A Martingale Representation for Matching Estimators

14 Pages Posted: 30 Mar 2009  

Alberto Abadie

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

Guido W. Imbens

Stanford Graduate School of Business

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Abstract

Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for matching estimators. This representation allows the use of martingale limit theorems to derive the asymptotic distribution of matching estimators. As an illustration of the applicability of the theory, we derive the asymptotic distribution of a matching estimator when matching is carried out without replacement, a result previously unavailable in the literature.

Keywords: matching, martingales, treatment effects, hot-deck imputation

JEL Classification: C13, C14, C21

Suggested Citation

Abadie, Alberto and Imbens, Guido W., A Martingale Representation for Matching Estimators. IZA Discussion Paper No. 4073. Available at SSRN: https://ssrn.com/abstract=1369819

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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