Inference on Finite Population Treatment Effects Under Limited Overlap

43 Pages Posted: 8 Mar 2018 Last revised: 21 Aug 2019

See all articles by Han Hong

Han Hong

Stanford University - Department of Economics

Michael P. Leung

University of Southern California - Department of Economics

Jessie Li

University of California, Santa Cruz - Department of Economics

Date Written: May 13, 2019

Abstract

This paper studies inference on finite population average and local average treatment effects under limited overlap, meaning some strata have a small proportion of treated or untreated units. We model limited overlap in an asymptotic framework sending the propensity score to zero (or one) with the sample size. We derive the asymptotic distribution of analog estimators of the treatment effects under two common randomization schemes: conditionally independent and stratified block randomization. Under either scheme, the limit distribution is the same and conventional standard error formulas remain asymptotically valid, but the rate of convergence is slower the faster the propensity score degenerates. The practical import of these results is twofold. When overlap is limited, standard methods can perform poorly in smaller samples, as asymptotic approximations are inadequate due to the slower rate of convergence. However, in larger samples, standard methods can work quite well even when the propensity score is small.

Keywords: treatment effects, overlap, instrumental variables, stratified randomization, propensity score

Suggested Citation

Hong, Han and Leung, Michael and Li, Jessie, Inference on Finite Population Treatment Effects Under Limited Overlap (May 13, 2019). Available at SSRN: https://ssrn.com/abstract=3128546 or http://dx.doi.org/10.2139/ssrn.3128546

Han Hong

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

Michael Leung

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave.
Kaprielian (KAP) Hall, 310A
Los Angeles, CA 90089
United States

Jessie Li (Contact Author)

University of California, Santa Cruz - Department of Economics ( email )

Santa Cruz, CA 95064
United States

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