Estimating a Game of Managing School District Capacity as Parents Vote with Their Feet∗

Many urban districts confront the necessity of closing schools due to declining enrollments. To address this important policy issue, we formulate a sequential game of managing a school district’s student capacity. We show that a Perfect Bayesian Equilibrium exists and characterize its properties. Using data for a mid-sized district with declining enrollments, we estimate the parameters of our model. We show that consideration of student sorting is vital to the assessment of any school closing policy. We find that the district can reduce excess school capacity by closing underperforming schools. This approach inevitably leads to disruptive displacement of students in closed schools. Moreover, a significant fraction of students leaves the district. We also show that superintendents confront a difficult dilemma: pursuing an equity objective, such as limiting demographic stratification across schools, results in the exit of many more students than are lost by an objective such as closing underperforming schools.