On the consistency of bootstrap for matching estimators

Summary In a landmark paper, Abadie & Imbens (2008)showed that the naive bootstrap is inconsistent when applied to nearest neighbour 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, in this work we show 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 & Imbens (2008)thus arises solely from the use of a fixed $ M $.