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Nearest neighbor matching: M-out-of-N bootstrapping without bias correction vs. the naive bootstrap

Lookup NU author(s): Dr Chris WalshORCiD

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Abstract

It is well known that the limiting variance of nearest neighbor matching estimators cannotbe consistently estimated by a naive Efron-type bootstrap as the conditional variance of thebootstrap estimator does not generally converge to the correct limit in expectation. In essencethis is caused by the fact that the bootstrap sample contains ties with positive probabilityeven when the sample size becomes large. This negative result was originally derived in asimple setting by Abadie and Imbens (ECONOMETRICA, pp. 235–267, 76(6), 2008). Aproof of concept for a direct M-out-of-N boostrap on the data is provided in this setting. Itis proven that in this setting the conditional variance of a direct M-out-of-N-type bootstrapestimator without bias-correction does converge to the correct limit in expectation. The keyto the proof lies in the fact that asymptotically with probability one there are no ties in thebootstrap sample. The potential of the direct M-out-of-N-type bootstrap is investigated ina simulations.

Publication metadata

Author(s): Walsh C, Jentsch C

Publication type: Article

Publication status: Published

Journal: Econometrics and Statistics

Year: 2023

Issue: ePub ahead of Print

Online publication date: 28/04/2023

Acceptance date: 20/04/2023

ISSN (print): 2468-0389

ISSN (electronic): 2452-3062

Publisher: Elsevier

URL: https://doi.org/10.1016/j.ecosta.2023.04.005

DOI: 10.1016/j.ecosta.2023.04.005

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