On the Failure of the Bootstrap for Matching Estimators

39 Pages Posted: 29 Jun 2006  

Alberto Abadie

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

Guido W. Imbens

Stanford Graduate School of Business

Date Written: June 2006

Abstract

Matching estimators are widely used for the evaluation of programs or treatments. Often researchers use bootstrapping methods for inference. However, no formal justification for the use of the bootstrap has been provided. Here we show that the bootstrap is in general not valid, even in the simple case with a single continuous covariate when the estimator is root-N consistent and asymptotically normally distributed with zero asymptotic bias. Due to the extreme non-smoothness of nearest neighbor matching, the standard conditions for the bootstrap are not satisfied, leading the bootstrap variance to diverge from the actual variance. Simulations confirm the difference between actual and nominal coverage rates for bootstrap confidence intervals predicted by the theoretical calculations. To our knowledge, this is the first example of a root-N consistent and asymptotically normal estimator for which the bootstrap fails to work.

Suggested Citation

Abadie, Alberto and Imbens, Guido W., On the Failure of the Bootstrap for Matching Estimators (June 2006). NBER Working Paper No. t0325. Available at SSRN: https://ssrn.com/abstract=912426

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

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Paper statistics

Downloads
65
Rank
283,895
Abstract Views
685