The dynamic relationship between school size and academic performance: An investigation of elementary schools in Wisconsin

• We construct a model that allows for feedback from performance to school size.
• Results show that feedback is important and statistically significant.
• The relationship between size and performance is negative and large.

This paper constructs a panel model of school-level performance in which the key explanatory variable is school size. Typical panel models with unobserved effects impose the strict exogeneity assumption, which in this paper, implies a school׳s academic performance cannot impact its future school size. Yet it seems appropriate that, with school-level standardized test scores publicly available and widely reported, school size and school performance should be analyzed dynamically and jointly. We construct a panel model that explicitly allows for “feedback” from academic performance to future school size. We show that, not only is such feedback important, but once it is taken into account, the estimated relationship between school size and academic performance becomes far more negative, relative to models that ignore feedback.