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A Martingale Representation for Matching Estimators


Alberto Abadie


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

Guido W. Imbens


University of California, Berkeley - Department of Economics; National Bureau of Economic Research (NBER); Institute for the Study of Labor (IZA)

IZA Discussion Paper No. 4073

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.

Number of Pages in PDF File: 14

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

JEL Classification: C13, C14, C21

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Date posted: March 30, 2009  

Suggested Citation

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

Contact Information

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
University of California, Berkeley - Department of Economics ( email )
Agricultural and Resource Economics
549 Evans Hall # 3880
Berkeley, CA 94720-3880
United States
510-643-5843 (Phone)
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
Institute for the Study of Labor (IZA)
P.O. Box 7240
Bonn, D-53072
Germany
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