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

88 Pages Posted: 14 Jul 2021

See all articles by Alfred Galichon

Alfred Galichon

Sciences Po

Bernard Salanie

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

Date Written: June 2021

Abstract

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow's empirical application to illustrate the potential of our more general approach.

JEL Classification: C13, C78, D61

Suggested Citation

Galichon, Alfred and Salanie, Bernard, Cupid's Invisible Hand: Social Surplus and Identification in Matching Models (June 2021). CEPR Discussion Paper No. DP16228, Available at SSRN: https://ssrn.com/abstract=3886670

Alfred Galichon (Contact Author)

Sciences Po

28 Rue des Saint-Peres
Paris, 75006
France

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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