School choice, housing, and inequality (with Georgy Artemov)
Abstract: We study how school choice mechanisms affect sorting by wealth in a model with an endogenous location choice and a subsequent shock on preferences over schools. We show that the Deferred Acceptance (DA) mechanism induces a greater neighborhood sorting than the neighborhood rule (N), and that the Top Trading Cycles (TTC) mechanism makes it even greater than DA. The flexibility of school choice mitigates sorting by wealth at the school level, but this effect does not reverse the ranking; that is, school sorting is the lowest under N and highest under TTC. Housing price premium – a variable that affects residents with or without interest in schools – increases from N to DA to TTC. We also show that the total student welfare is higher under DA than under N.