Panel data methods for fractional response variables with an application to test pass rates

We revisit the effects of spending on student performance using data from the state of Michigan. In addition to exploiting a dramatic change in funding in the mid-1990s and subsequent nonsmooth changes, we propose nonlinear panel data models that recognize the bounded nature of the pass rate. Importantly, we show how to estimate average partial effects, which can be compared across many different models (linear and nonlinear) under different assumptions and estimated using many different methods. We find that spending has nontrivial and statistically significant effects, although the diminishing effect is not especially pronounced.