| Summary: | Many school districts allow students to report their preference rankings over schools and assign as many students as possible to their reported favorite schools. However, this well-intended assignment policy, known as the Boston mechanism, creates incentives for students to misreport their true preferences. I consider the problem of estimating students' preference parameters with reported rankings under this policy. Previous literature has made strong assumptions about the who and the how. In this paper I relax these assumptions. My identifying assumptions are that 1) students may have incorrect beliefs about their assignment probabilities as long as they correctly predict to which one of any given two schools they would have lower assignment probability; and 2) when deciding which ranking to report, students adhere to a simple rule: do not put a school on your ranking unless you prefer it to higher-probability ones. I construct moment inequalities that partially identify the preference parameters and propose an estimator of a confidence region of the parameters. Finally, I apply the method to data from Seoul, Korea to compare the efficiency and inequity of the Boston mechanism with Deferred Acceptance, an alternative assignment policy without incentives to misreport. Counterfactual simulations show that the Boston mechanism is more efficient than Deferred Acceptance, but it also penalizes students who naively report their true preferences.
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