Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility

We introduce an empirical framework for models of matching with imperfectly transferable utility and unobserved heterogeneity in tastes. Our framework allows us to characterize matching equilibrium in a flexible way that includes as special cases the classical fully- and non-transferable utility models, collective models, and settings with taxes on transfers, deadweight losses, or risk aversion. We allow for the introduction of a general class of additive unobserved heterogeneity on agents' preferences. We show existence and uniqueness of an equilibrium under minimal assumptions. We then provide two algorithms to compute the equilibrium in our model. The first algorithm operates under any structure of heterogeneity in preferences; the second is more efficient, but applies only in the case in which random utilities are logit. We show that the log-likelihood of the model has a simple expression and we compute its derivatives. As an empirical illustration, we build a model of marriage with preferences over the partner type and private consumption, which we estimate on a British dataset.