An Empirical Model of the Medical Match

This paper develops a framework for estimating preferences in two-sided matching markets with non-transferable utility using only data on observed matches. Unlike single-agent choices, matches depend on the preferences of other agents in the market. I use pairwise stability together with a vertical preference restriction on one side of the market to identify preference parameters for both sides of the market. Recovering the distribution of preferences is only possible in an environment with many-to-one matching. These methods allow me to investigate two issues concerning the centralized market for medical residents. First, I examine the antitrust allegation that the clearinghouse restrains competition, resulting in salaries below the marginal product of labor. Counterfactual simulations of a competitive wage equilibrium show that residents’ willingness to pay for desirable programs results in estimated salary markdowns ranging from $23,000 to $43,000 below the marginal product of labor, with larger markdowns at more desirable programs. Therefore, a limited number of positions at high quality programs, not the design of the match, is the likely cause of low salaries. Second, I analyze wage and supply policies aimed at increasing the number of residents training in rural areas while accounting for general equilibrium effects from the matching market. I find that financial incentives increase the quality, but not the number of rural residents. Quantity regulations increase the number of rural trainees, but the impact on resident quality depends on the design of the intervention.