Bounding the Population Shares Affected by Treatments

51 Pages Posted: 30 Jul 2014 Last revised: 19 Aug 2016

See all articles by Kirill Borusyak

Kirill Borusyak

University College London - Department of Economics

Date Written: March 25, 2015

Abstract

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

Borusyak, Kirill, Bounding the Population Shares Affected by Treatments (March 25, 2015). Available at SSRN: https://ssrn.com/abstract=2473827 or http://dx.doi.org/10.2139/ssrn.2473827

Kirill Borusyak (Contact Author)

University College London - Department of Economics

Drayton House, 30 Gordon Street
30 Gordon Street
London, WC1H 0AX
United Kingdom

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