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 resulting bounds substantially sharpen bounds based on classical inequalities. We apply our method to estimate bounds on the distribution of effects of attending a Knowledge is Power Program (KIPP) charter school on student academic achievement, and find that a substantial majority of students' math achievement benefitted from attendance, especially those who would have fared poorly in a traditional classroom.
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