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A growing number of central authorities use assignment mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms incentivize students to strategically misreport their preferences. In this paper, we provide an approach for identifying the causal effects of school assignment on future outcomes that accounts for strategic misreporting. Misreporting may invalidate existing point-identification approaches, and we derive sharp bounds for causal effects that are robust to strategic behavior. Our approach applies to any mechanism as long as there exist placement scores and cutoffs that characterize that mechanism's allocation rule. We use data from a deferred acceptance mechanism that assigns students to more than 1,000 university-major combinations in Chile. Matching theory predicts that students' behavior in Chile should be strategic because they can list only up to eight options, and we find empirical evidence consistent with such behavior. Our bounds are informative enough to reveal significant heterogeneity in graduation success with respect to preferences and school assignment.

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This paper builds, identifies and estimates a model of the labor market that features strategic interactions in wage setting and two-sided heterogeneity in order to shed light on the sources of wage inequality. We provide a tractable characterization of the model equilibrium and demonstrate its existence and uniqueness. This characterization of the equilibrium allows us to derive a rich set of comparative statics and to gauge the relative contributions of worker skill, preference for amenities and strategic interactions to equilibrium wage inequality. Using instrumental variables, we establish identification of labor demand and supply parameters and estimate them using matched employer-employee data from Denmark. Using our estimated structural model, we perform a series of counterfactual analyses in order to provide a quantitative evaluation of the main sources of wage inequality in Denmark.