We present a class of one-to-one matching models with perfectly transferable utility. We discuss identification and inference in these separable models, and we show how their comparative statics are readily analyzed.

Many questions in economics can be fruitfully analyzed in the framework of matching models. Until recently, empirical work has lagged far behind theory in this area. This review reports on recent developments that have considerably expanded the range of matching models that can be taken to the data. A leading theme is that in such two-sided markets, knowing the observable characteristics of partners alone is not enough to credibly identify the relevant parameters. A combination of richer data and robust, theory-driven restrictions is required. We illustrate this on leading applications.

Modeling Competition and Market Equilibrium in Insurance: Empirical Issues by Pierre-Andre Chiappori and Bernard Salanie. Published in volume 98, issue 2, pages 146-50 of American Economic Review, May 2008

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006, Journal of Political Economy, 114, 175–201), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow’s empirical application to illustrate the potential of our more general approach.

We show that even in the absence of data on individual decisions, the distribution of individual attitudes towards risk can be identified from the aggregate conditions that characterize equilibrium on markets for risky assets. Taking parimutuel horse races as a textbook model of contingent markets, we allow for heterogeneous bettors with very general risk preferences, including non-expected utility. Under a standard single-crossing condition on preferences, we identify the distribution of preferences among the population of bettors and we derive testable implications. We estimate the model on data from U.S. races. Specifications based on expected utility fit the data very poorly. Our results stress the crucial importance of nonlinear probability weighting. They also suggest that several dimensions of heterogeneity may be at work.