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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 12:07:46 +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 papers