Nearest neighbor matching: Does the M-out-of-N bootstrap work when the naive bootstrap fails?
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Date
2021
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Abstract
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).
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Keywords
ATET, M-out-of-N bootstrap, matching estimator