Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models

Abstract

We 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 very significantly extends Choo and Siow (2006). We first show that the stable matching maximizes a social gain function that trades off a sorting effect due to complementarities in observable characteristics, and a randomization effect caused by the presence of 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 present a a discussion of computational issues, including an algorithm which can be extremely efficient in important instances. We conclude by discussing some empirical approaches suggested by these results.