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On the consistency of bootstrap for matching estimators

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arxiv 2410.23525 v2 pith:VH2CIBOE submitted 2024-10-31 math.ST econ.EMstat.TH

Ziming Lin , Fang Han This is my paper · ORCID
classification math.STecon.EMstat.TH
keywords bootstrapmatchingabadieestimatorsfixedimbensinconsistencymatches
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abstract

In a landmark paper, Abadie and Imbens (2008) showed that the naive bootstrap is inconsistent when applied to nearest neighbor matching estimators of the average treatment effect with a fixed number of matches. Since then, this finding has inspired numerous efforts to address the inconsistency issue, typically by employing alternative bootstrap methods. In contrast, this paper shows that the naive bootstrap is provably consistent for the original matching estimator, provided that the number of matches, $M$, diverges. The bootstrap inconsistency identified by Abadie and Imbens (2008) thus arises solely from the use of a fixed $M$.

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