Title: On the mysteries of resampling for matching estimators
Authors: Christopher Walsh - TU Dortmund University (Germany) [presenting]
Carsten Jentsch - TU Dortmund University (Germany)
Shaikh Tanvir Hossain - TU Dortmund University (Germany)
Abstract: In a highly influential paper showed that, in general, the conditional variance of an Efron-type bootstrap for the matching estimator does not converge to the correct limit. However, they also conjecture that the asymptotic variance should be consistently estimable by using a wild bootstrap or an M-out-of-N bootstrap. We prove that the conditional variance of: (i) a wild-type bootstrap procedure recently proposed in general does not converge to the correct limit -- either in the setting considered for the ATET or in a slightly modified design for the ATE; (ii) an M-out-of-N-type bootstrap estimator does converge to the correct limit in expectation in the setting considered previously. Intuitively, the Efron-type bootstrap estimator fails, because it does not replicate the matching algorithm correctly due to the presence of ties in the resamples. This is not the case for the proposed M-out-of-N-type bootstrap as it does not contain any observations more than once with probability one. Extensive simulations support our theoretical findings for the wild-type bootstrap and the M-out-of-N-type bootstrap.