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Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models

65 Pages Posted: 9 Apr 2011 Last revised: 2 Mar 2015

Alfred Galichon

NYU, Department of Economics and Courant Institute

Bernard Salanie

Columbia University - Graduate School of Arts and Sciences - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: February 18, 2015

Abstract

We investigate a model of one-to-one matching with transferable utility when some of the characteristics of the players are unobservable to the analyst. We allow for a wide class of distributions of unobserved heterogeneity, subject only to a separability assumption that generalizes Choo and Siow (2006). We first show that the stable matching maximizes a social gain function that trades off exploiting complementarities in observable characteristic sand matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint surplus in every possible match and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. If transfers are observed, then the pre-transfer utilities of both partners are also identified. We discuss computational issues and provide an algorithm that is extremely efficient in important instances. Finally, we present two estimators of the joint surplus and we revisit Choo and Siow's empirical application to illustrate the potential of our more general approach.

Suggested Citation

Galichon, Alfred and Salanie, Bernard, Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models (February 18, 2015). Available at SSRN: https://ssrn.com/abstract=1804623 or http://dx.doi.org/10.2139/ssrn.1804623

Alfred Galichon (Contact Author)

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Bernard Salanie

Columbia University - Graduate School of Arts and Sciences - Department of Economics ( email )

420 W. 118th Street
New York, NY 10027
United States

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

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