A Martingale Representation for Matching Estimators

Abadie, Alberto; Imbens, Guido W.

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A Martingale Representation for Matching Estimators

IZA Discussion Paper No. 4073

14 Pages Posted: 30 Mar 2009 Last revised: 12 Sep 2024

See all articles by Alberto Abadie

Alberto Abadie

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

Guido W. Imbens

Stanford Graduate School of Business

There are 2 versions of this paper

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

JEL Classification: C13, C14, C21

Suggested Citation: 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