While the mechanism design paradigm emphasizes notions of efficiency based on agent preferences, policymakers often focus on alternative objectives. School districts emphasize educational achievement, and transplantation communities focus on patient survival. It is unclear whether choice-based mechanisms perform well when assessed based on these outcomes. This paper evaluates the assignment mechanism for allocating deceased donor kidneys on the basis of patient life-years from transplantation (LYFT). We examine the role of choice in increasing LYFT and compare realized assignments to benchmarks that remove choice. Our model combines choices and outcomes in order to study how selection affects LYFT. We show how to identify and estimate the model using instruments derived from the mechanism. The estimates suggest that the design in use selects patients with better post-transplant survival prospects and matches them well, resulting in an average LYFT of 9.29, which is 1.75 years more than a random assignment. However, the maximum aggregate LYFT is 14.08. Realizing the majority of the gains requires transplanting relatively healthy patients, who would have longer life expectancies even without a transplant. Therefore, a policymaker faces a dilemma between transplanting patients who are sicker and those for whom life will be extended the longest.
We study estimation and non-parametric identification of preferences in two-sided matching markets using data from a single market with many agents. We consider a model in which preferences of each side of the market are vertical, utility is non-transferable and the observed matches are pairwise stable. We show that preferences are not identified with data on one-to-one matches but are non-parametrically identified when data from many-to-one matches are observed. The additional empirical content in many-to-one matches is illustrated by comparing two simulated objective functions, one that does and the other that does not use information available in many-to-one matching. We also prove consistency of a method of moments estimator for a parametric model under a data generating process in which the size of the matching market increases, but data only on one market is observed. Since matches in a single market are interdependent, our proof of consistency cannot rely on observations of independent matches. Finally, we present Monte Carlo studies of a simulation based estimator.