Housing choices, sorting, and the distribution of educational benefits under deferred acceptance

I study the welfare and distributional consequences of introducing the student‐proposing deferred acceptance in a model where schools have exogenous qualities and the benefit from attending a school is supermodular in school quality and student type. Unlike neighborhood assignment, deferred acceptance induces nonpositive assortative matching where higher type students do not necessarily choose neighborhoods with better schools. Student types are more heterogeneous within neighborhoods under deferred acceptance. Assuming an elastic housing supply, deferred acceptance benefits residents in lower quality neighborhoods with more access to higher quality schools. Moreover, more parents will “vote with their feet” for deferred acceptance, other things equal, than for neighborhood assignment.