We are grateful for comments by Peter Bickel, Stéphane Bonhomme, Joel Horowitz, Francis Kramarz, Whitney Newey, seminar participants at Princeton, CEMFI, CREST, and Harvard/MIT, and two anonymous reviewers. Financial support for this research was generously provided through NSF Grants SES-0350645 (Abadie), SES-0136789, and SES-0452590 (Imbens).
On the Failure of the Bootstrap for Matching Estimators
Version of Record online: 24 NOV 2008
© 2008 The Econometric Society
Volume 76, Issue 6, pages 1537–1557, November 2008
How to Cite
Abadie, A. and Imbens, G. W. (2008), On the Failure of the Bootstrap for Matching Estimators. Econometrica, 76: 1537–1557. doi: 10.3982/ECTA6474
- Issue online: 24 NOV 2008
- Version of Record online: 24 NOV 2008
- Manuscript received May, 2006; final revision received May, 2008.
- Average treatment effects;
Matching estimators are widely used in empirical economics for the evaluation of programs or treatments. Researchers using matching methods often apply the bootstrap to calculate the standard errors. However, no formal justification has been provided for the use of the bootstrap in this setting. In this article, we show that the standard bootstrap is, in general, not valid for matching estimators, even in the simple case with a single continuous covariate where the estimator is root-N consistent and asymptotically normally distributed with zero asymptotic bias. Valid inferential methods in this setting are the analytic asymptotic variance estimator of Abadie and Imbens (2006a) as well as certain modifications of the standard bootstrap, like the subsampling methods in Politis and Romano (1994).