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).
Abadie, Alberto and Guido W. Imbens. "Bias Corrected Matching Estimators for Average Treatment Effects." Journal of Business & Economic Statistics 29.1 (January 2011): 1-11.