Matching on the Estimated Propensity Score

22 Pages Posted: 31 Aug 2009  

Alberto Abadie

Harvard University - Harvard Kennedy School (HKS); National Bureau of Economic Research (NBER)

Guido W. Imbens

Stanford Graduate School of Business

Date Written: August 2009

Abstract

Propensity score matching estimators (Rosenbaum and Rubin, 1983) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators. Moreover, we derive an adjustment to the large sample variance of propensity score matching estimators that corrects for first step estimation of the propensity score. In spite of the great popularity of propensity score matching estimators, these results were previously unavailable in the literature.

Suggested Citation

Abadie, Alberto and Imbens, Guido W., Matching on the Estimated Propensity Score (August 2009). NBER Working Paper No. w15301. Available at SSRN: https://ssrn.com/abstract=1463894

Alberto Abadie (Contact Author)

Harvard University - Harvard Kennedy School (HKS) ( email )

79 John F. Kennedy Street
Cambridge, MA 02138
United States
617-496-4547 (Phone)
617-495-2575 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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