Primary Submission Category: Matching, Weighting
Inference in Matching: A Novel Variance Estimation Approach for Overlapping Matched Sets
Authors: Xiang Meng, Aaron Smith, Natesh Pillai, Luke Miratrix,
Presenting Author: Xiang Meng*
Matching estimators are widely used in causal inference to estimate treatment effects by pairing treated units with similar control units. While their asymptotic properties are well-studied, finite-sample inference remains challenging, particularly when control units are reused across multiple matches. Existing methods, including the wild bootstrap procedure, can produce unreliable inference when there is substantial overlap in matched samples—a common scenario when the number of treated units is of similar order to the number of control units.
We address this challenge by developing a novel variance estimator that remains valid even under substantial overlap in matched samples. Our approach leverages a more general theoretical framework based on a derivative control condition that improves upon traditional Lipschitz assumptions. This allows for broader applicability in settings where the derivative grows moderately but not uniformly. We prove the consistency of our variance estimator under weaker conditions than existing methods and establish its asymptotic normality.
Through extensive simulation studies, we demonstrate that our method significantly outperforms the state-of-the-art wild bootstrap approach in settings with extensive control unit reuse. While the wild bootstrap achieves only 61% coverage with artificially short confidence intervals in high-overlap scenarios, our method maintains near-nominal coverage rates.