School Choice and the Housing Market

We develop a unified framework with schools and residential choices and study the welfare and distributional consequences of switching from the traditional neighborhood assignment to the celebrated Deferred Acceptance mechanism. We show that when families receive higher priorities at neighborhood schools, the Deferred Acceptance mechanism improves aggregate or average welfare compared to the neighborhood assignment. Moreover, the Deferred Acceptance mechanism improves the welfare of lowest-income families, both with and without neighborhood priorities. Our work also lays theoretical foundations for analyzing general assignment games with externalities.