Cupid's Invisible Hand
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Cupid's Invisible Hand: Social Surplus and Identification in Matching Models Alfred Galichon1 Bernard Salanie2 April 6, 20113 1Economics Department, Ecole polytechnique; e-mail: 2Department of Economics, Columbia University; e-mail: . 3The authors are grateful to Pierre-Andre Chiappori for useful comments and discussions. Galichon gratefully acknowledges support from Chaire EDF-Calyon “Finance and Developpement Durable,” Chaire Axa “Assurance et Risques Majeurs” and FiME, Laboratoire de Finance des Marches de l'Energie. Part of the research underlying this paper was done when Galichon was visit- ing the University of Chicago Booth School of Business and Columbia University. Galichon thanks the Alliance program for its support.
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Cupid's Invisible Hand: Social Surplus and Identification in Matching Models Alfred Galichon1 Bernard Salanie2 April 6, 20113 1Economics Department, Ecole polytechnique; e-mail: 2Department of Economics, Columbia University; e-mail: . 3The authors are grateful to Pierre-Andre Chiappori for useful comments and discussions. Galichon gratefully acknowledges support from Chaire EDF-Calyon “Finance and Developpement Durable,” Chaire Axa “Assurance et Risques Majeurs” and FiME, Laboratoire de Finance des Marches de l'Energie. Part of the research underlying this paper was done when Galichon was visit- ing the University of Chicago Booth School of Business and Columbia University. Galichon thanks the Alliance program for its support.
- optimal assignment algorithms
- match partners
- surplus function
- siow
- partners share
- positive assortative
- group can
Cupid’sInvisibleHand:SocialSurplusandIdentificationinMatchingModelsAlfredGalichon1BernardSalanie´2April6,201131EconomicsDepartment,E´colepolytechnique;e-mail:alfred.galichon@polytechnique.edu2DepartmentofEconomics,ColumbiaUniversity;e-mail:bsalanie@columbia.edu.3TheauthorsaregratefultoPierre-Andre´Chiapporiforusefulcommentsanddiscussions.GalichongratefullyacknowledgessupportfromChaireEDF-Calyon“FinanceandDe´veloppementDurable,”ChaireAxa“AssuranceetRisquesMajeurs”andFiME,LaboratoiredeFinancedesMarche´sdel’Energie.PartoftheresearchunderlyingthispaperwasdonewhenGalichonwasvisit-ingtheUniversityofChicagoBoothSchoolofBusinessandColumbiaUniversity.GalichonthankstheAllianceprogramforitssupport.
AbstractWeinvestigateamatchinggamewithtransferableutilitywhensomeofthecharacteristicsoftheplayersareunobservabletotheanalyst.Weallowforawideclassofdistributionsofunobservedheterogeneity,subjectonlytoaseparabilityassumptionthatgeneralizesChooandSiow(2006).Wefirstshowthatthestablematchingmaximizesasocialgainfunctionthattradesofftwoterms.Thefirsttermissimplytheaveragesurplusduetotheobservablecharacteristics;andthesecondonecanbeinterpretedasageneralizedentropyfunctionthatreflectstheimpactoftheunobservedcharacteristics.Weusethisresulttoderivesimpleclosed-formformulæthatidentifythejointsurplusineverypossiblematchandtheequilibriumutilitiesofallparticipants,givenanyknowndistributionofunobservedheterogeneity.Moreover,weshowthatiftransfersareobserved,thenthepre-transferutilitiesofbothpartnersarealsoidentified.Weconcludebydiscussingsomeempiricalapproachessuggestedbytheseresultsforthestudyofmarriagemarkets,hedonicprices,andthemarketforCEOs.Keywords:matching,marriage,assignment,hedonicprices.JELcodes:C78,D61,C13.
