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Partner Choice and the Marital College Premium

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Niveau: Supérieur, Doctorat, Bac+8
Partner Choice and the Marital College Premium Pierre-Andre Chiappori? Bernard Salanie† Yoram Weiss‡ December 13, 2010 Abstract Several theoretical contributions have argued that the returns to schooling within marriage play a crucial role for human capital investments. Our paper empirical inves- tigates the evolution of these returns over the last decades. We consider a frictionless matching framework a la Becker-Shapley-Shubik, in which the gain generated by a match between two individuals is the sum of a systematic effect that only depends on the spouses' education classes and a match-specific term that we treat as random; following Choo and Siow (2006), we assume the latter component has an additively separable structure. We derive a complete, theoretical characterization of the model. We show that under the null that supermodularity on the surplus function is invariant over time and errors have extreme value distributions, the model is overidentified even if the surplus function varies over time. We apply our method to US data on individu- als born between 1943 and 1972. The overidentification tests do not reject; moreover, we find that the deterministic part of the surplus is indeed supermodular and that, in line with theoretical predictions, the “marital college premium” has increased more for women than for men over the period. 1 Introduction Marital college premium and the demand for higher education The market rate of return to schooling has increased for both men and women in recent decades.

  • education classes

  • time obviously

  • stage has

  • marriage

  • match-specific term

  • within marriage

  • marital college

  • stable over time


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PartnerChoiceandtheMaritalCollegePremiumPierre-Andre´ChiapporiBernardSalanie´YoramWeissDecember13,2010AbstractSeveraltheoreticalcontributionshavearguedthatthereturnstoschoolingwithinmarriageplayacrucialroleforhumancapitalinvestments.Ourpaperempiricalinves-tigatestheevolutionofthesereturnsoverthelastdecades.Weconsiderafrictionlessmatchingframeworka`laBecker-Shapley-Shubik,inwhichthegaingeneratedbyamatchbetweentwoindividualsisthesumofasystematiceffectthatonlydependsonthespouses’educationclassesandamatch-specifictermthatwetreatasrandom;followingChooandSiow(2006),weassumethelattercomponenthasanadditivelyseparablestructure.Wederiveacomplete,theoreticalcharacterizationofthemodel.Weshowthatunderthenullthatsupermodularityonthesurplusfunctionisinvariantovertimeanderrorshaveextremevaluedistributions,themodelisoveridentifiedevenifthesurplusfunctionvariesovertime.WeapplyourmethodtoUSdataonindividu-alsbornbetween1943and1972.Theoveridentificationtestsdonotreject;moreover,wefindthatthedeterministicpartofthesurplusisindeedsupermodularandthat,inlinewiththeoreticalpredictions,the“maritalcollegepremium”hasincreasedmoreforwomenthanformenovertheperiod.1IntroductionMaritalcollegepremiumandthedemandforhighereducationThemarketrateofreturntoschoolinghasincreasedforbothmenandwomeninrecentdecades.Itwastobeexpected,therefore,thatbothmenandwomenshouldincreasetheirinvestmentinschooling.Howeverthedatashowsthatwomenincreasedtheirschoolingsubstantiallymorethanmen;inmanycountries,womenarenowmoreed-ucatedthanmen.Chiapporietal(2009)arguethatthisdifferencecanbeattributedtogenderdifferencesinthereturnstoschoolingwithinmarriage1.ThishypothesisisColumbiaUniversityColumbiaUniversity.TelAvivUniversity.1Another,largelycomplementaryexplanationproposedbyBecker,HubbardandMurphy(2009)reliesonthedifferencesbetweenmaleandfemaledistributionsofunobservedability.Still,theseauthorsalsoem-phasizethateducatedwomenmusthavereceivedsomeadditional,intrahouseholdreturntotheireducation.Itispreciselythatadditionaltermthatourapproachallowstoevaluate.1
supportedbythesubstantialimprovementsinhouseholdandbirthcontroltechnology,aswellasbythechangingrolesofwomenwithinthehousehold.Still,itishardtoproveempirically(seeGreenwoodetal,2004).Incontrasttothereturnstoschoolinginthemarketthatcanbeestimatedfromobservedwagesdata,thereturnstoschoolingwithinmarriagearenotdirectlyobservedandcanonlybeinferredindirectlyfromthemarriagepatternsofindividualswithdifferentlevelsofschooling.Inthispaper,weprovidesuchestimates.Ourempiricalapproachisbasedonastructuralmodelofmatchingonthemarriagemarketthatisclose,inspirit,tothatadoptedbyChiapporietal.(2009).Specifically,weconsiderafrictionlessmatchingframeworkalaBecker-Shapley-Shubik,inwhichthegaingeneratedbythematchofmaleiandfemalejisthesumofasystematiceffect,thatonlydependsonthespouses’educationclasses,andamatch-specifictermthatwetreatasrandom.Ourcrucialidentifyingassumption,similartothatinChooandSiow(2006),isthatthelattertermisadditivelyseparableintoamale-specificandafemale-specificcomponents.Anaturalinterpretationisthatthecomplementaritypropertiesofthemodel,whichdrivetheassortativenessofthestablematching,operateonlybetweenclasses,andarenotaffectedbytheunobservablevariables.Whileundoubtedlyrestrictive,thisassumptionallowsustofocusonourmaintopicofinterest,namelymatchingbetweeneducationclasses;inthatsense,ourmodelisessentiallymotivatedbyaconcernforparsimony.Moreover,ourseparabilityassumptiongeneratestestablerestrictionsthatthedatamarkedlyfailstoreject.2Underthisseparabilityassumption,wederiveasetofnecessaryandsufficientcon-ditionsforstability,andshowthattheseconditionscanbeinterpretedintermsofastandard,discretechoiceframework.Wethendiscusstheidentifiabilityofourtheoret-icalsetup.Inacross-sectionalcontext,thesimplestversion,whichreliesonastronghomoskedasticityassumptions,isexactlyidentified;sothatwecannotidentifyanypatternofheteroskedasticity.If,however,thesamestructure(assummarizedbythematrixofeconomicgainsbyspouses’educationclasses)isobservedforsubpopulationswithdifferentcompositions,thenthebasicmodelis(vastly)overidentified.Infact,onecanidentifyamoregeneralstructure,inwhichthesystematiccomponentofthesurplusinvolvesclass-specifictemporaldrifts;moreover,thisgeneralizedmodelstillgeneratesstrongoveridentificationrestrictions.3WeapplyourmodeltotheUSpopulation,forcohortsbornbetween1935and1975andmarriedbetweenages18and35.Weshowthatthereturnsfromschoolingreceivedwithinmarriage(the“maritaleducationpremium”)haveincreasedsharplyforwomenovertheperiod,whiletheyhavenotchangedmuchformen.Educatedwomenhavegainedrelativetouneducatedwomenintwoways:bymarryingathigherratesandbyreceivingahighershareofthemaritalsurplus.Wealsofindthatthegainsgeneratedbymarriageswithequallyeducatedpartnershavedeclinedforalltypesofmarriage,2Whilethefrictionlessnatureofourmodelwouldbeastrongassumptioninmanycontexts,webelievethatitisprobablymoreacceptableinourframework,preciselybecauseoftheseparabilityassumption.Inourseparableworld,theabsenceoffrictionsonlymeansthatanyagentcanmeetatleastonepotentialmatefromeachoftheeducationclassesunderconsiderationat(almost)nocost.3Weshowthatanevenmoregeneralstructure,inwhichthescaleofindividualheterogeneitymayvarybyeducationclass,couldalsobeidentified.Inpractice,however,theassumptionofidenticalhomogeneityisnotrejectedbythedata.2
reflectingthegeneralreductioninmarriageovertime.However,thesmallestdeclineisinmatcheswhenoneorbothpartnershavecollegeeducation.Thisfindingcanberelatedtoempiricalworkshowingthatsuchmarriagesarealsolesslikelytobreak(seeWeissandWillis1997andBruze,SvarerandWeiss2010).TheevolutionofassortativematchingArelatedissueiswhathappenedtoassortativemating.Theobservedpatternsarequitecomplex.Overall,thepercentageofcouplesinwhichbothspouseshaveacollegedegreehassignificantlyincreasedovertheperiod;however,aswomenwithcollegedegreebecamemoreabundant,thepropor-tionofeducatedwomenwhomarryeducatedmenhasdeclined(becausesomeeducatedwomenhadtomarrydownwardswithlesseducatedmen),whilemenwithhighschooldegreeshiftedupwardsfrommarryingwomenwithhighschooldegreetomarryingmoreoftenwomenwithcollegedegree.Allinall,manyobservershaveneverthelessconcludedthatassortativematchingwasstrongernowthanfourdecadesago,andthatthisevolutionhadadeepimpactonintrahouseholdinequality(seeforinstanceBurtless1999).Anoldquestioniswhetherthisphenomenonisentirelyduetothemechanicalef-fectoftheincreaseinfemaleeducation,orwhetheritalsoreflectsashiftinpreferencestowardsassortativematching(aswouldbethecase,forinstance,iftheshareofpub-licgoodsinhouseholdsriseswithtime-orincome-andsimilareducationfacilitatesagreementsonthecompositionandlevelofthesepublicgoods).Animportantad-vantageofourstructuralapproachisthatitallowstoformallydisentanglethetwoaspects.Inthisrespect,ourconclusionsareclear-cut.Wedonotfindanyevidenceforachangeinpreferencesforassortativematching.Infact,wedonotrejectthenullthattheinteractioninmaritalgainsbylevelofschooling(assummarizedbythesupermod-ularityofthematrixofsystematicgains)hasremainedstableovertime.Totheextentthatwefindanincreasingproportionofcouplesinwhichbothpartnersareeducated,thisisnotbecausethegainsfromhavingacollegedegreeforbothpartners(comparedwithonlyonepartnerhavingacollegedegree)haverisenovertime.Wefindstrongevidencethatforeducatedwomen,theadditivegainsfrommarriagehaveshiftedovertime.Onepossibleinterpretationisthatitbecamelesscostlyforeducatedwomentomarrymainlybecausehouseholdchoreshavebeenreduced,sothatmarriedwomencanparticipatemoreinthelabormarket(seeGreenwood,SeshadriandYorukoglu2005),andalsobecausebirthcontroltechnologieshavedrasticallyimprovedovertheperiod,allowingforbetterplanningoffamilyfertility(seeMichael,2000,andGoldinandKatz2002).However,ourfindingssuggestthatthese”liberatingeffects”aremoreorlessindependentoftheschoolingofthehusband.Asaby-productofourinvestigation,wecanidentifythematrixofsystematicgains;wefindthatitis,indeed,significantlysupermodular.Thisfindingseemstocontradictresultsinthesociologicalliteraturethathaveshown,usingloglinearmodels,thatevenafteraccountingforchangesintherelativenumberofmenandwomenineachskillgroup,homogamyhasincreasedintheUSandseveralothercountries(seeMare,1991,2008).However,theseconclusionsweredrawnfromreduced-formmodelswithnodirecteconomicinterpretation.Weshow,inparticular,thefollowingresult.Assumewetakeourstructuralframeworkundertheassumptionthattheforcesdrivingassortativematching(i.e.,thematrixofmarital3
gainsbyeducationclasses)remainconstant,andweuseittogeneratemarriagedata.Ifthelog-linearregressionadoptedinthesociologicalliteraturewereappliedtosuchdata,theywould(spuriously)concludethatpreferencesforhomogamyhavechanged.Thesefindingsfurtheroutlinetheimportanceofastructuralapproachtoguidetheinterpretationoftheempiricalresults.Finally,anotheroutcomeofourstructuralapproachistheidentificationofthegroupspecific“prices”thatdeterminethedivisionofthegainsfrommarriagebetweenhusbandsandwivesofdifferenttypes.Wefindthatincouplesinwhichbothspouseshaveacollegedegree,theshareofthewifeinthegainsfrommarriagehasincreasedovertime,despitetheriseinthenumberofeducatedwomenrelativetoeducatedmen.Thishappenedbecausethemarginalcontributionofeducatedwomentothesurpluswitheducatedmenhasrisenovertime.Wefindthattheincreaseismainlyduetothevariablecomponent:educatedwomenbecamemoreproductiverelativetolesseducatedwomeninallmarriages,irrespectiveofthetypeofthehusband.ThisfindingconfirmstheanalysisofChiapporietal.(2009),accordingtowhichtheincreaseinthemaritalcomponentoftheeducationpremiumforwomencouldexplainthespectacularincreaseinfemaledemandforhighereducation.RelatedliteratureTheanalysisofthemarriagemarketasamatchingprocess,whichdatesbacktoBecker’sseminalcontributions(seeBecker1981),hasrecentlyattractedrenewedattention.ProbablythemostimportantempiricalworkisduetoChooandSiow(2006),whoproposeoneofthefirstimplementationsofaBecker-Shapley-Shubikmodelbasedonadiscretechoicemodel.Ourpaperextendstheircontributioninthreedirections.First,weclarifytheunderlyingtheoreticalstructure,inparticularbyworkingouttheassumptionsneededonthefundamentalsofthemodel(i.e.,thematrixofsystematicgain)andtheirimplicationsfortheendogenousvariables(individualutilitiesatthestablematch).Secondly,weconsideramodelthatallowsforinterclassheteroskedasticityoftherandomcomponents.Thirdly,westudytheevolutionofmatchingpatternsthroughouttime,inaframeworkthatalsoallowsthegainsformarriagetoevolveinaclass-specificway.Ourultimategoalistostudymatchingoneducation,andmorespecificallytoprovideadynamicperspectiveontheevolutionofthecorrespondingpatternsoverseveraldecades.Thesevariousextensionsarenecessaryforourpurpose.Evaluatinghowthe‘mar-italcollegepremium’evolvesovertimeobviouslynecessitatesadynamicanalysis.Italsorequirescomparing(expected)utilitiesbetweenclasses,ataskforwhichtheho-moskedasticityassumptionofthestandardversionispotentiallyinappropriate.InChooandSiow’sapproach,thebasic,homoskedasticversionisexactlyidentified,im-plyingthatanygeneralizationwillfacesevereidentifiabilityproblems.Weshowthattheseproblemscanhoweverbeovercomeinamoredynamiccontext,providedthatthestructuresdrivingassortativematchingremainsconstant.Inparticular,ouriden-tificationstrategyisoriginal.AnotherrelatedapproachisduetoGalichonandSalanie´(2010),whoprovideatheoreticalandeconometricanalysisofmulticriterionmatchingunderthesamesepa-rabilityassumption.Theirfocusisdifferent:whileourpaperconsidersasmallnumberofclasses,theyseektoprovideageneralmethodtoestimateandtestflexibleparamet-ricspecificationsofthegainsfrommarriagewhenmanycovariatesareavailable.4