Matching in Closed-Form: Equilibrium, Identification, and Comparative Statics

30 Pages Posted: 16 Oct 2014 Last revised: 12 Apr 2016

See all articles by Raicho Bojilov

Raicho Bojilov

Pontifical Catholic University of Chile - School of Business

Alfred Galichon

NYU, Department of Economics and Courant Institute

Date Written: October 7, 2015

Abstract

This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identiļ¬ed from the optimal matching distribution, also in closed-form. The analytical formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.

Keywords: matching, marriage, assignment

JEL Classification: C78, D61, C13

Suggested Citation

Bojilov, Raicho and Galichon, Alfred, Matching in Closed-Form: Equilibrium, Identification, and Comparative Statics (October 7, 2015). Available at SSRN: https://ssrn.com/abstract=2510732 or http://dx.doi.org/10.2139/ssrn.2510732

Raicho Bojilov

Pontifical Catholic University of Chile - School of Business ( email )

Vicuna Mackenna 4860
Santiago
Chile

Alfred Galichon (Contact Author)

NYU, Department of Economics and Courant Institute ( email )

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

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