Econometrics and Applied Micro Seminar

This paper develops a new method for estimating preferences using data  from single unit  assignment  mechanisms that are not  necessarily  truthfully implementable. Our approach views the report made by an agent as a choice of a probability distribution over her assignments.  We introduce a large class of mechanisms, called report-specific priority  + cutoff mechanisms, for which consistent estimates of these probabilities can be obtained. This class includes almost all known school choice mechanisms used in practice.  We then  study  identification of a latent utility preference model under  the assumption that agents  play a limit Bayesian Nash Equilibrium.  This equilibrium assumption is testable using the available data.  Preferences are non-parametrically identified under either sufficient variation in choice environments or sufficient variation in a special regressor.  We then propose a tractable estimation procedure for a parametric model based on Gibbs' sampling.

We apply our techniques using data from elementary school admissions in Cambridge, MA.  We find evidence that suggests that ranking behavior responds to the strategic incentives in the mechanism.  Our estimates suggest that while 84% of students are assigned to their stated first choice, only 75% are assigned to their true first choice.  The difference occurs because students avoid ranking competitive schools in favor of less competitive schools.  Although the Cambridge mechanism is manipulable, we estimate  that welfare for the  average student would be lower in the  Deferred Acceptance mechanism.

Additional  information can be found at: http://economics.mit.edu/faculty/psomaini