Bounding the Population Shares Affected by Treatments
51 Pages Posted: 30 Jul 2014 Last revised: 19 Aug 2016
Date Written: March 25, 2015
The fraction of a population that is affected by a treatment (the “responders”) may be as important to identify as the average magnitude of the treatment effect. I show that if the distributions of potential outcomes with and without treatment are identified, then the total variation distance between them serves as the sharp lower bound on the share of responders. It can be computed for randomized control trials, instrumental variables, and other empirical designs. I demonstrate the usefulness of the approach in three examples of economic interest, related to behavioral biases in retirement savings, electoral fraud, and student cheating.
Keywords: Partial identification, Share of responders, Total variation distance, Treatment effect
JEL Classification: C21, C31
Suggested Citation: Suggested Citation