Causal Effects in Matching Mechanisms with Strategically Reported Preferences

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. Misreporting complicates the identification of causal parameters that depend on true preferences, which are necessary inputs for a broad class of counterfactual analyses. In this paper, we provide an identification approach that is robust to strategic misreporting and derive sharp bounds on causal effects of school assignment on future outcomes. 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 and empirical evidence suggests that students behave strategically in Chile because they face constraints on their submission of preferences and have good a priori information on the schools they will have access to. Our bounds are informative enough to reveal significant heterogeneity in graduation success with respect to preferences and school assignment.