Cupid's Invisible Hand: Social Surplus and Identification in Matching Models
Alfred Galichon (Ecole Polytechnique)
Abstract: We 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 fi rst show that the stable matching maximizes a social gain function that trades off 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 formulae 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 identi ed. We conclude by discussing some empirical approaches suggested by these results for the study of marriage markets, hedonic prices, and the market for CEOs.
Monday 5th March 2012, 13:00 - 14:00, W316
Abstract: We 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 fi rst show that the stable matching maximizes a social gain function that trades off 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 formulae 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 identi ed. We conclude by discussing some empirical approaches suggested by these results for the study of marriage markets, hedonic prices, and the market for CEOs.
Monday 5th March 2012, 13:00 - 14:00, W316