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Academic Commons Search Resultsen-usCupid’s Invisible Hand: Social Surplus and Identification in Matching Models
http://academiccommons.columbia.edu/catalog/ac:186702
Galichon, Alfred; Salanie, Bernardhttp://dx.doi.org/10.7916/D8S181NGFri, 19 Jun 2015 16:00:58 +0000We 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 formulæ 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.Economics, Economic theorybs2237EconomicsWorking papersThe Roommate Problem Is More Stable Than You Think
http://academiccommons.columbia.edu/catalog/ac:154183
Chiappori, Pierre A.; Galichon, Alfred; Salanie, Bernardhttp://hdl.handle.net/10022/AC:P:15211Wed, 07 Nov 2012 00:00:00 +0000Stable matchings may fail to exist in the roommate matching problem, both when utility is transferable and when it is not. We show that when utility is transferable, the existence of a stable matching is restored when there is an even number of individuals of indistinguishable characteristics and tastes (types.) As a consequence, when the number of individuals of any given type is large enough there always exist "quasi-stable" matchings: a stable matching can be restored with minimal policy intervention. Our results build on an analogy with an associated bipartite problem; it follows that the tools crafted in empirical studies of the marriage problem can easily be adapted to the roommate problem.Economicspc2167, bs2237EconomicsWorking papersCupid's Invisible Hand: Social Surplus and Identification in Matching Models
http://academiccommons.columbia.edu/catalog/ac:133162
Salanie, Bernard; Galichon, Alfredhttp://hdl.handle.net/10022/AC:P:10478Wed, 01 Jun 2011 00:00:00 +0000We investigate a matching game 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 of two terms. The first term is simply the average surplus due to the observable characteristics; and the second one can be interpreted as a generalized entropy function that reflects the impact of the unobserved characteristics. We use this result to derive simple closed-form formulæ that identify the joint surplus in every possible match and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. Moreover, we show that if transfers are observed, then the pre-transfer utilities of both partners are also identified. We conclude by discussing some empirical approaches suggested by these results for the study of marriage markets, hedonic prices, and the market for CEOs.Economic theorybs2237EconomicsWorking papersInference in incomplete models
http://academiccommons.columbia.edu/catalog/ac:113244
Galichon, Alfred; Henry, Marchttp://hdl.handle.net/10022/AC:P:378Mon, 28 Mar 2011 00:00:00 +0000We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical version of the latter, we derive a Kolmogorov-Smirnov statistic for Choquet capacity functionals, which we use to construct our test. We derive the limiting distribution of our test statistic under the null, and show that our test is consistent against certain classes of alternatives. When the model is given in parametric form, the test can be inverted to yield confidence regions for the identified parameter set. The approach can be applied to the estimation of models with sample selection, censored observables and to games with multiple equilibria.Economic theorymh530EconomicsWorking papersMatching with Trade-offs: Preferences over Competing Characteristics
http://academiccommons.columbia.edu/catalog/ac:127315
Galichon, Alfred; Salanie, Bernardhttp://hdl.handle.net/10022/AC:P:9186Tue, 06 Jul 2010 00:00:00 +0000We investigate in this paper the theory and econometrics of optimal matchings with competing criteria. The surplus from a marriage match, for instance, may depend both on the incomes and on the educations of the partners, as well as on characteristics that the analyst does not observe. The social optimum must therefore trade off matching on incomes and matching on educations. Given a flexible specification of the surplus function, we characterize under mild assumptions the properties of the set of feasible matchings and of the socially optimal matching. Then we show how data on the covariation of the types of the partners in observed matches can be used to estimate the parameters that define social preferences over matches. We provide both nonparametric and parametric procedures that are very easy to use in applications.Economic theorybs2237EconomicsWorking papers