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A Martingale Representation for Matching Estimators

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Author Info
Abadie, Alberto () (Harvard University)
Imbens, Guido W. () (Harvard University)

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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.

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Publisher Info
Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4073.

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Length: 14 pages
Date of creation: Mar 2009
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Handle: RePEc:iza:izadps:dp4073

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Related research
Keywords: matching; martingales; treatment effects; hot-deck imputation;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Guido Imbens & Jeffrey Wooldridge, 2008. "Recent developments in the econometrics of program evaluation," CeMMAP working papers CWP24/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  2. Imbens, Guido W. & Wooldridge, Jeffrey M., 2008. "Recent Developments in the Econometrics of Program Evaluation," IZA Discussion Papers 3640, Institute for the Study of Labor (IZA). [Downloadable!]
  3. Ben B. Hansen, 2004. "Full Matching in an Observational Study of Coaching for the SAT," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 609-618, January. [Downloadable!] (restricted)
  4. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Blackwell Publishing, vol. 65(2), pages 261-94, April. [Downloadable!] (restricted)
  5. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, 01. [Downloadable!] (restricted)
  6. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366 Elsevier. [Downloadable!] (restricted)
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  7. Guido M. Imbens & Jeffrey M. Wooldridge, 2008. "Recent Developments in the Econometrics of Program Evaluation," NBER Working Papers 14251, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November. [Downloadable!] (restricted)
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  9. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, 06. [Downloadable!] (restricted)
    Other versions:
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