Partner Choice and the Marital College Premium

Pierre-André Chiappori

Description

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

Sujets

• Willis
• Marriage

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 12
• Langue: English

Extrait

PartnerChoiceandtheMaritalCollegePremium Pierre-Andre´Chiappori ∗ BernardSalanie´ † YoramWeiss ‡ December13,2010 Abstract Severaltheoreticalcontributionshavearguedthatthereturnstoschoolingwithin marriageplayacrucialroleforhumancapitalinvestments.Ourpaperempiricalinves- tigatestheevolutionofthesereturnsoverthelastdecades.Weconsiderafrictionless matchingframeworka`laBecker-Shapley-Shubik,inwhichthegaingeneratedbya matchbetweentwoindividualsisthesumofasystematiceffectthatonlydepends onthespouses’educationclassesandamatch-specifictermthatwetreatasrandom; followingChooandSiow(2006),weassumethelattercomponenthasanadditively separablestructure.Wederiveacomplete,theoreticalcharacterizationofthemodel. Weshowthatunderthenullthatsupermodularityonthesurplusfunctionisinvariant overtimeanderrorshaveextremevaluedistributions,themodelisoveridentifiedeven ifthesurplusfunctionvariesovertime.WeapplyourmethodtoUSdataonindividu- alsbornbetween1943and1972.Theoveridentificationtestsdonotreject;moreover, wefindthatthedeterministicpartofthesurplusisindeedsupermodularandthat,in linewiththeoreticalpredictions,the“maritalcollegepremium”hasincreasedmorefor womenthanformenovertheperiod. 1Introduction Maritalcollegepremiumandthedemandforhighereducation The marketrateofreturntoschoolinghasincreasedforbothmenandwomeninrecent decades.Itwastobeexpected,therefore,thatbothmenandwomenshouldincrease theirinvestmentinschooling.Howeverthedatashowsthatwomenincreasedtheir schoolingsubstantiallymorethanmen;inmanycountries,womenarenowmoreed- ucatedthanmen.Chiapporietal(2009)arguethatthisdifferencecanbeattributed togenderdifferencesinthereturnstoschoolingwithinmarriage 1 .Thishypothesisis ∗ ColumbiaUniversity † ColumbiaUniversity. ‡ TelAvivUniversity. 1 Another,largelycomplementaryexplanationproposedbyBecker,HubbardandMurphy(2009)relies onthedifferencesbetweenmaleandfemaledistributionsofunobservedability.Still,theseauthorsalsoem- phasizethateducatedwomenmusthavereceivedsomeadditional,intrahouseholdreturntotheireducation. Itispreciselythatadditionaltermthatourapproachallowstoevaluate. 1

supportedbythesubstantialimprovementsinhouseholdandbirthcontroltechnology, aswellasbythechangingrolesofwomenwithinthehousehold.Still,itishardto proveempirically(seeGreenwoodetal,2004).Incontrasttothereturnstoschooling inthemarketthatcanbeestimatedfromobservedwagesdata,thereturnstoschooling withinmarriagearenotdirectlyobservedandcanonlybeinferredindirectlyfromthe marriagepatternsofindividualswithdifferentlevelsofschooling. Inthispaper,weprovidesuchestimates.Ourempiricalapproachisbasedona structuralmodelofmatchingonthemarriagemarketthatisclose,inspirit,tothat adoptedbyChiapporietal.(2009).Specifically,weconsiderafrictionlessmatching frameworkalaBecker-Shapley-Shubik,inwhichthegaingeneratedbythematchof maleiandfemalejisthesumofasystematiceffect,thatonlydependsonthespouses’ educationclasses,andamatch-specifictermthatwetreatasrandom.Ourcrucial identifyingassumption,similartothatinChooandSiow(2006),isthatthelatter termisadditivelyseparableintoamale-specificandafemale-specificcomponents.A naturalinterpretationisthatthecomplementaritypropertiesofthemodel,whichdrive theassortativenessofthestablematching,operateonlybetweenclasses,andarenot affectedbytheunobservablevariables.Whileundoubtedlyrestrictive,thisassumption allowsustofocusonourmaintopicofinterest,namelymatchingbetweeneducation classes;inthatsense,ourmodelisessentiallymotivatedbyaconcernforparsimony. Moreover,ourseparabilityassumptiongeneratestestablerestrictionsthatthedata markedlyfailstoreject. 2 Underthisseparabilityassumption,wederiveasetofnecessaryandsufficientcon- ditionsforstability,andshowthattheseconditionscanbeinterpretedintermsofa standard,discretechoiceframework.Wethendiscusstheidentifiabilityofourtheoret- icalsetup.Inacross-sectionalcontext,thesimplestversion,whichreliesonastrong homoskedasticityassumptions,isexactlyidentified;sothatwecannotidentifyany patternofheteroskedasticity.If,however,thesamestructure(assummarizedbythe matrixofeconomicgainsbyspouses’educationclasses)isobservedforsubpopulations withdifferentcompositions,thenthebasicmodelis(vastly)overidentified.Infact, onecanidentifyamoregeneralstructure,inwhichthesystematiccomponentofthe surplusinvolvesclass-specifictemporaldrifts;moreover,thisgeneralizedmodelstill generatesstrongoveridentificationrestrictions. 3 WeapplyourmodeltotheUSpopulation,forcohortsbornbetween1935and1975 andmarriedbetweenages18and35.Weshowthatthereturnsfromschoolingreceived withinmarriage(the“maritaleducationpremium”)haveincreasedsharplyforwomen overtheperiod,whiletheyhavenotchangedmuchformen.Educatedwomenhave gainedrelativetouneducatedwomenintwoways:bymarryingathigherratesandby receivingahighershareofthemaritalsurplus.Wealsofindthatthegainsgenerated bymarriageswithequallyeducatedpartnershavedeclinedforalltypesofmarriage, 2 Whilethefrictionlessnatureofourmodelwouldbeastrongassumptioninmanycontexts,webelieve thatitisprobablymoreacceptableinourframework,preciselybecauseoftheseparabilityassumption.In ourseparableworld,theabsenceoffrictionsonlymeansthatanyagentcanmeetatleastonepotential matefromeachoftheeducationclassesunderconsiderationat(almost)nocost. 3 Weshowthatanevenmoregeneralstructure,inwhichthescaleofindividualheterogeneitymayvary byeducationclass,couldalsobeidentified.Inpractice,however,theassumptionofidenticalhomogeneity isnotrejectedbythedata. 2

reflectingthegeneralreductioninmarriageovertime.However,thesmallestdecline isinmatcheswhenoneorbothpartnershavecollegeeducation.Thisfindingcanbe relatedtoempiricalworkshowingthatsuchmarriagesarealsolesslikelytobreak(see WeissandWillis1997andBruze,SvarerandWeiss2010). Theevolutionofassortativematching Arelatedissueiswhathappenedto assortativemating.Theobservedpatternsarequitecomplex.Overall,thepercentage ofcouplesinwhichbothspouseshaveacollegedegreehassignificantlyincreasedover theperiod;however,aswomenwithcollegedegreebecamemoreabundant,thepropor- tionofeducatedwomenwhomarryeducatedmenhasdeclined(becausesomeeducated womenhadtomarrydownwardswithlesseducatedmen),whilemenwithhighschool degreeshiftedupwardsfrommarryingwomenwithhighschooldegreetomarrying moreoftenwomenwithcollegedegree.Allinall,manyobservershavenevertheless concludedthatassortativematchingwasstrongernowthanfourdecadesago,andthat thisevolutionhadadeepimpactonintrahouseholdinequality(seeforinstanceBurtless 1999). Anoldquestioniswhetherthisphenomenonisentirelyduetothemechanicalef- fectoftheincreaseinfemaleeducation,orwhetheritalsoreflectsashiftinpreferences towardsassortativematching(aswouldbethecase,forinstance,iftheshareofpub- licgoodsinhouseholdsriseswithtime-orincome-andsimilareducationfacilitates agreementsonthecompositionandlevelofthesepublicgoods).Animportantad- vantageofourstructuralapproachisthatitallowstoformallydisentanglethetwo aspects.Inthisrespect,ourconclusionsareclear-cut.Wedonotfindanyevidencefor achangeinpreferencesforassortativematching.Infact,wedonotrejectthenullthat theinteractioninmaritalgainsbylevelofschooling(assummarizedbythesupermod- ularityofthematrixofsystematicgains)hasremainedstableovertime.Totheextent thatwefindanincreasingproportionofcouplesinwhichbothpartnersareeducated, thisisnotbecausethegainsfromhavingacollegedegreeforbothpartners(compared withonlyonepartnerhavingacollegedegree)haverisenovertime.Wefindstrong evidencethatforeducatedwomen,theadditivegainsfrommarriagehaveshiftedover time.Onepossibleinterpretationisthatitbecamelesscostlyforeducatedwomento marrymainlybecausehouseholdchoreshavebeenreduced,sothatmarriedwomencan participatemoreinthelabormarket(seeGreenwood,SeshadriandYorukoglu2005), andalsobecausebirthcontroltechnologieshavedrasticallyimprovedovertheperiod, allowingforbetterplanningoffamilyfertility(seeMichael,2000,andGoldinandKatz 2002).However,ourfindingssuggestthatthese”liberatingeffects”aremoreorless independentoftheschoolingofthehusband.Asaby-productofourinvestigation, wecanidentifythematrixofsystematicgains;wefindthatitis,indeed,significantly supermodular. Thisfindingseemstocontradictresultsinthesociologicalliteraturethathave shown,usingloglinearmodels,thatevenafteraccountingforchangesintherelative numberofmenandwomenineachskillgroup,homogamyhasincreasedintheUS andseveralothercountries(seeMare,1991,2008).However,theseconclusionswere drawnfromreduced-formmodelswithnodirecteconomicinterpretation.Weshow, inparticular,thefollowingresult.Assumewetakeourstructuralframeworkunder theassumptionthattheforcesdrivingassortativematching(i.e.,thematrixofmarital 3

gainsbyeducationclasses)remainconstant,andweuseittogeneratemarriagedata. Ifthelog-linearregressionadoptedinthesociologicalliteraturewereappliedtosuch data,theywould(spuriously)concludethatpreferencesforhomogamyhavechanged. Thesefindingsfurtheroutlinetheimportanceofastructuralapproachtoguidethe interpretationoftheempiricalresults. Finally,anotheroutcomeofourstructuralapproachistheidentificationofthe groupspecific“prices”thatdeterminethedivisionofthegainsfrommarriagebetween husbandsandwivesofdifferenttypes.Wefindthatincouplesinwhichbothspouses haveacollegedegree,theshareofthewifeinthegainsfrommarriagehasincreased overtime,despitetheriseinthenumberofeducatedwomenrelativetoeducatedmen. Thishappenedbecausethemarginalcontributionofeducatedwomentothesurplus witheducatedmenhasrisenovertime.Wefindthattheincreaseismainlyduetothe variablecomponent:educatedwomenbecamemoreproductiverelativetolesseducated womeninallmarriages,irrespectiveofthetypeofthehusband.Thisfindingconfirms theanalysisofChiapporietal.(2009),accordingtowhichtheincreaseinthemarital componentoftheeducationpremiumforwomencouldexplainthespectacularincrease infemaledemandforhighereducation. Relatedliterature Theanalysisofthemarriagemarketasamatchingprocess, whichdatesbacktoBecker’sseminalcontributions(seeBecker1981),hasrecently attractedrenewedattention.Probablythemostimportantempiricalworkisdueto ChooandSiow(2006),whoproposeoneofthefirstimplementationsofaBecker- Shapley-Shubikmodelbasedonadiscretechoicemodel.Ourpaperextendstheir contributioninthreedirections.First,weclarifytheunderlyingtheoreticalstructure, inparticularbyworkingouttheassumptionsneededonthefundamentalsofthemodel (i.e.,thematrixofsystematicgain)andtheirimplicationsfortheendogenousvariables (individualutilitiesatthestablematch).Secondly,weconsideramodelthatallows forinterclassheteroskedasticityoftherandomcomponents.Thirdly,westudythe evolutionofmatchingpatternsthroughouttime,inaframeworkthatalsoallowsthe gainsformarriagetoevolveinaclass-specificway.Ourultimategoalistostudy matchingoneducation,andmorespecificallytoprovideadynamicperspectiveonthe evolutionofthecorrespondingpatternsoverseveraldecades. Thesevariousextensionsarenecessaryforourpurpose.Evaluatinghowthe‘mar- italcollegepremium’evolvesovertimeobviouslynecessitatesadynamicanalysis.It alsorequirescomparing(expected)utilitiesbetweenclasses,ataskforwhichtheho- moskedasticityassumptionofthestandardversionispotentiallyinappropriate.In ChooandSiow’sapproach,thebasic,homoskedasticversionisexactlyidentified,im- plyingthatanygeneralizationwillfacesevereidentifiabilityproblems.Weshowthat theseproblemscanhoweverbeovercomeinamoredynamiccontext,providedthat thestructuresdrivingassortativematchingremainsconstant.Inparticular,ouriden- tificationstrategyisoriginal. AnotherrelatedapproachisduetoGalichonandSalanie´(2010),whoprovidea theoreticalandeconometricanalysisofmulticriterionmatchingunderthesamesepa- rabilityassumption.Theirfocusisdifferent:whileourpaperconsidersasmallnumber ofclasses,theyseektoprovideageneralmethodtoestimateandtestflexibleparamet- ricspecificationsofthegainsfrommarriagewhenmanycovariatesareavailable. 4