You can't always get what you want: Capacity constraints in a choice-based school system

Centralized school enrollment is designed to improve the allocation of seats in choice-based systems. We study the quality of K-12 public school placements relative to revealed family preferences using data from New Orleans, where a market-based school system allocates most seats through a centralized enrollment lottery. We propose a theory of family utility maximization under school choice systems with and without guaranteed placements. Using an instrumental variables strategy, we estimate the causal effect of losing a school placement lottery on the school quality a student receives. We find a significant gap between preferred and actual school quality for students who do not win a first-choice assignment, some of which is regained when multiple rounds of assignment are offered. From the supply side, this allows schools of choice to operate with weak demand by enrolling students who fail to win assignment to oversubscribed schools of greater quality and higher preference ranking.