Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand

49 Pages Posted: 1 Nov 2006  

Richard K. Crump

Federal Reserve Banks - Federal Reserve Bank of New York

V. Joseph Hotz

Duke University; National Bureau of Economic Research (NBER); IZA Institute of Labor Economics

Guido W. Imbens

Stanford Graduate School of Business

Oscar A. Mitnik

Inter-American Development Bank; IZA Institute of Labor Economics

Date Written: September 2006

Abstract

Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1, 0.9].

Keywords: average treatment effects, causality, unconfoundedness, overlap, treatment effect heterogeneity

JEL Classification: C14, C21, C52

Suggested Citation

Crump, Richard K. and Hotz, V. Joseph and Imbens, Guido W. and Mitnik, Oscar A., Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand (September 2006). IZA Discussion Paper No. 2347. Available at SSRN: https://ssrn.com/abstract=937912

Richard K. Crump (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States

V. Joseph Hotz

Duke University ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708
United States
919-660-1841 (Phone)
919-684-8974 (Fax)

HOME PAGE: http://www.econ.duke.edu/~vjh3

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

IZA Institute of Labor Economics ( email )

P.O. Box 7240
Bonn, D-53072
Germany

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Oscar A. Mitnik

Inter-American Development Bank ( email )

1300 New York Ave, NW
Washington, DC 20577
United States

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

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