We study the effect of different school choice mechanisms on schools' incentives for quality improvement. To do so, we introduce the following criterion: A mechanism respects improvements of school quality if each school becomes weakly better off whenever that school becomes more preferred by students. We first show that no stable mechanism, or mechanism that is Pareto efficient for students (such as the Boston and top trading cycles mechanisms), respects improvements of school quality. Nevertheless, for large school districts, we demonstrate that any stable mechanism approximately respects improvements of school quality; by contrast, the Boston and top trading cycles mechanisms fail to do so. Thus a stable mechanism may provide better incentives for schools to improve themselves than the Boston and top trading cycles mechanisms.
C78: Bargaining Theory; Matching Theory
D78: Positive Analysis of Policy-Making and Implementation
H75: State and Local Government: Health; Education; Welfare; Public Pensions
I21: Analysis of Education