Identification and Estimation in Many-to-one Two-sided Matching without Transfers.

In a setting of many-to-one two-sided matching with non-transferable utilities, e.g., college admissions, we study conditions under which preferences of both sides are identified with data on one single market. The main challenge is that every agent's actual choice set is unobservable to the researcher. Assuming that the observed matching is stable, we show nonparametric and semiparametric identification of preferences of both sides under appropriate exclusion restrictions. Our identification arguments are constructive and thus directly provide a semiparametric estimator. In Monte Carlo simulations, the estimator can perform well but suffers from the curse of dimensionality. We thus adopt a parametric model and estimate it by a Bayesian approach with a Gibbs sampler, which works well in simulations. Finally, we apply our method to school admissions in Chile and conduct a counterfactual analysis of an affirmative action policy.