TY  - JOUR
AU  - Abadie,Alberto
AU  - Imbens,Guido W.
TI  - On the Failure of the Bootstrap for Matching Estimators
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 325
PY  - 2006
Y2  - June 2006
UR  - http://www.nber.org/papers/t0325
L1  - http://www.nber.org/papers/t0325.pdf
N1  - Author contact info:
Alberto Abadie
John F. Kennedy School of Government
Harvard University
79 JFK Street
Cambridge, MA 02138
Tel: 617/496-4547
Fax: 617/496-5960
E-Mail: alberto_abadie@harvard.edu

Guido Imbens
Department of Economics
Littauer Center
Harvard University
1805 Cambridge Street
Cambridge, MA 02138
Tel: 617/384-7485
Fax: 617/495-7730
E-Mail: imbens@fas.harvard.edu
M2  - featured in NBER digest on 2006-06-26
AB  - 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.
ER  -