Bias-Corrected Matching Estimators for Average Treatment Effects

TLDR

Matching estimators suffer from a conditional bias that decays slower than \(N^{1/2}\), so they are not \(N^{1/2}\)-consistent in general. This paper proposes a bias‑correction that renders matching estimators \(N^{1/2}\)-consistent and asymptotically normal. The authors illustrate the correction on the National Supported Work data and conduct a small simulation study based on that example. In the simulation, the bias‑corrected estimator achieves lower bias, smaller root‑mean‑squared error, and better coverage than both simple matching and regression estimators. Software implementing the proposed estimators is available on the authors’ web pages (http://www.economics.harvard.edu/faculty/imbens/software.html).

Abstract

In Abadie and Imbens (2006), it was shown that simple nearest-neighbor matching estimators include a conditional bias term that converges to zero at a rate that may be slower than N1/2. As a result, matching estimators are not N1/2-consistent in general. In this article, we propose a bias correction that renders matching estimators N1/2-consistent and asymptotically normal. To demonstrate the methods proposed in this article, we apply them to the National Supported Work (NSW) data, originally analyzed in Lalonde (1986). We also carry out a small simulation study based on the NSW example. In this simulation study, a simple implementation of the bias-corrected matching estimator performs well compared to both simple matching estimators and to regression estimators in terms of bias, root-mean-squared-error, and coverage rates. Software to compute the estimators proposed in this article is available on the authors' web pages (http://www.economics.harvard.edu/faculty/imbens/software.html) and documented in Abadie et al. (2003).