Nearest neighbor matching: Does the M-out-of-N bootstrap work when the naive bootstrap fails? - Walsh, Christopher; Jentsch, Carsten; Hossain, Shaikh Tanvir (Technische Universität Dortmund, 2021)
In a seminal paper Abadie and Imbens (2008) showed that the limiting variance of the classi- cal nearest neighbor matching estimator cannot be consistently estimated by a naive Efron-type bootstrap. Specifically, they show that the conditional variance of the Efron-type boostrap es- timator does not converge to the correct limit in expectation. In essence this is due to drawing with replacement such that original observations appear more than once in the bootstrap sample with positive probability even when the sample size becomes large. In the same paper, it is con- jectured that the limiting variance should be consistently estimable by an M-out-of-N bootstrap. Here, we prove that the conditional variance of an M-out-of-N-type bootstrap estimator does in- deed converge to the correct limit in expectation in the setting considered in Abadie and Imbens (2008). The key to the proof lies in the fact that asymptotically the M-out-of-N-type bootstrap sample does not contain any observations more than once with probability one. The finite sample performance of the M-out-of-N-type bootstrap is investigated in a simulation study of the DGP considered by Abadie and Imbens (2008).
Discussion Paper / SFB823;5/2021
Keywords: ATET; M-out-of-N bootstrap; matching estimator; 310; 330; 620