Reliable Inference for Matching Estimators with Control Reuse: A Single-Matching Variance Approach
Matching estimators are fundamental in causal inference for drawing population-level conclusions from observational data, yet reliable inference remains challenging. While recent methodological advances have developed asymptotically valid bootstrap procedures and robust standard errors for regression after matching, practical applications reveal severe undercoverage—sometimes missing nominal rates by 20 percentage points even with thousands of observations. Bootstrap methods struggle when control units are extensively reused across matches, while regression-based approaches depend on additional outcome model specification. We refine the inference framework for matching estimators along three fronts. First, we establish a central limit theorem for a broad class of matching procedures—including nearest-neighbor, propensity score, and synthetic-control-based matching—under general heteroskedastic errors. Our proof relies on a weight-regularity condition governing control reuse and extends existing asymptotic theory from Abadie and Imbens (2006), which focuses on fixed-MM nearest-neighbor matching. Second, we propose a single-matching variance estimator that requires only the treated-to-control matching already performed for the point estimate. Unlike Abadie and Imbens (2006), which requires additional treated-to-treated and control-to-control matching, our estimator is consistent for the total asymptotic variance without additional matching and is therefore computationally efficient. Third, extensive simulations demonstrate dramatic improvements in finite-sample coverage: our method achieves 94–99% coverage in challenging nonlinear settings where bootstrap methods achieve only 75%, while maintaining robustness across dimensions and overlap conditions. We also discuss preliminary extensions of the same framework to ATT weighting estimators.
LOCATION:CGIS Knafel Building, Room K354 STATUS:CONFIRMED DTSTART:20260415T160000Z DTEND:20260415T173000Z END:VEVENT END:VCALENDAR