughunifiedamountofcountiesthereshouldnotbesignificantlydifferent
findings,basedonmedianincomelevels,theremaystillbevariationslimitingthe
abilityofthesefindingstobeextended.Inareaswithhighmedianincomessayin
MarinCountyifthereisoneprimaryearner,theremaybestrongerevidenceof
“strategicdivorce”,versusalowerincomecounty.
InthecaseofAlamedaCountyhowever,theevidenceispromisingthat
economicdriversdonotplayasignificantroleinindividuals’decisionstofilefor
divorce.Inparticularwhereitmighthaveseemedlogicalfortheretobegender
differencesaswellinfilingtimes,thefindingssuggestthatthetwodistributionsalso
donotvary.
6. Acknowledgements
IwouldliketothankmyadvisorAaronEdlinforhishelpfulcommentsand
suggestionstowardsthedirectionofmyresearch.Iamalsoverygratefulto
MatthewBotschforhisinvaluableadviceandinsightintheprocessoftransitioning
myresearchintotractablehypothesesandtests.
Anyviewsexpressedareminealoneandnotnecessarilythoseofmyadvisor
ormydepartment.
27
7. References
[1]Blair,Sandra,BobPickus,andCarolAmyx.CaliforniaMaritalSettlement&Other
FamilyLawAgreements.Berkeley,CA:ContinuingEducationoftheBar,
California,1997.Print.
[2]Friedberg,Leora."DidUnilateralDivorceRaiseDivorceRates?EvidenceFrom
PanelData."TheAmericanEconomicReview88.3(1998):608‐27.
Www.jstor.org.AmericanEconomicAssociation,19Sept.2005.Web.24Apr.
2012.
[3]Laskin,Jared."AChronologicalSummaryofCalifornia"Palimony"LawSince
Marvin."UnmarriedCouplesandtheLaw.Goldman&KagonLawCorporation.
Web.25Apr.2012.<http://www.palimony.com/>.
[4]Lurvey,Ira,KathrynKirkland,andDianaRichmond.CaliforniaFamilyLaw:
PracticeandProcedure.2nded.Vol.2.MatthewBender,1994.Print.
[5]Rasul,Imran.2006.Marriagemarketsanddivorcelaws.JournalofLaw,
Economics,andOrganization22,no.1:30–69.
[6]Stevenson,Betsey."TheImpactofDivorceLawsonMarriage‐SpecificCapital."
JournalofLaborEconomics25.1(2007):75‐94.Print.
[7]Stevenson,Betsey."Divorce‐LawChanges,HouseholdBargaining,andMarried
Women'sLaborSupplyRevisited."PSCWorkingPaperSeries(2007):1‐24.
UniversityofPennsylvaniaScholarlyCommons.PopulationStudiesCenter,10
May2007.Web.25Apr.2012.<http://repository.upenn.edu>.
[8]Wolfers,Justin."DidUnilateralDivorceLawsRaiseDivorceRates?A
ReconciliationandNewResults."NBERWorkingPapersSeries(2003):1‐29.
NationalBureauofEconomicResearch,Oct.2003.Web.25Apr.2012.
<http://www.nber.org/papers/w10014>.
28
Figure1 Pre-10 Years Post-10 Years Total Female 184 132 316 Male 118 100 218 Total 302 232 534
Figure2
Pre-10 Years Post-10 Years Total Female 35 27 62 Male 21 16 37 Total 56 43 99
Graph1.1 Graph1.2
Graph1.3
29
Graph1.4
Graph1.5
30
Graph1.6
Figure3Smaller Group D P-Value Corrected
1 0.0000 1.0000 2 -1.0000 0.0000
Combined K-S 1.0000 0.0000 0.0000 Figure4Smaller Group D P-Value Corrected
1 0.7413 1.0000 2 -1.0000 0.0000
Combined K-S 0.7413 0.0000 0.0000 Figure5Smaller D P-Value Corrected
31
Group 1 0.0952 0.607 2 -0.1973 0.117
Combined K-S 0.1973 0.234 0.176 Figure6Smaller Group D P-Value Corrected
1 0.1797 0.110 2 -0.0025 1.000
Combined K-S 0.1797 0.219 0.168 Figure7Smaller Group D P-Value Corrected
1 0.0007 1.000 2 -0.2978 0.001
Combined K-S 0.2978 0.002 0.001 Figure8Smaller Group D P-Value Corrected
1 0.1299 0.335 2 -0.0503 0.849
Combined K-S 0.1299 0.645 0.572 Figure9Smaller Group D P-Value Corrected
1 0.0864 0.696 2 -0.0743 0.764
Combined K-S 0.0864 0.993 0.988 Figure10Smaller Group D P-Value Corrected
1 0.2062 0.184 2 -0.1018 0.662
Combined K-S 0.2062 0.367 0.288 Figure11Smaller Group D P-Value Corrected
1 0.6015 0.000 2 0.000 1.000
Combined K-S 0.6015 0.000 0.000 Figure12Smaller D P-Value Corrected
32
Group 1 0.0736 0.247 2 -0.0081 .983
Combined K-S 0.0736 0.486 0.444 Figure13Smaller Group D P-Value Corrected
1 0.0667 0.890 2 -0.2762 0.135
Combined K-S 0.2762 0.268 0.190 Figure14Smaller Group D P-Value Corrected
1 0.1690 0.563 2 -0.1875 .493
Combined K-S 0.1875 0.872 0.803 Figure15Smaller Group D P-Value Corrected
1 0.0894 0.620 2 -0.1245 0.396
Combined K-S 0.1245 0.744 0.676 Figure16Smaller Group D P-Value Corrected
1 0.1731 0.320 2 -0.2028 0.210
Combined K-S 0.2028 0.416 0.328 Figure17
Figure18
33
Table1Year Pr(Div|Marr) Nt Tt0 0 0 10001 .02 20 10002 .0302 29 9803 .0321 34 9514 .0462 29 9175 .0347 27 8886 .0658 48 8617 .0731 47 8138 .0534 30 7669 .0587 30 73610 .0564 26 70611 .0572 24 68012 .0498 12 65613 .0597 21 63714 .0500 16 61615 .0608 18 60016 .0778 21 58217 .0292 7 56118 .0479 11 55419 .0466 10 54320 .0598 12 533