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ECONOMIC RESEARCH REPORTS
C.V. STARR CENTERFOR APPLIED ECONOMICS
NEW YORK UNIVERSITYFACULTY OF ARTS AND SCIENCE
DEPARTMENT OF ECONOMICSWASHINGTON SQUARE
NEW YORK, NY 10003-6687
Cultural Transmission, Marriage andthe Evolution of Ethnic
and
Religious Traits
by Alberto Bisinand
Thierry Verdier
RR# 98-40 November 1998
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CulturalTransmission, M
arriageandtheEvolutionofEthnicandReligiousTraits
A lbertoB isinN Y U
T hierryVerdierCER A S, D EL T A , CEPR
N ovember19 9 8¤
A bstract
T
hispaperpresentsaneconomicanalysisoftheevolutionofreligiousandethniccharacteristicsinamodelofintergenerationaltransmissionofculturaltraitswhichoccursthroughfamilysocializationandmaritalsegregationdecisions.
T hemodelimpliesthatthefrequencyofintragroupmarriage(homogamy),
aswellasthesocializationratesofreligiousandethnicgroups,
dependsonthegroup’sshareofthepopulation;minoritygroups
searchmoreintenselyforhomogamousmates,
andspendmoreresourcestosocializetheiro¤spring.
W
estudytheimplicationsofthemodelregardingthee¤ectofthesocialmatch-ingtechnology,
divorceratesandthedegreeofculturaltolerancebetweengroupsontheevolutionofculturaltraits.
Existingempiricalevidencebearingdirectlyandindirectlyontheimplicationsofthemodelisdiscussed.
Keywords: CulturalTransmission, M arriageJEL : I2, Z 1, D 9
¤T hanks totworeferees and to A . Shleifer, whorecommended this
cutfora paperon culturaltransmission, and to G . B ecker, J. B
enhabib, L . Iannaccone, A . L izzeri, S. R osen, A . Schotter, G
.Topaforcommentsandencouragement. T hanksalsotoA .CasagrandeandJ. G
oldbergforassistance.T he…nancialand institutionalsupportoftheC. V
. StarrCenterforA ppliedEconomics is gratefullyacknowledged.
1
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1 IntroductionH
istorycontainsseveralexamplesofthestrikingpersistenceofethnicandreligioustraits.Basques,
Catalans, Corsicans, IrishCatholics, inEurope, andQ
uebecoisinCanada, haveallremainedstronglyattachedtotheirlanguages
andculturaltraits
eventhroughtheformationofpoliticalstateswhichdidnotrecognizetheirethnicandreligiousdiversity.Jewsofthediasporahavemaintainedatenaciousreligiousandethnicidentityresistingmanyattemptsatacculturationandevenextermination.
M anysmallethnicandreligiousenclaves arehighlyresilient.
Forexample, smallcommunities ofO rthodoxChristianA lbanians
livingin thesouthofItalysincetheyemigratedthere inthe15th
century,maintainedtheirlanguageandreligiousfaith. Similarly,
smallwhitecommunitiesintheFrenchCaribbeanislands, ‘B lancs M
atignons’, preservethemselves from
racialmixing,andhavedonesosincethe18thcentury. L
ong-liveddivisionsalongculturalandtriballinesarestillcommonplaceinmodernA
frica(M cEvedy, 19 9 6).
T heseandthemanyotherexamples ofthepersistenceofculturaltraits
inhistoryshouldobviouslynotbeinterpretedasevidencethatculturaltraitsarenecessarilymain-tainedagainstallodds.
T herapidassimilationofJewsinItalyisaclearcounter-example(D
ellaPergola, 19 7 2). B
utthepersistenceofculturaltraitsandthedi¢cultyofaccul-turatingminoritiesdoesoftentakesociologistsandanthropologistswhostudyculturalevolution
by surprise. Forinstance, mostsociologicalworkon A merican Jews in
the50s and60s predictedthe‘extinction’ofJewishO rthodoxy,
therebyfailingtoidentifytheroots ofthedemographic‘R
enaissance’thatO rthodoxJewishculture in theU .S.has been
experiencingsince the 7 0s (M ayer, 19 7 9 , Ch. 1). M ore
generally, ClaudeL evi Strauss (19 9 7 ) has
recentlyobservedthattherisks
ofculturalassimilationhavebeenmuchover-statedintheanthropologicalandsociologicaldebateofthe50s,
becausecultureshavedemonstrateda‘veryresilientstrongcore’. 1
T
hepersistenceoftheevolutionofethnicandreligioustraitsismirroredinhighandpersistentintragroup
marriage (homogamy) rates, even forsmallethnicand religiousgroups.
Forinstance, ethnicintermarriagewasvirtuallyunknowntoimmigrants
intheU .S.attheturnofthecentury. Pagnini-M organ(19 9 0),
forinstanceestimatethatItalianandPolishimmigrantsaroundthebeginningofthecenturyintheU
.S.weremorethan2 ;0 0 0 timesmorelikelytomarryintheirethnicgroup
thantointer-marry. T
heyalsonotelowlevelsofinter-marriagepersistinginsecondandthirdgenerationimmigrants.R
eligioushomogamyisalsoverywelldocumentedformostreligiousgroups(e.g.,
Sander,
1W ecan even readthepoliticaldebateon assimilation in theU nited
States as areaction
tothepersistenceofculturaltraitsdespitethee¤ortsoftheassimilationandA
mericanizationmovementborninthebeginningofthecenturytoincludeimmigrants,
ando¤eroffullparticipation.
Facinggrowingresistancetoassimilation(religiouslyandevenlinguisticallysegregatedparochialschools,
forinstance,spread inthis period;seeTyack, 19 7 4), bythe 20 s
themovementturned intoan
increasinglyhostiledemandforimmigrants’acculturationtotheEnglishlanguageandA
mericanculture(seeD avis, 19
20,foraselectionofearlyreadingsonassimilation). T
heheateddebateovermulti-culturaleducationhascontinuedandhasrecentlytakenaradicalturn;seeG
lazer(19 9 7 ).
2
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19 9 3, forCatholics, andJohnson, 19 80, Schoen-W einick, 19 9
3,
forotherdenominations).InSection2wereportinsomedetailontwoethnographicexamplesofpopulationswhichadoptextremestrategiesofmarriagesegregationtopreservespeci…cculturaltraitsandtosocializechildren:
aristocrats inFranceandO rthodoxJewsinN ewYork.
T hehistoricalexamples and
evidenceofculturalpersistenceandhomogamyraiseimportantquestions
regardingculturaltraits, particularly ethnicand religious
traits,theirdeterminants
intheshortrunandtheirlongrundistributioninthepopulation.
T
hispaperstudiestheevolutionandpersistenceofculturaltraitsasdynamicproper-tiesofculturaltransmissionandsocializationmechanisms.
Inparticular, weconcentrateon segregation bymarriagealongethnicand
religious lines as amechanism
tofavorsocializationatthefamilylevel.2
T hemodelofsocializationwedevelop and study is motivated
byvarious stylizedfacts which emergefrom thesociologicalliterature
(seethenextsection). W emodelculturaltransmission as amechanism
which interacts socialization inside the
familyandsocializationoutsidethefamilyinsocietyatlargeviaimitationandlearningfrompeers
and rolemodels. In themodel, altruism motivates parents’e¤orts
tosocializetheirchildren, andtotransmittheirownculturaltraits.
(Socializatione¤ortconsists,forinstance, inthechoiceofneighborhood,
school, orchurchattendance.) Families inwhich parents
haveahomogeneous culturaltraitareadvantaged in the
socializationprocess forthis trait, withrespecttoheterogamous
families. Sinceeachparentwishestotransferhis owntraittohis
children, thechoiceofamateinthemarriagemarketis
functionaltothedesiretosocializetheeventualchildrenarisingfrom
suchaunion.W
hilethenperfectassortativematching(completehomogamy)wouldariseoptimallyintheabsenceofsearchcosts,
wemodelthemarriageprocess as characterizedbysearchfrictions. M
orespeci…cally,
weassumethatbothmalesandfemalescansearchforamateinsomerestrictedpoolwhereadmissioniscostly,
butwhereeverybodywhoisadmittedhasthesameculturaltrait(henceallmarriages
inthepoolarehomogamous).
W ederiveimplicationsofsuchculturaltransmissionmechanisms
intermsofdi¤er-entialbehaviorofculturalminoritiesandmajoritieswithrespecttotheire¤orttomarryhomogamouslyandtosocializechildrentotheirowntrait.
W ealsostudythedynam-icsofthedistributionofculturaltraits
inthepopulationimpliedbysuchtransmissionmechanisms,
andthedeterminantsofthelongrunstabledistributionoftraits,
withtheobjectiveofunderstandingtheobservedpersistenceofminorityculturaltraits.
Someoftheresultsandtheintuitionbehindthemaresummarizedbelow.
2Culturaltransmission, butwith random matingand exogenous
propensities forsocialization, isstudied in biology;seee.g.,
Cavalli Sforza-Feldman (19 81). T heroleofmarriageas an
institutionoftransmission ofculturalvalues has been stressed in
anthropology, forinstance by Boas (19 28) andL evi Strauss (19 49
). Economists havemostlyconcentrated
insteadontheagents’choiceoftheirownpreferences andvalues, as e.g.,
B ecker(19 9 6), B ecker-M ulligan (19 9 7 ), and, speci…cally
forreligiouspreferences, Iannaccone(19 9 0, 19 9 8) .
Forgeneticrathenthanculturaltransmissionmodels, seee.g.,Kockesen-O
k-Sethi (19 9 7 ). W erefertoBowles(19 9 8)
forasurveyandcompletereferences.
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M inorities, otherthings equal,
havemorehighlysegregatedmarriagemarkets,
andexercisemoree¤ortindirectlysocializingtheirchildren. T heyhave,
infact, astrongerincentivetosegregate, tobe homogamous and
tosocialize theirchildren. Sincethepopulation atlarge is mostly
populated bymajority types, amemberofaminorityculturalgroup is
likelytomarryheterogamouslyifhedoes notstructurehis
lifesoastomeetmostlymates withthesametraits (e.g.,
bygoingtotheappropriatechurch,livingintherightneighborhood, etc.).
M oreover,
aminoritytypeinanheterogamousmarriagewillhavedi¢cultytransmittinghis
owntraits, sincethespousewillfavoradi¤erentsetoftraits,
andpeersandrolemodelswillbetakenfromapopulationmostlyofthemajoritytypes.
Patterns ofmaritalsegregations and socializationacross
culturalgroups
alsohavee¤ectsontheevolutionofculturaltraitsinsociety. W
eshowthattheculturaltransmis-sionmechanismswestudygeneratedynamicsinthedistributionofculturaltraitswhichtendtomulticulturalpopulations
andawayfrom
completeassimilationofminorities.Culturalminoritiestendtoreactinequilibriumtotheprospectofculturalassimilationwithmarriage
segregation, homogamous marriages, andwith more intense
strategiesforthedirectsocializationofchildren. T houghmajorities
havehigherhomogamyandsocializationrates overall, itis
thesocialization e¤ort(which is
higherforminorities)todeterminethetransitionaldynamics
ofthedistribution oftraits whenonetraitisclosetoextinction. A s
aconsequence, the fraction ofthepopulation ofagents
withminoritytraits tends toincrease,
minoritytraitsappearquitepersistent,
andlong-runmulticulturalpopulationsarestable.
Inotherwords, linearextrapolationsofinter-marriagerates,
socializationpractices,anddemographicdynamics,
tendtounderestimatethepersistenceofculturaltraits,
be-causeminoritiesreacttotheirassimilation. T
heresilienceofmanyethnicandreligiousneighborhoodsinA mericancities,
theincreasingdemandformulticulturaleducationinA merican society,
aswellas inmanyW esternEuropeancountries,
andthehistoryofmanyculturalcommunitiessuchas A mericanO
rthodoxJewscanhoweverbeexplainedbythecomplexinteractionofmarriagesegregation,
directculturalsocializationoffam-ilies,
andchildren’sexposuretotheculturaltraitsofthemajorityofthepopulationatlarge.
O urmodelofculturaltransmissionalsoallows us
tostudythedynamice¤ects
onthecompositionofthepopulationwithrespecttoethnicandreligioustraitsofvariousinstitutionalarrangementswithinmarriage.
Inparticularwestudythelong-rune¤ectsinthedynamicsduetostructuralchangesi)
intheavailabilityofinter-culturalrelationships(due
forinstancetourbanization orinformation technologies), ii) in the
freedom tochooseones’mate, andiii)
intheorganizationofthefamily(divorcerates, singleparentfamilies,
femalelabormarketparticipation).
W
eshowthatifthedistributionofthepopulationwithrespecttotheculturaltraitsissuchthatamajorityandaminoritytraitareidenti…able,
thenahigheravailabilityof
4
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interculturalrelationships causes agents toreactwithhighere¤orts
atmarriagesegre-gationandsocializationofchildren. A
negativedirecte¤ectviarandommatchingandapositiveindirecte¤ectduetotheincreaseinthee¤orttomarryhomogamouslyandsocializecountereachotherina¤ectinghomogamyrates.
T hedirecte¤ectonhomogamyratestendstobestronger, andhence,
homogamydecreaseswitheasierinterculturalre-lationships. A
sthehomogamyratesdecrease,
theprobabilityofhomogamousmarriagesdecreases
forbothgroupsbutlessrapidlyforthemajoritygroupthanfortheminoritygroup.
A saconsequence, easierinter-culturalrelationshipsincrease,
inthelong-run, thefractionofthepopulationwiththemajoritytrait.
G reaterfreedom tochooseones’mate,
arguablyarelativelyrecenthistoricaltrendinmanyculturalpopulations,
has similare¤ects. B y increasingthecosts ofmarriagesegregation,
segregatione¤ortandhomogamyrates aredecreased. G reaterfreedom
ofmatingchoiceincreases, inthelong-run,
thefractionofthepopulationwiththemajoritytrait.
W
ealsoshowthatahigherprobabilityofdivorcereducesatthemarginthevalueofhomogamousmarriage,
therebydecreasinghomogamyrates inequilibrium.
Theproba-bilityofdivorcereducestheresources
spenttosegregateinmarriageandhencebringsmoreheterogamyintheshortrun.
A s
inthecaseofeasierinterculturalrelationships,theprobabilityofhomogamousmarriagesdecreasesforbothgroupsbutlessrapidlyforthemajoritygroupthanfortheminoritygroup.
H igherprobabilitiesofdivorcetendtoincrease, inthelong-run,
thefractionofthepopulationwiththemajoritytrait.
Similarly, changes in levels oftolerancebetween culturalgroups
a¤ecthomogamyratesandthepersistenceofculturalminorities.
Inparticular,
anincreaseinculturaltol-erancebetweentwogroupsinduceslessmaritalsegregationandlessfamilysocializationin
theshort-runtendingtobias culturalevolution, inthelong-run, towards
thetraitofthemajoritygroup in society. (G
reatertoleranceonthepartofthemajoritywithrespecttointermarriagewithminoritypopulationsgeneratesaformofacculturationoftheminority.)3
T hepaperisorganizedasfollows. First, inSection2.1,
weintroducevariousstylizedfactsonculturaltransmissionandsocializationwhichmotivateourmodelling.
InSection2.2
weanalyzetheimplicationsofthebasicmodelofmarriageandculturaltransmission,providesomeextensions,
andperformsomecomparativestatics. Section2.3.
introducessomeempiricalevidenceonhomogamy, socializationpractices,
andsegregationanddi-vorce,
o¤eringsupportfortheimplicationsofourmodelwithrespecttothetransmissionofethnicandreligioustraits.
Finally, Section3studiesthedynamicsofthedistributionoftraits
inthepopulationandderivesseveralcomparativedynamicimplications.
3T hegreatertoleranceofintermarriagewithJewsafterW orldW arII
intheU .S.mightbethecauseofthetrendtowardacculturationofJews,
asnotedbyseveralcontributorsinthecurrentdebateonthe‘Jewishidentity’intheU
.S.;seeD ershowitz (19 9 7 ).
5
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2 M
arriageandsocializationVariousstylizedfactsonmarriagesasculturaltransmissionmechanismscanbecollectedfromananalysisoftheempiricalliteratureinsociologyandsocialpsychology.
1. Culturaltraits are usually adopted in the early formative
years ofchildren’spsychology. Family,
peersandrolemodelsplayacrucialroleintheadoptionofculturaltraits. T
hishasbeenextensivelydocumentedforreligiousandethnictraits,
forinstance,byClark-W orthington(19 8 7 ), Cornwall(19 88), D
eVaus(19 83), Erickson(19 9 2), H ayes-P ittelkow(19 9 3).4
2.
Familiescareabouttheirchildren’sculturaltraitsandconsciouslyexercisee¤ortinanattempttosocializechildren.
A lso, homogamous families (i.e., families
inwhichparentshavehomogeneousculturaltraits)predominantlyfavorthetransmissionoftheirowntraits.
Psychologicalstudiesofheterogamouscouplesconsistentlyreporttheircon-cernaboutthepossibleculturalattitudes
ofchildrenwhendecidingtoform afamily(seeR osenblattetal., 19 9 5,
forracialtraits, andM ayer, 19 85, Smith, 19 9 6,
forethnicandreligioustraits). G ussinPaley(19 9 5)
providesavividethnographicdocumentationofschoolchoiceofmiddle-class
A frican-A mericanparentsinChicago’sSouthSide. T
hemainissueinthechoiceconsists intradingo¤
thelowacademicqualityofthepredom-inantlyblackpublicschools
andtheexposureto‘whiteculture’in integratedschools.O ’B
rien-Fugita(19 9 1)
documenttheperceivedimportanceforJapanesefamiliesofthedevelopmentofJapaneseschoolsafterW
orldW arII intheU .S.
(oftencontrarytothepreferencesoftheirchildren).
Similarattitudesaredocumentedformanyethnicgroups(e.g., M ayer, 19
85, forJews, andTyack, 19 7 4, forG ermans, and, morerecently, G
lazer,19 9 7 , forA frican-A mericans).
3. T he e¤ectiveness offamily socialization depends stronglyon
parentalagree-mentonthetraittobetransmitted.
Childrenofmixedreligiousmarriageshaveweakerreligiouscommitments
thanthoseofreligiouslyhomogamousmarriages (H oge-Petrillo,19 7 8),
andO zorak, 19 89 ). A lso,
childrenofmixedreligiousmarriagesareless
likelytoconformtoanyparentalreligiousideologies,
andtopracticessuchaschurchattendance,orprescribedfertilitybehavior(H
eaton, 19 86, H oge-Petrillo-Smith, 19 82, andO zorak,19 89 ).
T hesefacts motivateourmodelofsocialization. In particular,
wemodelculturaltransmissionasamechanismwhichinteractssocializationinsidethefamilywithsocial-izationoutsidethefamily,
insocietyatlarge.
(Socializationinsidethefamilyisalsocalled‘directvertical’socialization,
whilesocializationbysociety, whichoccurs
viaimitationandlearningfrompeersandrolemodels,
isalsocalled‘oblique’socialization.)5
4T hetransmission oftraitswhich areformedlaterin
thepsychologicaldevelopementofchildren,though,
isoftendominatedbytheroleofpeers;seee.g., East-Felice-M organ(19 9
3) forevidenceonthetransmissionofattitudestowardsexualbehavior.
5T histerminologyistakenfromCavalli Sforza-Feldman(19 81).
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W emodeldirectverticalsocialization through parents
havingaltruisticattitudestowards theirchildren. A ltruism motivates
parents toexerte¤ortto socialize theirchildren,
andtotransmittheirownculturaltraits. A
nimportantassumptionwemakeinthisrespectisthatparentswishtotransmittheirowntrait,
anddonotjustinternalizetheirchildren’spreferencesorsomemeasureoftheirsuccess.
Indirectevidenceforsuch‘paternalisticaltruism’comes, as
alreadynoted, from studies ofparentalschoolchoicedecisions. A lso,
an analysis ofnorms regardinginter-religious marriages reveals
thatparents ofmostmajordenominations (from Catholics toBaptists
andJews;butalsoforinstanceSeventh-D ayA dventistsandL utherans)
atleasttendtowarnchildrennottointer-marry,
justifyingtheirpositionwith aconcern aboutthereligious
educationofgrand-children(Smith, 19 9 6)6.
Someevidenceinsupportof‘paternalisticaltruism’canalsobederivedfrom
socio-economicsurveys. Forinstance, inresponsetoN O RC’sG
eneralSocialSurvey’squestion, ‘W
hichthreeofthequalitieslistedwouldyousayarethemostdesirableforachildtohave?’,
‘obedience’iscitedonaverageacrossthesamplemorethan, (inorder)
‘self-control’, ‘success’, ‘studiousness’, ‘cleanliness’,
andlessonlythan‘honesty’.7 8
T hisassumptionofparents’paternalisticattitudes is
consistentwithourmodellingofculturaltraitsas‘pure’traits,
withnodirecteconomice¤ect. Forinstance,
weimplic-itlyassumethatagents’economicopportunities, e.g.,
theirexpectedpresentdiscountedincomeortheirhumancapitalaccumulationcosts,
areindependentoftheirtrait. T hisis, ofcourse,
anabstractionmeanttodisentangletheculturaltransmissionmechanismfromothereconomicconsiderations.
Ethnicandreligioustraits, morethanotherculturaltraitsandattitudes,
seemtoapproximatesatisfactorily‘pure’traits.9
W e…nallyassumethatfamilies
inwhichparentshaveahomogeneousculturaltraitareadvantagedinthesocializationprocessforthistrait,
withrespecttoheterogamousfamilies. Sinceeachparentwishes
totransferhis owntraittohis children, thechoiceofamate in
themarriagemarketis
functionaltothedesiretosocializetheeventualchildrenfromsuchaunion.
W
hileassortativematchingwouldarisethenatequilibriumintheabsenceofsearchcosts
(seeBecker, 19 7 3, 19 7 4), wemodelthemarriageprocess
6Forexample, the19 83 CodeofCanonlawfortheCatholicChurch says: ”
W ithouttheexpresspermission ofthecompetentauthority, marriage is
forbidden between twobaptized persons, one
ofwhomwasbaptizedintheCatholicChurch...andtheotherofwhomisamemberofaChurch...
whichisnotinfullcommunionwiththeCatholicChurch” (801). M oreover,
thepermissioncannotbegrantedunless thefollowingcondition is
full…lled: ”theCatholicpartydeclares thatheorsheis
preparedtoremovedangersoffallingawayfromthefaithandmakesasincerepromisetodoallinhisorherpowertohaveallchildrenbaptizedandbroughtup
intheCatholicChurch”.
7 A similarpatternofanswers is reportedtoasimilarquestion inthe
N ationalSurveyofFamiliesandH ouseholds.
8Foranaturalselectionexplanationofpaternalisticformsofaltruism,
seeB isin-Verdier(19 9 8).9 H owever, someevidenceon
thee¤ectofreligious and ethnictraits oneconomicopportunities is
found in W arren (19 7 0) and Sowell(19 9 4). A …rstanalysis
ofthesee¤ects oftraits canbefound inB isin-Verdier(19 96).
7
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ascharacterizedbysearchfrictions. M orespeci…cally,
weassumethatwhilebothmalesandfemalescansearchforamateinsomerestrictedpoolwhereeveryoneadmittedhasthesameculturaltrait(henceallmarriages
inthepoolarehomogamous), admissiontothepooliscostly. (W
ethinkofdirectadmissioncosts, butalsoofthecosts
intermsofotherunmodelleddesirablecharacteristicsofthematch,
whichderivefromconstrainingoneselftosearchinarestrictedpool.)
M
anydi¤erentinstitutionsdofunctionatleastpartiallyasmarriagepoolsrestrictedalongculturaltraits.
ForinstanceKwon (19 9 7 ) documents
thecentralityoftheKo-reanEthnicChurchinH oustonasamechanism
forculturalidentityandasanetworkofcontacts
among…rstandsecondimmigrationKoreanimmigrants. A
similarpictureregardinglocalcatholicchurches isdrawnbyM atovina(19
9 5) fortheSpanish-speakingpopulationinSanA ntonio, Texas,
between1821 to1860. Tobetterillustrateouranaly-sis
ofthemarriageprocess as amechanism fortransmissionofculturaltraits,
and
inparticulartoisolatetheinstitutionswhichmayfunctionasrestrictedmarriagepools,
weconsidertwoexamplesofpopulationswithratherextremesocializationpractices:
aris-tocratsinFranceandO rthodoxJews inN ewYork.The Bottin M ondain
andtheRallye. Various ethnographicstudies ofaristocrats
haverevealedthe importanceoftheirattachmenttospeci…cculturalvalues
andtheircon-cernfortheinter-generationaltransmissionoftheirsymbolicandculturalcapitalsuchas
familynames, negativeattitudes towardsworkandmoney, andthe
importanceoflandproperty(G range(19 9 6), M ension-R igau(19 9 3),
P incon-P inconCharlot(19 8 9 ), deSaintM artin(19 9 3)).
B
uthowarethesevaluestransmitted?InFrancethemostrelevantinstitutionswiththispurposearetheBottinM
ondain, themainaristocracy’slistingbook, andtheR
allye,achainofdancingparties(G range, 19 9 6).
Families
canbelistedintheBottinonlyifinvitedbyfamiliesalreadylisted. M
ostinformationpublishedintheBottin M undain
isfamilyanddynasticoriented, andpro-fessionalindications
arekepttoastrictminimum. 10 T heR allye, whichorganizes
agatheringofbetween100 and500 youngpeopleeachmonth, consists
insteadofagroupofyoungsinglewomen, whosefamilies arelisted
intheBottin M ondain. T hefamilyofeachwoman, when subscribingtotheR
allye, commits tohostapartyforalltheparticipantsoftheR allye.
A longwiththeBottin M ondain, theRallye is thereforean
institution intendedtostimulatehomogamousaristocraticmating.
Itinvolvessubstantialresourcesspentbythedi¤erentfamilies(partiesaregenerallyorganizedinsumptuouspalaces),
andwellre‡ectsourvisionofarestrictedpoolinwhichresourcesarespenttoincreasetheprobabilityofbeingmarriedhomogamouslywithrespecttotherelevantculturaltrait.
Fromasurveyof39 14nuclearfamiliesintheBottinM
ondainduringtheperiod19 03-10D
atesofbirtharenotmentionedexceptforminorchildren,
whichisusefulifthebookistobeused
asamarriagepool.
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19 8 7 , A rrondel-G range(19 9 3)
estimatetheprobabilityofhomogamousmarriageforachildofafamilyintheBottinM
ondain. T
hey…ndasigni…cantrateofhomogamywellabovethatimpliedbyrandommatching.
T heaverageprobabilityofbeingmarriedwithsomeoneoftheBottinM
ondainforadaughterofacouplelistedintheBottinis44% (intheperiod19
50-19 69 ) and39 % (intheperiod19 7 0-19 83).
Foryoungmalestheaverageestimatedprobabilityineitherperiods is 39 %
. W henthetwoparents shareimportantaristocraticattributes (e.g.,
oldaristocracy, afamilycastle, ormembership inanaris-tocraticclub),
this probabilityis over65% foryoungfemales, andover80%
foryoungmales.TheShadchan. O rthodoxJews
liveinmostlysegregatedneighborhoodsandadheretoveryextremenormstopreservetheirreligiousandculturaltraits(seetheethnographicstudiesofH
eilman, 19 9 5, andM ayer, 19 7 9 ).
Inareligiouscommunitywhosevariouspro-scriptionslimitcasualencounterbetweenthesexes,
manymarriagesarearranged. T heethnographicstudyofO rthodoxJews
inBoroPark, anO rthodoxJewishneighborhoodinBrooklyn, N ewYork,
conductedbyM ayer(19 7 9 ) inthe 7 0s,
surveysmatch-makers(shadchans). T
hisstudyrevealsthatnotonlydoshadchans
serveasgo-betweens(‘tele-phonenumbers’distributors’),
butmostimportantlytheyalsoinform bothparties ofeachother’s
adherencetoreligious norms, prescriptions andproscriptions (e.g.,
aboutthedress codeofthewoman,
thetenureattherabbinicalseminaryoftheman, etc.).Essentially,
theroleoftheshadchan inguaranteeingthepreservationofreligious
andculturaltraitsinmarriageispreserved,
evenifitshistoricalroleinprotectingandmatch-ingfamilies’assetshaslostmuchofits
importanceandisnotanymoreanintegralpartofthetraditionalmarriagesystem.
A s importantasmatch-makingis (asarestrictedmarriagepool) inO
rthodoxJew-ishcommunities,
‘love-marriages’areslowlyreplacingarrangedones. N onetheless,
forinstanceinBoroPark, manyinstitutions,
fromkosherpizzaparlorsandcafeteriasofthehundredsoftheYeshivas
(religiousschools) intheneighborhood, toO rthodoxsummercamps,
andYoungM en’s& W omen’s H ebrewA ssociation’sco-edactivities,
operatetosubstitutetheshadchan
infacilitatingmatingbyreligiousandculturaltraits(seeagainM ayer, 19
7 9 ).
T he institutions ofarrangedmarriages,
segregatedlivingarrangements, segregatededucationinreligiousschool,
andthecreationofrestrictedmarriagepoolslikesummercamps, has been
exceptionally e¤ective in promotinghomogamy forO rthodox Jews.A
ccordingtothe N ationalJews Population Survey, theintermarriagerate
in 19 9 0 forO rthodox Jews was only3% , as opposed to37%
forConservative Jews and 53% forR eform Jews.
T
hepatternofhomogamyandsegregationobservedforFrencharistocratsandO
rtho-doxJews, whileextreme, iscertainlynotunique. B aker(19 7 9 ),
forinstance, documentssimilarratesofhomogamyforacommunityofU
pperSilesianfarmerslivinginsegregatedneighborhoodsaroundanethniccatholicparishinTexas,
from1850 to19 20. H omogamy
9
-
rates inthiscommunityarestillveryhigh, ataround50 % .
2.1 TheA nalysisSupposetherearetwopossibletypes, fa;bg,
ofculturaltraits in thepopulation. Inparticular,
di¤erenttraitsmightcapturesomeaspectofethnictraitsorreligiousbeliefs.
Ineachperiodtherearetwostationary,
equallysizedpopulationsofadultmalesandfemales. A gents
livetwoperiods. Youngagentsarebornwithoutwellde…nedculturaltraits,
whichtheyacquire(inawaydescribedbelow)beforebecomingadult.
Inhisadultlife,
amalegetsmatchedwithanadultfemale(inawaytobedescribedbelow)toformahousehold.
Inordertomaintainthesizeofeachpopulationstationary,
weassumethateachfamilyunionhastwochildren, amaleandafemale.
Parentsarealtruistictowardstheirchildrenandwanttosocializethemtotheirownspeci…cculturalmodel.
L etV
ijdenotetheutilityatypeiparentderivesfromatypejchild(i2fa;bg). W
eassumethenV ii> V ij(andV jj> V ji).11
T he socialization process is modelled as follows. T hefraction
ofindividuals withtraitiinthepopulationisdenotedqi. A
ll‘naive’children, withoutde…nedpreferencesorculturaltraits,
livinginafamilyinwhichbothparentshavethesametrait,
are…rstexposedtotheirfamilytrait, sayi. ‘D
irectvertical’socializationtotraitioccurswithprobability ¿i. W e
imposetheextremeassumption thatonly families inwhich
bothparentshavethesametraitcanverticallysocializetheirchildren.
Childreninfamilieswitha‘mixed’traitpickthetraitofarolemodelchosenatrandom
inthepopulation(i.e., they picktraitiwith probability qi and
traitjwith probability qj = 1 ¡qi).Similarly ifa child from afamily
with, say, traiti is notdirectly socialized, whichoccurswith
probability 1¡¿i, hepicks thetraitofarolemodelchosenrandomly
inthepopulation. Finally, socialization is costly. Socialization
costs increasewith
theprobabilityofsuccessfuldirectsocializationbyparents,
andaredenotedH (̄ ¿i), fori2fa;bg (̄
isjustaparameterwhichweshalluseinthecomparativestaticsexercises). T
hemarriagechoice, then,
hasacruciale¤ectonthesocializationtechnologyavailable, andagents,
choosingthebestmatetosocializechildren,
aspireforhomogamyinmarriage.
11SupposeagentschoosewhenadultsomeabstractactionxinsomesetX .
Childrenwithpreferencesoftypej, uj(x), thenwill, ingeneral,
makeadi¤erentchoicethanparentsoftypeiwould, andviceversa.A
ltruisticparentswillnecessarilypreferchildrenwiththeirowntypeofpreferences
whenevaluatingtheirchildren’schoiceswiththeirown(theparents’)
utilityfunction. Formally:
V ij=ui(xj); wherexj= argmaxx2X uj(x)
andhencetypicallyV ii > V ij (symmetricallyfortraitj). Itis
importanttonotice, though, thatifthechoicesetX
dependsonthepreferencetype, andforinstanceislargerforagentsoftypei
(e.g. becausetype i agents arefavored inthelabourmarkets),
thenparentsoftypej
mightwanttosocializetheirchildrentotheoppositetypei. B
yassumingthatV ii > V ij, asalreadymentioned,
wee¤ectivelyrestricttherelevanceofouranalysis
to‘pure’culturaltraitswhichhavenoe¤ectontheobjectiveeconomicsuccessoftheagents.
10
-
W emodelmarriagechoice inwhatfollows (wesetthenotation
forthegeneralagenti2fa;bg).
M atchingofadultindividuals isorganizedviaamarriagegame.
Theprobabilityofenteringanhomogamousmarriageisendogenouslychosenbyeachagent.
M
oreprecisely,weassumetherearetworestrictedmarriagematchingpools(oneforeachculturaltrait)whereindividualswiththesametraitcanpossiblymatchinmarriage.
W ithprobability®ianagentoftypeienters therestrictedpooland is
marriedhomogamously. W
ithprobability1¡®ianagentoftypeidoesnotgetmarriedintherestrictedpool.
H
ethenentersacommonpoolmadeofallindividualswhohavenotbeenmatchedinmarriageintheirownrestrictedpools.
Inthiscommonpoolindividualsmatchrandomly.
IfAiisthefractionofindividualsoftypeiwhoarematchedintheirrestrictedpool(inequilibrium,bysymmetry,
allindividualswiththesametraitbehaveidenticallyandhence®i= Ai)the
probability an individualoftype i in the common
unrestrictedmarriagepoolismatched inmarriagewithan
individualofthesametype is then (1¡A
i)qi
(1¡Ai)qi+
(1¡Aj)(1¡qi);andhencetheprobabilityofhomogamousmarriageofan
individualoftypeiis givenby:
¼i(®i;Ai;Aj;qi) = ® i+ (1¡®i) (1¡Ai)qi
(1¡Ai)qi+ (1¡Aj)(1¡qi) (1)
W
eassumethatindividualsoftypeicana¤ecttheprobabilityofbeingmatchedintheirrestrictedpoolbychoosing®iatacostC
(±®i), where± is
justaparameterwhichwewilluseinthecomparativestaticsexercises. T
hetypicalproblem
ofamaleoftypeiwillbetochoosetheprobabilityofmatchingintherestrictedmarriagepoolknowingthat,
ifheismatched inanhomogamous household, hehas access
toatechnologytosocializehis children. A nagentwithtraitichooses ®i2
[0 ;1], forgivenAi, Aj, qi, tomaximize
¼i(® i;Ai;Aj;qi)W i(qi)+ [1¡¼i(®i;Ai;Aj;qi)][qiV ii+ (1¡qi)V
ij]¡C (±®i) (2)
whereqiV ii+ (1¡qi)V ijrepresents
theexpectedutilityofatypeiparentinanhet-erogamousmarriage(inwhichthesocializationofthechildrenisdeterminedbyrandommatchingonly);whileW
i(qi)representsthecorrespondingexpectedutilityinanhomog-amousmarriage.
Sincehomogamousmarriagesareendowedwithadirectsocializationtechnology,
W i(qit) dependsontheparents’choiceofsocializatione¤ort, ¿i,
aswellasonmatchingprobabilityqi:
W i(qit) = max¿i [¿i+ (1¡¿i)qi]V ii+ (1¡¿i)(1¡qi)V ij]¡H (̄ ¿i)
(3)
N otethatagentsiandjinteractnon-triviallyinthemarriagegame:
agent’simax-imization problem depends (via ¼i(:)) on Aj, the
fraction ofagents oftypejin therestrictedpool.
Infactthemoreagentsoftypejintherestrictedpool,
thelessofthemintheresidualpopulation,
andthemorefavorableforagentsoftypeithestrategyofnotenteringtheirownrestrictedpool(andbeingmatchedinthecommonresidualpool).
11
-
A symmetricN ashequilibrium ofthemarriagegameis
thenrepresentedbymappings®i(qi)whichare…xedpoints ofthebestreplies
ofagents i2 fa;bg derivedfrom themaximizationofequation(2). T
heprobabilityofhomogamousmarriageforagents
oftypeiistheninequilibrium justfunctionofqi,
andisdenoted¼i(qi).
Proposition1 U nderconvexityandregularityassumptionsoncostsC (±®
i)andH (̄ ¿i)(explicitelystatedintheappendix),
ThereexistauniquesymmetricN ashequilibriumofthemarriagegame,
denoted[® (qi)]=[® i(qi)]i2fa;bg;moreover, ®(qi) is
acontinuousmapping.
Thesolutionofthesocializatione¤ ortchoiceofhomogamousfamilies,
i.e. ofthemax-imizationinequation(3), denoted [¿i(qi)]i2fa;bg, is
acontinuousmapping.
2.2 ImplicationsIn this section we study severalimplication
ofthemarriage and socialization modelforagivendistribution oftraits
in thepopulation, qi. T he implieddynamics
ofthedistributionoftraits is studiedinthenextsection.
Proposition2 The equilibrium probabilityofmatchingin the
restricted pool, ® i(qi),andtheequilibrium socializatione¤
ortofhomogamousfamilies, ¿i(qi), aredecreasinginqi, fori2fa;bg.
T
heprobabilityofmatchingintherestrictedpoolandthechoiceofsocializatione¤ortofhomogamousfamiliesarehigherforminorities,
otherthingsequal.12 M inoritieshaveastrongerincentivetosegregate,
tobehomogamous, andtosocializechildren.
Infact,anindividualinaculturalminorityhasalargeprobabilityofmakinganheterogamousmarriage
ifhedoes notentertherestrictedpool,
sincethecommonunrestrictedpoolwouldbemostlypopulatedbymajoritytypes.
M oreover,
aminoritytypeinanheterog-amousmarriagewillnothaveaccesstothetechnologyofsocializationandhischildrenwillbesocializedtotheexternalculturalenvironment,
thatis, withlargeprobability,themajoritytrait. T
hismotivatesagentswithminoritytraitstohomogamy. O nceho-mogamous,
familieswithaminoritytraitstillhavelargeincentivestodirectlysocializetheirchildrenbecauseifdirectsocializationisunsuccessful,
onceagain,
childrenwillbesocializedtotheexternalculturalenvironment, i.e.
mostprobablytothemajoritytrait.
12Itis importanttostress thatthis
cross-sectionalinterpretationofProposition 2 requires
culturaltraitsnottoomuchdi¤erentintermsoftolerancetoeachother, i.e.
intermsofV ii¡V ij=¢V i;i2fa;bg. M oreover,
theidenti…cationofculturalminoritiesandmajorities
isonlypossibleifthedynamicsofthedistributionofculturaltraits is
notatits stationarystate,
sinceotherwisethepopulationwilltendtobeevenlydistributedacrossculturaltraits;seeSection3.
T hecross-sectionalinterpretationiscentraltoouranalysis
becausemostoftheempiricalevidenceavailableonmarriageandsocializationis
infactcross-sectional;seeSection2.3.
12
-
Itisalsoeasilyshownthatforanygivendistributionoftraits, qi,
both®i(qi)and¿i(qi)aredecreasingin socialization costs, ¯ , and
increasingin thegain from socialization,V ii¡V ij= ¢ V i. A lso,
®iisdecreasingin(while¿iisuna¤ectedby)marriagesegregationcosts,
parametrized by ±. A positive change in the
costofdirectsocialization, notsurprisingly, negativelya¤ects
directsocialization e¤ort,
butitalsonegativelya¤ectsentrytotherestrictedmarriagepoolsincethebene…tsoftherestrictedpoolconsistintheoptiontousethedirectsocializationtechnology,
which is nowmorecostly. Inthesameway,
highergainsfromsocializationpositivelya¤ectbothdirectsocializatione¤ortandentry
intotherestrictedmarriagepool, whilehighermarriagesegregationcosts
±negativelya¤ectmarriagesegregation,
withouthavinganye¤ectonfamilysocialization,whichispossibleonlyforhomogamousfamilies.
T heequilibriumhomogamyrateofthetypeipopulationatequilibrium
isgivenby:
¼i(® i;®i;®j;qi) = ¼i(qi) = ®i(qi)+ (1¡®i(qi)) [1¡®i(qi)]qi
[1¡®i(qi)]qi+ [1¡®j(1¡qi)](1¡qi)(4)
H owdohomogamyratesdependonthecompositionofthepopulation?H
omogamyratesofminoritypopulationsre‡ectthetrade-o¤
ofstrongermarriagesegregationstrategies(®i(qi) is
decreasinginqibyProposition2)withtheadversee¤ectduetotheirhigherinterculturalmatchinginthecommonpool,
wherematchingisrandomandhencere‡ectsrelativepopulationsizes. A
saconsequence,
thedependenceof¼ionqiisnotmonotonic.Itcanbeshownthat,
ifpopulationiis intolerantenough(i.e. forhighenough¢ V i),
itshomogamyrate…rstdecreasesandthenincreases inqi. M
inoritypopulationshencewilltendtohavehomogamyrates
inverselyrelatedtotheirshareinthewholepopulation.
Socializationrates, asmeasuredbytheprobabilityofanhomogamous
familywithtraitiofhavingachildofthesametrait, Pii= ¿i(qi)+
(1¡¿i(qi))qi, alsodonotdependmonotonicallyonqi. Itiseasytoshowthat,
aswiththehomogamyrate, thesocializationrateofgroup
i…rstdecreasesandthenincreases inqi, if¢ V i is largeenough.
2.2.1 Extensions
T
hemarriagemodeljustintroducedcanbeextendedinvariousdirectionswiththeob-jectiveofderivingricherempiricalimplications.
W e summarily reporthereon someextensions wepursued. (T
hecompleteanalysis is reported in an A ppendix
availablefromtheauthorsuponrequest.)
Supposeafractionofthepopulation,
thesameacrossgenderandculturaltype,
cannot(ordoesnotwantto)havechildren. W eassume, forsimplicity,
thatsuchagentsformamarriagepoolbythemselves.
Sincetheonlyadvantageofhomogamyinourset-up
liesinthetechnologyofchildren’s socialization,
theyhaveinfactnointerestinhomogamyalongtheculturaltraitdimension.
Insuchamodel, thedi¤erentialhomogamyoffamilies
13
-
withchildrenwithrespecttofamilieswithoutchildrenismeasuredbyas
¢ H M i(qi) = H M i(qi)¡[qi]2
where [qi]2 is
theprobabilityofhomogamyforanagentwithtraitiifhecannothavechildren,
calculatedfrompurerandommatching.
Itcanbeshownthatsuchhomogamydi¤erential, ¢ H M i(qi), is
positiveinequilib-rium.
Supposemarriageinthecommonpoolis
biasedinfavorofhomogamousmatching.Forinstance, thebias
couldarisefrom segregatedneighborhoods inthepopulation,
orfromtheexistenceofinstitutionswhichfunctionasrestrictedmarriagepoolsandwhoseentry
is free. W ewritethe probability ofan individualoftype
ibeingmatched
inmarriagewithanindividualofthesametype(thehomogamyrateoftypei)
as
¼i(®i;Ai;Aj;qi;°) = ® i+ (1¡®i)(1¡Ai)qi+ (1¡Aj)(1¡qi)°
(1¡Ai)qi+ (1¡Aj)(1¡qi) (5)
wherethesecondterm ontheright-hand-sideof(5) represents
thefractionoftypeiindividuals
homogamouslymatchedinthecommonresidualmarriagepool, giventhatthere
is abiasedmatchingprocess parametrizedby°2 [0 ;1]. W hen°= 0 ;
there israndom matchingin thecommon pool. W hen°= 1; individuals
matchwith prob-ability 1 tosomeoneofthe sametype in thecommonpool:
there is
perfectassorta-tivematchingforeachcommunityindependentoftheexistenceofrestrictedpools
(i.e.¼i(® i;Ai;Aj;qi;1) = 1 forany® i).
Forthisextensionofthemarriagemodel,
comparativestaticsexercisesshowthat®iisdecreasingin°. A
nincreaseinsegregationofthepopulationoutsideoftherestrictedpool,
(i.e., apositivechange in°), reduces the incentives foragents
toenterthere-strictedpool. T hee¤ectonhomogamyrates is,
ontheotherhand, ambiguous,
becausethechgangein°hasalsoadirecte¤ectonhomogamyrates(homogamousmarriagesbyrandommatchingarenoweasier).
U ndersomeweakconditions(detailedintheA ppen-dix),
itcanbeshownthatthedirecte¤ectonhomogamyrates is stronger,
andhencethatapositivechangein°hasapositivee¤ectonequilibriumhomogamyrates.13
T
helastextensionweconsiderinvolvesaddinganexogenousprobabilityofdivorce.Supposeeach
familyhas aprobabilitycofseparating. W eassumeseparation
occursafterchildrenareborn,
butbeforetheyaresocializedtotheculturaltraits. Ifseparationoccurs,
weassumethatoneoftheparents is chosenrandomlytoform
asingleparentfamily. W
ealsoassumethatsocializationismorecostlyforsingleparentfamilies
(see
13O bviously ° hasnoe¤ecton¿i and¼i. Itcanalsobeshownthat¢HM i
decreaseswith ° .A similaranalysis, with qualitatively
similarcomparative statics results, can be carried overfor
distortionswhichfavortheparents’traitintheobliquephaseofsocialization.
14
-
T homson-M cL anahan-Curtin, 19 9 2, forsomeevidenceonthis
point). N otethatsingleparentfamilies, as opposed toheterogamous
families, have atechnology
tosocializechildren;noambiguityonwhichtraittotransmitarises
inthiscase.
Inthiscasethetypicalproblemofanindividualoftypeiisbecomestomaximize
¼i(®i;Ai;Aj;qi)[(1¡c)W im (qi)+ cW
is(qi)]+[1¡¼i(®i;Ai;Aj;qi)][(1¡c)W ih(qi)+ cW is(qi)]¡C (±® i)
whereW im (qi), W is(qi), andW ih (qi) denote, respectively,
thegains from socializingchil-dreninsideanhomogamousmarriage,
asingleparentfamily, andanheterogamousmar-riage. G
ivenourassumptionsaboutthesocializationtechnologiesofthedi¤erentfamilytypes,
thegainsfromsocializationaregivenby:
W im (qi) = max¿i [¿i+ (1¡¿i)qi]V ii+ (1¡¿i)(1¡qi)V ij]¡H m (̄
¿i) (6)
W is(qi) = max¿i [¿i+ (1¡¿i)qi]V ii+ (1¡¿i)(1¡qi)V ij]¡H s(̄ ¿i)
(7 )
W h (qi) = [qiV ii+ (1¡qi)V ij]withH m (̄ ¿i)andH s(̄
¿i)beingthesocializationcostfunctionsofhomogamouscouplesandsingleparentfamily.
W eassumeH m (̄ ¿i) < H s(̄ ¿i), forall¿i2 (0 ;1).
T
hesolutiontothesocializationproblemsprovidessocializatione¤ortsforhomoga-mousparents,
¿im (qi), andsingleparentfamilies, ¿is(qi), withthepropertythat¿im
(qi) >¿is(qi);homogamous families haveabetterdirectsocialization
technologythan singleparentfamilies, andhenceinequilibrium
theyactuallydosocializetheirchildrenmoreintensely.
Comparativestatics exercises showthathigherdivorcerates
inequilibriumimplylowersegregationrates inrestrictedmarriagepools,
lowerhomogamyrates,
andlowerdi¤erentialsinhomogamywithrespecttoagentswhocannothavechildren.
W henlookingforamate, agents anticipatethatthemarriagemightfail. T
hevalueofthehomogamyinmarriageisthenreduced, because,
ifthemarriageends, childrenwillbesocializedwith arelatively
ine¢cienttechnology. A gents’ incentives
toenterthere-strictedmarriagepool, i.e., tolookforanhomogamousmate,
arelowerthehighertheprobabilityofdivorce, c.
2.3 EvidenceT his section collects
someoftheexistingempiricalevidence, mostlydrawn from
thesociologicalliterature,
ontheimplicationsofthemodelregardinghomogamyandsocial-izationwithrespecttoethnicandreligioustraits.
2.3.1 H omogamy
H igh rates ofhomogamy alongculturaldimensions and positive
di¤erentials in ho-mogamywith respecttofamilies which
cannothavechildren arecertainlyafact, at
15
-
leastalongthereligiousandtheethnicdimensions. T
hehomogamyofnewimmigrantsintheU .S. attheturnofthecenturywas
‘almostcastelike’, andquitepersistentoversuccessivegenerations. H
igh rates ofhomogamybyethnicgroup
aremoregenerallydocumentedbyPeach(19 80). T
heexamplesofFrencharistocrats, O rthodoxJews, andU
pperSilesianfarmersreportedinSection2 alsosupporttheseobservations.
R eligioushomogamyisalsopervasive(seeSander, 19 9 3, forCatholics,
andJohnson, 19 80, Schoen-W einick, 19 9 3,
forotherdenominations).14 H
omogamyrateswellabovethoseimpliedbyrandom matching, ofcourse,
mightwellhavemanyexplanationsotherthanthedesiretopreserveoneorseveralculturaltraits
inchildren. M
easuresofpsychologicalcostsofreligiousintermarriagearequitelow,
bothintermsofcostsbornebyspouses(e.g., mar-italinstability;seeL
ehrer-Chiswick, 19 9 3, H eaton, 19 9 4) andbychildren(e.g.,
anomie,lackofself-esteem;seeA ellen-L ambert, 19 69 , Johnson-N
agoshi, 19 86, Stephan-Stephan,19 9 1),
therebysupportingtheargumentthatthesocializationofchildrenisanimportantdeterminantoftheobservedreligioushomogamy.
Themarriagemodelwehave developedmore speci…cally implies
thathomogamyrates should behigherforfamilies which
expecttohavechildren. In particular,
ho-mogamyratesshouldbehigherinmarriageunionsthanincohabitations,
sincefertilityexpectationsofcohabitersarenotstatisticallydi¤erentfromthoseofsingleindividuals,asdocumentedbyR
indfuss-VandenH euvel(19 9 0). Consistently, 51% ofmarriagesintheN
ationalSurveyofFamiliesandH ouseholds(19 8 7
-88)arereligiouslyhomogamous, com-paredtoonly37% ofcohabitations
(Schoen-W einick, 19 9 3). R elatedly, L ehrer(19 9
6)reportshigherintendedfertilityforreligiouslyhomogamouscouples.
O urmodelofculturaltransmissionhas itsmostimportantclass
ofimplicationsforthebehaviorofminorities. M inorities, otherthings
equal, shouldexercisemoree¤ortin marriage segregation. W hile
e¤ortin marriage segregation is di¢culttomeasuredirectly,
populations withminoritytraits, such as O rthodox Jews orA mish,
seem tosegregatemoreintenselyandtodevelop
institutionsforsegregatedmarriages.
Evenforapopulationwithlessextremehomogamypatterns, Japanese-A
mericans, O ’Brien-Fugita(19 9 1)
reportthatculturalandethnicinstitutionsandclubs(whichwewouldinterpretasrestrictedmarriagepools)
aremostprevalentinareaswhereJapanese-A mericanareminorities.
FormalevidenceonhomogamyratesforreligioustraitshasbeenreportedandstudiedbyJohnson(19
80). U singdatafrom thepooled19 7 3-7 6N O RC G
eneralSocialSurvey,the1960 G rowthofFamilies Survey,
andothersources, Johnson(19 80)
constructsmar-riagetablesforsixreligiousgroups.15 H
ethenestimatesalog-linearmodelofmarriage
14Indirectevidencefortheperceivedimportanceofreligioushomogamyinmarriagedecisionscomesfromthestudyofconversions:
bothW arren(19 7 0) andG reeley(19 7 9 ) foundthatmostreligious
iden-ti…cationchangeswereattributabletotheconversionsofspousestoestabilishhomogamyinreligiouslyheterogamousmarriages.
15T hemaindenominationsineachofthesixgroupsare: B aptists, M
ethodists, Presbyterians, L uther-ans, Catholics, andO thers.
16
-
frequencies foreachreligiousgroup to…tthemarriagetables,
identifyingtwomainex-planatoryfactors intheanalysis
ofassortativemarriage: thereligious compositionofthepopulation, and
the‘intrinsicendogamy’ofeachreligious group,
where‘intrinsicendogamy’isameasureofthegroup’se¤ortinmarriagesegregation,
i.e., ameasureof®i inournotation.
Boththeestimatesofthemodelrelativetothenationalandthere-gionallevel(i.e.,
relativetothenationalortheregionalcompositionofthepopulationbyreligiousgroup),
showthattheintrinsichomogamycoe¢cientsaregenerallyhigherforthegroupswhichcompriseasmallerproportionofthepopulation,
asourresults imply.A tthenationallevel, forinstance,
thesmallestgroup, ‘O thers’(theresidualgroup),
hasthehighestintrinsichomogamy, whilethelargestgroups,
BaptistsandCatholics, havethelowest. A ttheregionallevel, also,
thesmallestintrinsichomogamyforCatholics isin theN orth-East,
whereCatholics comprisemorethan 4 5% ofthepopulation,
whilethelargest(morethanthreetimesaslarge) is intheSouth,
whereCatholicsconstituteonly10 % ofthepopulation.
2.3.2 Socializationandsocializatione¤ort
Socializationtotraitiinthemodeldependspositivelyonsocializatione¤ort,
¿i, andontheshareofthepopulationwithtraiti, qi. M oreover,
sinceweassumedheterogamousfamilies
arenotendowedwithasocializationtechnology,
homogamyshouldproxyforsocialization e¤ort, ¿i. Consistentlywith
these implications ofouranalysis, there
isevidencethatsuccessfulsocialization occurs morefrequently in
homogamous families(H ayes-P ittelkow, 19 9 3, H eaton, 19 86, H
oge-Petrillo, 19 7 8 , H oge-Petrillo-Smith, 19 82,O zorak, 19 89
). A lso, M ayer(19 85) constructed a survey ofmixed
Jewish-Christianmarriages in19 83,
comparingseveralmeasuresofsocializationsuccessofconversionarymarriages
(in which the Christian spouse converted toJudaism atmarriage)
tothesamemeasuresforheterogamousmarriages. H
eestimatesthatchildrenofconversionarymarriagesaremorethanthreetimesaslikelytoidentifythemselvesasJewsthanchildrenofheterogamousmarriages.M
oreimportantly, intheirstudyofreligiousbeliefinA ustralia, H ayes-P
ittelkow(19 9
3)…ndthatthee¤ectofhomogamyonsocializationvanisheswhenameasureofsocializatione¤ort(e.g.,
‘parentaldiscussionofreligiousbeliefs’) is
introducedintheregression. T
hisisconsistentwithourmodel’simplicationthathomogamya¤ectssocializationonlyasaproxyforhighersocializatione¤ort.
Interm ofdirectsocializatione¤ort, ourmodelimplies
thathomogamous familiesexercisemoree¤orton children socialization
(because they haveabettertechnologytothis e¤ect), and families
withminority culturaltraits exercisehighersocializatione¤orts,
coeteris paribus. T he presence ofhighersocialization
e¤ortforhomogamousfamilieswithchildren is suggestedbytheanalysis
ofthesurveypanelconstructedbyThornton-A xinn-H ill(19 9 2)onD
etroitfamiliesbetween1962 and19 80. M
arriedfamiliesinthepanelengagemoreinreligiousactivities(proxyingforreligioussocialization),
after
17
-
conditioningforreligiosityatthemomentinwhichthefamilyis formed,
thanfamiliesin cohabitation (as alreadynoted, cohabitations aremuch
less fertileandmuchmoreheterogamousthatmarriages).D irectevidence
forthe socialization behaviorofminorities is ratherscarce. B
arber(19 9 4), however, doesdocumentthatblackandH
ispanicfamiliesmoreaggressivelyso-cializetheirchildren:
theybothhavehigherstandardsforbehaviorandarebetterabletoenforcethosestandard.O
therinterestingevidenceonsocializatione¤ortcanbeobtainedbyanalyzingneigh-borhoodsegregationbyethnicandreligiousgroup,
insofarasneighborhoodsegregationisendogenouslydeterminedpartlybythedesiretosocializeo¤spring.
Ethnicneighbor-hoodshavebeenadominantaspectofA
mericansocietysinceitsearlyhistory,
especiallysincethemassmigrationstotheU .S. inthelastcentury. A
searlyas17 03, forinstanceN ewYorkstreetswere identi…edas eitherD
utchorBritish (H omberger, 19 9 4). A
lso,extremeresidentialsegregation byethnicityofturnofthecentury
immigrants iswelldocumented, e.g., byD uncan-L ieberson (19 59 ),
Peach (19 80). W hileadjustmentcostexplanations
arealsoconsistentwithhigh segregationlevels alongethniclines
of…rstgenerationmigrants, suchexplanations canhardlybeextended,
inouropinion,
tosig-ni…cantlevelsofethnicsegregationofneighborhoodswhichpersistafterthesecondandthirdgenerations.
Inthisrespect, using19 7 0 CensusD ata, Borjas(19 9 5)
estimatesthattheprobabilitythatasecondgenerationethnicfamilygroup
lives
nearfamilygroupsofthesameethnicoriginismuchhigherthanonewouldexpectiffamilieswerespreadacrossneighborhoods
independentlyoftheirethnicorigin. Forinstance,
amongsecondgenerationworkers, thetypicalfamilyofPolishancestrylives
inaneighborhoodthatis7:8% Polish,
eventhough…rstandsecondgenerationPolishmakeuponly1:7%
ofthepopulation. Similarly, secondgeneration Italians live in 12
:1% Italianneighborhoods,eventhough Italians
…rstandsecondgeneration immigrants accountforonly 2 :8%
ofthepopulation.16 M oreover, accordingtoBorjas (19 9 5),
highsegregationrates persistforthirdgenerationimmigrants,
andthereislittleevidencethatonlyeconomicallydis-advantagedgroupsaregeographicallysegregated.
2.3.3 Segregationanddivorce
O
urmodelimpliesthatabiasinfavorofhomogamousmarriageintheunrestrictedpoolhas
anegativee¤ectoneachculturalgroup’s e¤ortinmarriage segregation,
becauseagentsreacttothebiasbydecreasingtheire¤orttoentertherestrictedpool.
Johnson(19 80) …ndshigher‘intrinsichomogamy’rates
inurbanenvironmentthaninruralenvi-ronments,
whichisconsistentwiththeimplicationsofourmodelifurbanenvironmentsarecharacterizedbyeasierinterculturalrelationships.
W hen extendingtheanalysis tosingleparentfamilies anddivorce,
weexpectless16EvenstrongersegregationpatternsbyethnicityarerevealedintheN
ationalL ongitudinalSurveyof
Youth (B orjas, 19 9 5).
18
-
directsocializatione¤ortforsingleparentfamiliesthanforhomogamousfamilies.
T hisisconsistentwithT homson-M cL anahan-Curtin(19 9 2),
which…ndweakercontrolofandfewerdemandplacedonchildrenofsingleparentfamilies
(independentoftheparent’sgender). W
ewouldalsoexpectadeclineinhomogamyratesespeciallystartingfromthe60s,
asaconsequenceofhigherdivorcerates(seeforexampleD avis, 19 85,
forasurveyofthemain trends in marriagerelationships in the U .S.).
T his is broadlyconsistentwiththetrendstowardcohabitations intheU
.S.fromthe60s(Spanier, 19 85), since, aswealreadynoted,
cohabitations arerelativelyheterogamous. A lso,
andmoredirectly,theaveragefractionofreligiouslyhomogamousmarriages
inthe G eneralSocialSurveysampleslowlydeclinesfrom :9 inthe20sto:83
inthe60s, andthendropsto:75 inthe7 0s
(andremainsconstantinthe80s).
3
ThedynamicsofthedistributionofculturaltraitsIntheprevioussections,
weanalyzedhowmaritalstrategiesacrossculturalcommunitiesarea¤ectedbytheagents’concernfortransmittingculturalvalues,
assumingthedistri-butionofculturaltraits inthepopulation, qi, was
exogenouslydetermined. H
owever,patternsofmaritalsegregationsandsocializationacrossculturalgroupshavee¤ectsonthedynamicsofculturaltraits
insociety, oronthedynamicsofqi.
Takingthedynamicsofculturaltraitsexplicitlyintoaccountallowsustoaskques-tionslike:
W hatdistributionoftraitswillprevailinthelong-run?D
oesthepopulationremainmulticulturalinthelimit,
ordoweobserveatendencytowardsculturalhomo-geneity?W
hatarethee¤ectsofvariousstructuralchangesininstitutionalarrangementswithinmarriage?Inthissectionweinvestigatetheseissuesbyanalyzingtheexplicitdynamicsofculturaltraits
inthepopulation, andthedependenceofthedynamics onvarious
historicalin-stitutionalchanges inmarriagerelationships,
likeagreateravailabilityofinterculturalrelationships
(dueforinstancetourbanizationorinformationtechnologies);agreaterfreedomofchoosingones’mate;agreateracceptanceofdivorce,
singleparentfamilies,andfemalelabormarketparticipation.
L etus…rstconsiderthemodelwithabiasinthecommonpool(°6=
0)butnodivorceandsingleparentfamilies (c= 0). T
heprobabilitythatachildwithafatherwithtraitiwilldeveloptraitiis
Pii= ¼i(qi;°)[¿i(qi;°)+ (1¡¿i(qi;°))qi]+ [1¡¼i(qi;°)]qi
where¼i(qi;°) is theequilibrium
homogamyrateprobabilityofpopulationi. W
enoteitsdependenceinequilibriumontheparameter°. Similarly,
theprobabilitythatachildwithafatherwithtraitjwilldeveloptraitiis
Pji= ¼j(qj;°)[(1¡¿j(qj;°))qi]+ [1¡¼j(qj;°)]qi
19
-
L
etqitdenotethefractionofthepopulationwithtraitiattimet(weomittheindextwhennotnecessary).
T hedynamics ofthepopulationofagentswithtraitiis
thendeterminedbythedi¤erenceequation:
qit+ 1 = Piitq
it+ P
jit (1¡qit) = qit+
qit(1¡qit)[¼i(qit;°)¿i(qit)¡¼j(qjt;°)¿j(qjt)]
T hisdynamicalprocesshascornerstationarystates, qi= 0 andqi= 1,
andpossiblyinteriorstationarystates, qi¤, whichsatisfy
¼i(qi¤;°)¿i(qi¤) = ¼j(1¡qi¤;°)¿j(1¡qi¤); i;j2fa;bg; i6= j
(8)
T hefollowingresultstates thatcornerstationarystates
areunstable,
andthatthereexistsatleastoneinteriorlocallystablestationarystate.
Proposition3 Thecornerstationarystates, qi = 0 andqi = 1, are
locallyunstable.Therealways exists oneinteriorsteadystateqi¤,
which, underconvexityconditions oncostfunctions (intheA ppendix),
is locallystable. 17
T
hemechanismofmarriageandculturaltransmissionwestudygeneratesdynamicsofthedistributionofculturaltraitswhichtendtomulticulturalpopulationsandawayfromcompleteassimilationofminorities.
T
hisisbecausethetransmissionmechanismhasthepropertythatculturalminoritiestendtoreactinequilibriumtotheprospectofculturalassimilationwithmarriagesegregation,
homogamousmarriages, andwithmoreintensestrategies
forthedirectsocializationofchildren. Eventhoughmajorities
havehighersocializationrates, duesimplytothee¤ectofpeers
androlemodels, thedynamics
ofthedistributionoftraitsinthepopulation,
whenonetraitsisclosetobecomingextinct,dependsessentiallyondirectsocializatione¤ort,
whichishigherforminorities.18
Itis importanttostressthatsucharesultdependsonthetraits
nothavinge¤ectsontheagents’economicopportunities. T his is,
ofcourse, anabstraction. T heresultsofProposition 3 aremostproperly
interpretedas identifyingaform ofpersistence inthedynamics
ofculturaltraits, anon-linearity in
thedegreeofculturalassimilation.Suchpersistenceoftraits,
andthedi¢culty inacculturationofminorities,
whilehardtomeasureanddocument, is
evidentinmanyhistoricalandethnographicaccounts
oftheevolutionofethnicandreligious traits, as discussed
intheIntroduction.19 O
neofthefeweconometricattemptsatmeasuringthepersistenceofculturaltraits
is Borjas’s
1 7 M ultiple interiorstationarystates mightarise. T hereason is
thatwhiletheprobabilityofbeingmarried in the restricted pool,
®i(qi), is a decreasingfunction ofthe frequency ofthe traitin
thepopulation, theprobabilityofbeinghomogamouslymarried, ¼i(qi),
maybeincreasingwithqi. A s
aconsequenceequation(8)mayhavemorethanonesolutioninqi¤.
18Foranexampleofhowinsteadpeerpressureandsocialinteractionsmightleadtohomogeneity,
seeG laeser-Sacerdote-Scheinkman, 19 9 6.
19 T he‘R enaissance’ofO rthodoxJews is onesuchaccounts (M ayer,
19 85). Itis notjustexplainedbyextremehomogamyrates,
butalsobyrelativelyhighfertilityrates. T
heaveragenumberofchildrenperfamilyofO rthodoxJews in19 9 0,
accordingtothe N ationalJewishPopulation Survey, wasabove
20
-
19 9 5 studyoftheassimilationofimmigrants’‘ethniccapital’intheU
.S. Consistentlywithourresults,
he…ndsquiteslowratesofculturalconvergence,
explainedmainlybyneighborhood…xede¤ects,
whichweinterpretasaproxyforhomogamyratesanddirectsocializatione¤ort.
H owwillchanges
inthemaritalandsocialenvironmenta¤ectthelong-rundistrib-utionofculturaltraits?
W ewillconsiderthreesuchchanges. First,
observethattheconditionforaninteriorstationarystate, equation(8),
canberestatedas:
qa¤¡H T ab(qa¤;°)(1¡qa¤)¡H Tab(qa¤;°) =
qa¤
1¡qa¤¿b(1¡qa¤)¿a(qa¤)
where H Tab(qa¤;°) measures theheterogamyofthepopulation in
equilibrium atthestationarystatefractionofpopulationwithtraita,
qa¤. T his equation is representedinFigure1, wheretheLL and R R
curvesrepresentrespectivelytheleftandtherighthand-sideofequation(8)
asafunctionofqa¤.i) D ecreasein°;increasein ±.
Consideranegativechangein°, thedistortiontowardshomogamy in
theunrestricted pool. Typically, urbanization and
thedevelopmentofcommunication and transportation technologies
should beassociatedwith
anegativechangein°;assuchstructuralchangestendtoincreaseandfacilitateinterculturalcon-tacts.
A negativechange in°increases equilibrium marriagesegregation, ®i,
ofbothculturalgroups. Itgenerallyincreasesheterogamy, H Tab,
anditdoesnota¤ecttheso-cializatione¤ortofhomogamousmarriages(theR R
curveinFigure(1)doesnotmove).N otethatanincreaseinH Tab
shiftsup(down)theLL curve, toLL0, whenqa¤ islarger(smaller) than 12
(seeFigure1). T hereason is thatan increasein H T
ab decreases forbothgroupstheprobability¼i(qi;°)
ofgettinganhomogamousmarriage. H
oweverthedecreaseismorepronouncedfortheminoritygroup
thanforthemajoritygroup,
sincerandommatchingintheunrestrictedpoolfavorsbyde…nitionhomogamyofthemajoritygroup.
A s theLL curverepresents theratioofhomogamous marriages ingroup a
togroup b, itisthenincreasing(decreasing)withH T ab whena
isthemajority(minority)group(i.e., qa¤larger(smaller)than1=2 ). A
reductionin°,
thoughleadingintheshortruntohighere¤orttomaritalsegregationbybothgroups,
generallytends toincreaseheterogamyinsociety, and, as
showninFigure1, favors
inthelimitthemajoritytrait(thestationarystatefrequencyofthemajoritygroup,
i.e., thegroup iwith qi¤ > 12 ,increases).
A nincreasein±, ameasureofthecostofmarriagesegregation,
captures, forinstance,greaterfreedom inchoosingones’mate,
arelativelyrecentdevelopmentinmarriagein-
4, as opposedtoless than 2 forConservativeandR eform Jews. O
urmodelofsocialization, extendedtoendogenous fertility, would
explain such positivecorrelation between fertility, homogamyand
so-cialization,
sincehighlevelofhomogamyandsocializationareequivalenttohighexpected‘quality’ofchildren(B
isin-Verdier, 19 9 6). A s alreadynoted,
higherintendedfertilityforhomogamous couples isalsodocumentedbyL
ehrer(19 9 6).
21
-
stitutionsacrossmanyethnicgroupsatleastinthewesternworld(seee.g., D
avis, 19 85).A nincreasein±
decreasesequilibriummarriagesegregation, ®i, therebyincreasingH T
ab,whileitdoesnota¤ectthesocializatione¤ortofhomogamousmarriages(theR
R curveinFigure) doesnotmove). A n increasein ±, implyingan
increasein H Tab, decreasesforboth groups the probability ¼i(qi;°)
ofgettingan homogamous marriagematch.H owever, asbefore,
thedecreaseismorepronouncedfortheminoritygroupthanforthemajoritygroup.
A n increasein ±, thenfavors
themajoritytraitinthelimit(thesta-tionarystatefrequencyofthemajoritygroup,
i.e., thegroupiwithqi¤> 12 , increases).ii) Increasein ¯ . Itis
alsointerestingtoconsidertheimpactofchanges
inthecostofdirectfamilysocialization, ¯ .
Suchchangesmaybeassociatedwithstructuralchangesingenderroles
insidethefamily,
liketheincreasedfemaleparticipationrateinthela-bormarket. T his
phenomenon increases theopportunitycosts
towomenofspendingtimesocializingchildren insidethefamily,
andtherefore,
shouldbeassociatedwithapositivechangeinthecostofdirectculturalsocialization.
A notherhistoricalstructuralchangemovingin thesamedirection, is
theshiftfrom afamily-laborbasedeconomytowards
amarket-wagebasedeconomy,
makingitagainmorecostlyforthefamilytodirectlytransmititsownculturaltrait.
Formally, theimpactofalesse¢cientsocializa-tiontechnology,
bychangingdirectlyfamilysocialization, ¿i(qi),
andindirectlymaritalsegregationstrategies, ®i(qit), a¤ectsboththeLL
andtheR R curves inFigure1. A s
itinducesareductioninthemaritalsegregationstrategy, ®i,
andinthefamilysocializatione¤ort,
¿i;theimpactonthemarriagegameistoinducealargerequilibriumheterogamy,H
T ab. A sbefore, this
e¤ectdecreasestheprobabilityofhomogamousmatchingfortheminoritygroup
morethan forthemajoritygroup, hence
implyingalargerfractionofagentsofthemajoritygroup
inthelongrundistributionofthepopulation. H owever,thereis
nowinprincipleanothere¤ectemanatingfrom thedirectdecreasein
¿istim-ulatedbytheparameter’s change. Ifthe increase in
socializationcosts, ¯ , a¤ects
thetechnologyoffamilysocializationinthesamewayforbothgroups,
theratioofsocializa-tione¤orts ¿
b(qb)¿a(qa) isnota¤ected: theR R curvedoesnotshift. T
hee¤ectofanincrease
inthecostofdirectfamilysocialization, ¯ , is equivalent, then,
toadecreasein°:
itincreasesinthelimitthefractionofagentswiththemajoritytrait(i.e.,
qi¤, forthetraitisuchthatqi¤> 12 ).iii) Changes in ¢ V i. A s
inthecaseofchanges inthecosts offamilysocialization,
achangeintheperceivedculturaldistanceofgroupi, ¢ V i,
withrespecttotheothergroupwilla¤ectboththeLL andR R curves.
Forinstance, iftheminoritygroup(say,
groupb)tendstobemoretoleranttowardsthemajoritygroup (¢ V b
decreases), thenthatgroupbecomeslesshomogamousandtheequilibrium
heterogamyrateH Tab consequentlyin-creases,
meaninganupwardshiftofLL. A tthesametime, familysocialization¿b(qb)
isalsoreduced, implyingadownwardshiftofR R .
Bothe¤ectstendtoincreasethefrac-tionofthemajoritygroup a,
andthe‘culturalassimilation’oftheminoritygroup. A
nincreaseinculturaltoleranceofthemajoritygroup, group a,
similarlyincreases inter-marriagebetweenthetwocommunities. O
ntheotherhand, italsoimpliesareduction
22
-
oftheintensityoffamilysocializationofthatgroup. T
he…rste¤ectpositivelya¤ectsthelongrun proportion
ofthemajoritygroup, whilethesecond e¤ecttends, on thecontrary,
tofavortheminority. T hetotale¤ectis ambiguous. H owever, itis
easytoseethatwhenthemajoritygroup is largeenough (qa¤
closeenoughto1), the impactofachangein ¢ V a onlymarginallya¤ects
thesocializatione¤ort, ¿a(qa), leavingtheR R curvealmostuna¤ected.
In thatcase, onlythepositive impactofadecrease in¢ V a onLL
remains,
implyinganincreaseinthesteadystatefrequencyofthemajoritygroup, and,
conversely, asmallersizedminoritygroup. Forexample, as noted
intheIntroduction, A mericanJews’fasteracculturationsincetheendofW
orldW arII
mightbeexplainedbyothermajorreligiousgroups’increasingtoleranceofinter-marriagewithJews(seeD
ershowitz, 19 9 7 ).
Finally, webrie‡ydiscuss the implications
ofincreasingtheprobabilityofdivorce,
c,onthelongrundistributionofculturaltraitsinthepopulation. T
hedynamicsequationisnowgivenby:
qit+ 1¡qit= qit(1¡qit)£(1¡c)[¼i(qit)¿im (qit)¡¼j(qjt)¿jm (qjt)]+
c[¿is(qit)¡¿js(qjt)]
¤(9 )
Inequation(9
)weseethattheculturalselectionforcesoperatethroughtwosocializationchannels.
H omogamous couples whohave notdivorced (in proportion (1 ¡c)¼
a(qt)and (1 ¡c)¼ b(1 ¡qt)) socialize theirchildren with
directfamily socialization e¤ort,¿im (qit). D
ivorcedcouplesandsingleparentfamilies(inproportionc¼a(qt)andc¼b(1¡qt))socializetheirchildrenwithdirectfamilysocializatione¤ort¿is(qit).
Clearlywhenthetotale¤ective socialization e¤ortofgroup i(homogamous
couples plus single parentfamilies) is largerthantheothergroup’s,
thenthefrequencyoftraitiincreases inthepopulation. A
swehavepointedoutinSection2.3,
anincreaseincreducestheresourcesspenttomatchintherestrictedpoolsandbringsmoreheterogamyintheshort-run.
A shomogamyforbothculturalgroups decreases, homogamyrates
alsodecreaseforbothgroups,
butlessrapidlyforthemajoritygroupthanfortheminoritygroup. T
hisimpliesabias in theevolutionoftraits which favors
themajoritygroup. A tthesametime,an increase in divorcerates
increases the importanceofsingleparentsocialization
inthedynamicsofthedistributionoftraits. Clearly,
itbringsanadvantagetothegroupwhich is more
successfulatsocializingin single parentcontexts. W hen both
groupsareequallysuccessfulatsocializingtheirchildreninsingleparentfamilycontexts
(i.e.,theyhaveaccesstothesametechnologiesofsocialization),
thise¤ecttendstofavortheminorityculturalgroup,
asagentsofthatgrouphavelargerincentivestospendresourcesforculturaltransmission.
H ence,
itappearsthatwhilereducinghomogamytheoveralle¤ectofhigherdivorceratesonpreferencesisambiguous.
W hen, however,
singleparentfamiliesarenotabletosigni…cantlybiastheculturaltransmissionprocess,
wegetsomeclearerimplications. Inthiscasethetermc(¿as(q)¡¿bs(1¡q))
isclosetozeroinequation(9 ). W
earethereforeleftwithonlythee¤ectofconthegroups’maritalstrategies.
T hatis, an increaseintheprobabilityofdivorce, c,
reducesmaritalsegregationstrategiesof
23
-
bothgroupsandincreasesheterogamy. Thisfavors, inthelong-run,
theculturaltraitofthemajoritygroup.
4 ConclusionT
hispaperanalyzesmaritalsegregationdecisionsandtheirimpactonthetransmissionofethnicandreligious
traits. W
econcentrateontheinteractionbetweendirectfamilysocializationandobliquesocializationbyteachers,
peersandrolemodels. W
hilemostre-searchonculturaltransmissionhasstressedthisinteraction(e.g.,
CavalliSforza-Feldman,19 81, B oyd-R icherson, 19 85),
wecomplementthisemphasisbymodellingmarriageanddirectfamilysocializationaseconomicdecisionsofagents.
T hiseconomicapproachgen-eratesmanyinterestingrestrictions,
aswellastestableimplications,
whichweattempttoidentifyandstudyinthepaper.
O uranalysis ofsocialization is relativelyabstract, and, hence,
in principle,
canbeextendedtoanalyzetheevolutionofotherculturaltraitsordi¤erentsocializationmech-anisms.
H owever, theassumptionthatculturaltraitsare‘pure’,
ordonothaverelevante¤ectsonagents’economicopportunities,
isquiterestrictive. T
hisassumptionneedstoberelaxedinparticulartoapplyouranalysis
tostudytheevolutionofmanyinterest-ingculturaltraitsandpreferenceparameters,
likepoliticalattitudes, riskaversion, andintertemporaldiscounting.
Suchtraits, infact, a¤ecthowagents interacteconomicallyandsocially,
especiallyinstrategicenvironments.
24
-
A ppendix
T heproblemofanindividualoftypeiistochoose®i2 [0 ;1],
foragivenAi, Aj, qi,tomaximize
¼i(®i;Ai;Aj;qi)W i(qi)+ [1¡¼i(®i;Ai;Aj;qi)]V i(qi)¡C (±®i)
(10)
whereW i(qi) isgivenby
W i(qi) = max¿i [¿i+ (1¡¿i)qi]V ii+ (1¡¿i)(1¡qi)V ij]¡H (̄
¿i)
andV i(qi) = qiV ii+ (1¡qi)V ij
W eassume:
A ssumptionA .Fori2fa;bg, C (±®i) andH (̄ ¿i)
aremonotonicincreasing, ofclassC3, andconvex. M oreover,
A -i) @3C@®i3·0
A -ii) ± @C@®i(±) > [W i(0 )¡V i(0 )];
A -iii) (1¡®i) @2 C@®i)2
¡ @C@®i > 0 at®i= ®imax suchthat± @C@®i(±® imax) = W i(0 )¡V
i(0 ):
A ssumptions A -1) - A -iii)
providesu¢cientconditionsfortheexistenceandunique-ness ofthe N ash
equilibrium in themarriagegame. A -i) requires
thatthemarginalcostofmarriagesegregationisincreasingandconcave. A
-ii) ensuresthatmatchingwithprobability1
intherestrictedpoolisprohibitivelycostly. Finally, A
-iii)requiresthat,
atsomelargestpossiblerestrictedpoolmatchingprobability, ® imax;
thecostfunctionC (:)isconvexenough.
Foranindividualoftypei, the…rstorderconditionforthechoiceof®i
is:
±@C@®i
(±®i) = pi(Ai;Aj;qi)[W i(qi)¡V i(qi)]; (11)
withpi(Ai;Aj;qi) =
(1¡Aj)(1¡qi)(1¡Ai)qi+ (1¡Aj)(1¡qi)
A symmetricN ashequilibrium
ofthemarriagegamehastheproperythatallagentsoftypeichoosethesame® i,
andisrepresentedbymappings ®
i(qi)whichare…xedpointsofthebestrepliesofagentsi2fa;bg derivedfrom
themaximizationofequation(10).Bestrepliesmustthensatisfyequation(11),
whichcanberewrittenas
±@C@®i
(±® i) =(1¡®j)(1¡qi)
(1¡®i)qi+ (1¡®j)(1¡qi)[Wi(qi)¡V i(qi)]= 0 (12)
25
-
fori;j2fa;bg andi6= j:
ProofofProposition 1 (underA ssumption A ). A ta symmetric N ash
equilibrium®i = Aiandthe…rstorderconditionofan
individualoftypeiforthechoiceof® i isequation(12). D enoteby© i( ®
i;®j;qi)thelefthandsideofequation(12). T hen
@© i
@® i=
@ 2 C@®i2
(±® i)¡ (1¡®j)(1¡qi)qi
[(1¡® i)qi+ (1¡®j)(1¡qi)]2[W i(qi)¡V i(qi)]
and
@ 2 © i
@®i2=
@3C@®i3
(±® i)¡ 2 (1¡®j)(1¡qi)(qi)2
[(1¡® i)qi+ (1¡®j)(1¡qi)]3[W i(qi)¡V i(qi)]< 0 ;
becauseofA -i). H ence © i is continuous and concave in ®i
forany (®j;qi) 2 [0 ;1]2 .A lso© i(0 ;®j;qi) · 0 and © i(1;®j;qi)
> 1, becauseofA -ii). H ence, forany (®j;qi)2 [0 ;1]2
;thereexistsaunique® i2 [0 ;1]satisfying© i(® i;®j;qi) = 0:L
etusdenotesuch®iby v®
i(®j;qi). v®
i(®j;qi) canbeviewedas abestresponsefunctionofthemarital
segmentatione¤ortofgroup i. B ecauseoftheconcavityof© i,
asimpleargumentbycontradiction
shows that, at v®i(®j;qi), necessarily @© i@®i(
v®i;:::) > 0:A lso, equation (12) implies
0 < v®i(0 ;qi) < 1 and v®
i(1;qi) = 0 . Finally,
@v®i(®j;qi)@®j
= ¡@© i@®j(
v®i;:::)
@© i@®i(
v®i;:::)
;
whichhasthesignof¡@© i@®j(v®i;:::):B ut
¡@©i
@®j(v®i;:::) = ¡ (1¡®
i)qi(1¡qi)[(1¡®i)qi+ (1¡®j)(1¡qi)]2
[W i(qi)¡V i(qi)]< 0 ;
andtherefore v®i(®j;qi) is adecreasingfunctionof®j. D
i¤erentiationofequation(12)
showsthat
@© i
@qi=
(1¡®j)(1¡®i)[(1¡®i)qi+ (1¡®j)(1¡qi)]2
[W i(qi)¡V i(qi)]
¡ (1¡®j)(1¡qi)
(1¡®i)qi+ (1¡®j)(1¡qi)d [W i(qi)¡V i(qi)]
d qi;
butW i(qi)¡V i(qi) = ¿i(qi)[V ii¡V ij](1¡qi)¡H (¿i(qi)). A
pplyingtheEnvelopeThe-oremwehave d [W
i(qi)¡V i(qi)]d qi < 0 . H ence
@© i@qi > 0 , implyingthat
@v®i
@qi < 0 .
26
-
Considernowthemapping- (® a), de…nedon [0 ;1]andgivenby - (® a)
= v®a[v®
b(® a)]:A
symmetricN
ashequilibriumofthemarriagegameisa…xedpointofthismapping. A
sbothbestresponses functions v®
a(® b) and v®
b(® a) arecontinuous functions from [0 ;1]
into [0 ;1], - (® a) is alsoacontinuousmappingfrom [0 ;1] into
[0 ;1]:H encetheKaku-tani FixedPointTheorem
impliestheexistenceofasymmetricN ashequilibrium
inthemarriagegame.
Toprove uniqueness ofthe symmetric N ash equilibrium itsu¢ces to
showthat- (® a)¡® a is strictlydecreasingin® a:Continuityof®i(qi)
thenfollowsdirectly.Since - (® a) is di¤erentiable, - (® a)¡® a is
strictlydecreasingin ® a i¤ - 0(® a) < 1;or,moreprecisely,
@ v®a
@® b£@
v®b
@® a< 1
L ettingD = (1¡® a)qa + (1¡® b)(1¡qa)andK i(qai) = [W i(qi)¡V
i(qi)], wehave
@ v®a
@® b£@
v®b
@® a=
(1¡®a)qa(1¡qa)D2 K
a
±@2 C@®a 2 (±® a)¡
(1¡®b)(1¡qa)qaD2 K b
£±@ 2 C@®b2 (±®
b)¡(1¡® a)(1¡qa)qaD2 K a(1¡®a)qa(1¡qa)
D2 K b
W iththisnotation, the…rstordercondition, equation(12),
canberewrittenas
±@C@®i
(±®i) =(1¡qi)(1¡®j)
DK i(qi)
Substituting, weobtainthat@v®a
@®b £ @v®b
@®a < 1 holdsi¤
@C@®b
(1¡qa)D
K aK b
d 2 Cd ® a2 ¡
qaD
@C@® a
£@2 C@®b2 ¡
(1¡qa)D
@C@®b
@C@®a
qaD
K bK a
< 1;
whichisequivalentto:
qa@ 2 C@® b2
@C@® a
+ (1¡q)@2 C
@® a 2@C@® b
< D£ @2 C
@® a 2£ @
2 C@® b2
A saconsequence @v®a
@®b £ @v®b
@®a < 1 holds i¤
@ 2 C@® b2
qa [(1¡® a)@2 C
@® a 2¡ @C@® a
]+@ 2 C@® a 2
(1¡qa)[(1¡® b)@2 C
@® b2¡ @C@® b
]> 0 ;
whichissatis…edunderA ssumptionA . M oreprecisely, as @3C@®i3·0
, (1¡®i)@2 C
@®i2 ¡ @C@®i isdecreasingin ® i, and
isthereforepositiveforallrelevant®i, since, bycondition A
-iii),itispositiveforthelargestpossible® i, ®imax, givenby±
@C@®i(±®
imax) = K i(0 ).
27
-
T hechoiceof¿i isderivedfromthefollowingoptimizationproblem:
W i(qi) = max¿i [¿i+ (1¡¿i)qi]V ii+ (1¡¿i)(1¡qi)V ij]¡H (̄
¿i)
whichisaconvexproblemunderA ssumptionA .T
hisimmediatelyimpliesthecontinuityofthesolutionasafunctionoftheparameters,
¿i(qi). }
ProofofProposition 2 (underassumption A ). N ote that @® a@qa =
¡@-@qa@-@®a¡1
has the
signof @ -@qa:U singthefactthatv®a(® b;qa) isdecreasingin® b,
and @
v®a
@qa < 0 , itiseasyto
seethat @ -@qa =@v®a
@qa +@v®a
@®b £@v®b
@qa < 0:H encetheresultthat®a(qa) isdecreasinginqa. By
asymmetricargument® b(qb) isdecreasinginqb = 1¡qa:T
he…rstorderconditionforthechoiceof¿i, is
¯@H@¿i
(̄ ¿i) = [V ii¡V ij](1¡qi)
BecauseoftheconvexityofH (:), thesecondorderconditionis
satis…edanddi¤erenti-atingthepreviousequation, weget
@¿i
@qi= ¡[V
ii¡V ij]¯ 2 @ 2 H@¿2
< 0: }
T hecomparativestatics results inSection2.2,
andtheextensionsandthecompar-ative statics analysis ofSection
2.2.1, arestudied in an A ppendixavailable from theauthors.
W enowstudythedynamics ofthedistributionoftraits,
followingtheanalysis ofSection3, where°6= 0 andc= 0:T
hegeneralcaseinwhichc6= 0 is studied intheA
ppendixavailablefromtheauthors. T
heequationforthedynamicsofthedistributionoftraits
inthepopulationis
qit+ 1 = qit¼
i(qit)Piim + q
it(1¡¼i(qit))Piih + + qjt¼j(qjt)Pjim + qjt(1¡¼j(qjt))Pjih ;
(13)
wherePiim ; Piih ;(resp. Pjim ; Pjih ) arethetransition
probabilities foraparentoftypei
(resp. j)ofanhomogamousandheterogamousfamily,
ofhavingchildrenoftypei;thatis,
Piim = ¿im + (1¡¿im )qit; Piih = qit
Pjim = (1¡¿jm )qit; Pjih =
qitSubstitutingthesetransitionprobabilities inequation(13),
andsubtractingqitonbothsides, weget, afterrearrangement,
qit+ 1¡qit= qit(1¡qit)£¼i(qit)¿
im (q
it)¡¼j(qjt)¿jm (qjt)
¤
28
-
ProofofProposition3. L
etqitdenotethefractionofthepopulationwithtraitiattimet.i)Fromthe…rstorderconditionsofthesocializationprobleminequation(6),
¿im (1) = 0 .A lso¿im (0 ) > 0 , ¼i(1) = 1;¼i(0 ) = ® i(0 )+
(1¡® i(0 ))°> 0:H ence"
@¡qat+ 1¡qat
¢
@qat
#
qa= 0
= [¼a(0 )¿am (0 )¡¼b(1)¿bm (1)]
= [¼a(0 )]¿am (0 ) > 0
and "@¡qat+ 1¡qat
¢
@qat
#
qa= 1
= ¡£[¼ a(1)¿am (1)¡¼ b(0 )¿bm (0 )]
¤
= [¼b(0 )]¿bm (0 ) > 0
T
hetwopreviousexpressionsensurethatthecornerstationarystatesqa¤= 0
andqa¤= 1arelocallyunstable.ii) Considerthefunction
£ (qa) = ¼ a(qa)¿am (qa)¡¼b(1¡qa)¿bm (1¡qa)
T hisfunctioniscontinuouson [0 ;1]:M oreover
£ (0 ) = ¼ a(0 )¿am (0 ) > 0
and£ (1) = ¡¼b(0 )¿bm (0 ) < 0
Bycontinuityof£ (:)thereexistsaninteriorpointqa¤2 (0 ;1)
suchthat£ (qa¤) = 0 and£ 0(qa¤) < 0 .
Suchapointisaninteriorstationarystateandsatis…es
¼a(qa¤)¿am (qa¤) = ¼ b(1¡qa¤)¿bm (1¡qa¤)
iii) A ninteriorstationarystateqa¤willbelocallystableif"@¡qat+
1¡qat
¢
@qat
#
q= qa¤
= qa¤(1¡qa¤)£ 0(qa¤) 2 (¡2 ;0 )
But·@(qat+ 1¡qat)
@qat
¸
q= qa¤< 0 is ensuredby£ 0(qa¤) < 0 . M oreover,
·@(qat+ 1¡qat)
@qat
¸
q= qa¤> ¡2
canberewrittenasqa¤(1¡qa¤)j£ 0(qa¤)j< 2 (14)
A su¢cientconditionforequation(14) tobesatis…edis: j£
0(qa¤)j< 8, whichinturnissatis…edif @¿i@qai and
@®i@qai aresu¢cientlybounded, i.e., ifH (̄ ¿
i) andC (±® i) areconvexenoughin¿iand®i:}
29
-
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