This paper introduces a simple school choice model in which all students have the same ordinal preferences over schools but only some have access to an outside option. Our model predicts that, under a manipulable school choice mechanism, students with the outside option are more likely to apply to popular schools. We show that while students with the outside option beneﬁt from manipulable systems, students without the outside option may experience either welfare gains or welfare losses. We evaluate the positive predictions of the model using a diﬀerence-in-diﬀerences design that leverages a change from the Boston mechanism to a deferred acceptance mechanism in the New Haven, Connecticut school district. Consistent with the theoretical predictions, students with an outside option are more likely to list popular, highly-rated schools under the manipulable mechanism, but this gap disappears after the switch to the deferred acceptance mechanism.
This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice
participants in a strategic setting, we show that beliefs about admissions chances differ from
rational expectations values and predict choice behavior. To quantify the welfare costs of belief
errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate
the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of
improving households' belief accuracy. Allowing for belief errors reverses the welfare comparison
to favor the deferred acceptance algorithm.