As standards and accountability have become an increasingly prominent feature of the educational landscape, educators have relied more on remedial programs such as summer school and grade retention to help low-achieving students meet minimum academic standards. Yet the evidence on the...

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...