While there is a substantial literature on the relationship between general teacher characteristics and student learning, school districts and states often rely on in-service teacher training as a part of school reform efforts. Recent school reform efforts in Chicago provide an opportunity to...

We bound the distribution of treatment effects under plausible and testable assumptions on the joint distribution of potential outcomes, namely that potential outcomes are mutually stochastically increasing. We show how to test the empirical restrictions implied by those assumptions. The...