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

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 classical fullyand non-transferable utility models, collective models, and settings with taxes on transfers. We allow for the introduction of a general class of additive unobserved heterogeneity on agents’ preferences. We show existence and uniqueness of an equilibrium under minimal assumptions. We then provide two algorithms to compute the equilibrium in our model. The first algorithm operates under any structure of heterogeneity in preferences; the second is more efficient, but applies only in the case in which random utilities are logit. We show that the log-likelihood of the model has a simple expression and we compute its derivatives. An empirical illustration is provided in the appendix. Date: March 12, 2018. Galichon gratefully acknowledges funding from NSF grant DMS-1716489, and from the European Research Council under the European Union’s Seventh Framework Programme (FP7/20072013) / ERC grant agreement no. 312503. Kominers gratefully acknowledges the support of the NSF (grants CCF-1216095 and SES-1459912), the Harvard Milton Fund, and the Ng Fund of the Harvard Center of Mathematical Sciences and Applications. The authors thank the editor (James Heckman) and three anonymous reviewers for very helpful comments. Additionally, the authors appreciate the insightful comments of Pierre-André Chiappori, Edoardo Ciscato, Matthew Gentzkow, Yinghua He, Yu-Wei Hsieh, Murat Iyigun, Sonia Jaffe, Thierry Magnac, Ismael Mourifié, Bernard Salanié, Aloysius Siow, Heidi Williams, and seminar participants at the AEA Meetings, the University of California, Berkeley, Boston University, the University of Chicago, EIEF, the Fields Institute, Harvard, MIT, NYU, Penn State University, Princeton, Sciences Po, Stanford, the University of Toronto, UCLA, the University of Pennsylvania, Yale, and the University of Zürich. Yue Li provided great research assistance. Galichon is grateful for the hospitality of MIT, where part of this paper was written. 1 2 A. GALICHON, S. D. KOMINERS, AND S. WEBER