Partial Identification of the Distribution of Treatment Effects

This article develops bounds on the distribution of treatment effects under plausible and testable assumptions on the joint distribution of potential outcomes, namely that potential outcomes are stochastically increasing. We show how to test the empirical restrictions implied by those assumptions. The resulting bounds substantially sharpen the classical bounds based on FrechetHoeffding limits. We present an application in which we identify bounds on the distribution of effects of attending a Knowledge is Power Program (KIPP) charter school on student academic achievement.