Primary Submission Category: Matching, Weighting
Resampling with Control Reuse: A Valid Bootstrap for Fixed-M Nearest-Neighbor Matching
Authors: Xiang Meng, Aaron Smith,
Presenting Author: Xiang Meng*
Inference after fixed-M nearest-neighbor matching remains challenging because matching induces nonstandard dependence through control reuse. Abadie and Imbens (2008) showed that the naive bootstrap fails when the number of matches is fixed, prompting a substantial literature proposing alternative resampling methods. More recently, Lin and Han (2024) establish that the naive bootstrap is consistent when the number of matches diverges, demonstrating that the classical inconsistency is fundamentally a fixed-M phenomenon. While valid bootstrap procedures are now available when M goes to infinity, a general and practically implementable solution for valid inference under fixed M—the regime most commonly used in applications—remains lacking.
We therefore study inference directly in the fixed-M setting and develop a weighted unit bootstrap for the Average Treatment Effect on the Treated (ATT) that remains valid under fixed-M matching. The central insight is that valid resampling must replicate the unit-level covariance structure induced by shared controls. Rather than re-matching the data or perturbing outcomes independently, the proposed procedure resamples entire units together with their induced matching weights, thereby preserving the dependence created by control reuse.
We show theoretically that the weighted unit bootstrap consistently approximates the asymptotic variance in the general fixed-M framework. This perspective also yields a unified explanation for the failure o