Demand Analysis using Strategic Reports: An application to a school choice mechanism

Several school districts use assignment systems in which students have a strategic incentive to misrepresent their preferences. Indeed, we find evidence suggesting that reported preferences in Cambridge, MA respond to these incentives. Such strategizing can complicate the analysis of preferences. The paper develops a new method for estimating preferences in such environments. Our approach views the report made by a student as a choice of a probability distribution over assignment to various schools. We introduce a large class of mechanisms for which consistent estimation is feasible. We then study identification of a latent utility preference model under the assumption that agents play a Bayesian Nash Equilibrium. 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. Estimates from Cambridge 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 popular Deferred Acceptance mechanism.