Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility

Alfred  Galichon; Scott Duke Kominers; Simon  Weber

Article | Journal of Political Economy | Forthcoming

Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility

by Alfred Galichon, Scott Duke Kominers and Simon Weber

Abstract

We introduce an empirical framework for models of matching with imperfectly transferable utility and unobserved heterogeneity in tastes. Our framework allows us to characterize matching equilibrium in a flexible way that includes as special cases the classic fully- and non-transferable utility models, collective models, and settings with taxes on transfers, deadweight losses, and risk aversion. We allow for the introduction of a very general class of unobserved heterogeneity on agents' preferences. Under minimal assumptions, we show existence and uniqueness of equilibrium. We provide two algorithms to compute the equilibria in our model. The first algorithm operates under any structure of heterogeneity in preferences. The second algorithm is more efficient, but applies only in the case when random utilities are logit. We show that the log-likelihood of the model has a particularly simple expression and we compute its derivatives. As an application, we build a model of marriage with two-sided preferences over the partner type and private consumption. We estimate our model using the 2013 "Living Costs and Food Survey" database.

Keywords: sorting; matching; Marriage Market; intrahousehold allocation; Imperfectly Transferable Utility; Marketplace Matching; Mathematical Methods;

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Galichon, Alfred, Scott Duke Kominers, and Simon Weber. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility." Journal of Political Economy (forthcoming).

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Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility

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