A Martingale Representation for Matching Estimators
Matching estimators are widely used in statistical data analysis. However, the large sample distribution of matching estimators has been derived only for particular cases. This article establishes a martingale representation for matching estimators. This representation allows the use of martingale limit theorems to derive the large sample 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. In addition, we apply the techniques proposed in this article to derive a correction to the standard error of a sample mean when missing data are imputed using the “hot deck,” a matching imputation method widely used in the Current Population Survey (CPS) and other large surveys in the social sciences. We demonstrate the empirical relevance of our methods using two Monte Carlo designs based on actual datasets. In these Monte Carlo exercises, the large sample distribution of matching estimators derived in this article provides an accurate approximation to the small sample behavior of these estimators. In addition, our simulations show that standard errors that do not take into account hot-deck imputation of missing data may be severely downward biased, while standard errors that incorporate the correction for hot-deck imputation perform extremely well. This article has online supplementary materials.
Volume (Year): 107 (2012)
Issue (Month): 498 (June)
|Contact details of provider:|| Web page: http://www.tandfonline.com/UASA20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/UASA20|
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.:
- Guido W. Imbens, 2003.
"Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review,"
NBER Technical Working Papers
0294, National Bureau of Economic Research, Inc.
- 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, February.
- 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.
- Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
- 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.
- 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).
- Wooldridge, Jeffrey M. & Imbens, Guido, 2009. "Recent Developments in the Econometrics of Program Evaluation," Scholarly Articles 3043416, Harvard University Department of Economics.
- Imbens, Guido & Abadie, Alberto, 2008.
"On the Failure of the Bootstrap for Matching Estimators,"
3043415, Harvard University Department of Economics.
- 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.
- Alberto Abadie & Guido W. Imbens, 2006. "On the Failure of the Bootstrap for Matching Estimators," NBER Technical Working Papers 0325, National Bureau of Economic Research, Inc.
- Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
- 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.
- 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.
- 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
- Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working papers 98-7, Massachusetts Institute of Technology (MIT), Department of Economics.
- Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working Papers 780, Princeton University, Department of Economics, Industrial Relations Section..
- Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers 6586, National Bureau of Economic Research, Inc.
When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:833-843. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty)
If references are entirely missing, you can add them using this form.