Matching on the Estimated Propensity Score

• 成果类型: Article
• 署名作者: Abadie, Alberto; Imbens, Guido W.
• 署名单位: National Bureau of Economic Research; Stanford University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA11293
• 发表日期: 2016
• 页码: 781-807
• 关键词: Bias

摘要

Propensity score matching estimators (Rosenbaum and Rubin (1983)) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators, and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATET). The adjustment for the ATE estimator is negative (or zero in some special cases), implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples. However, for the ATET estimator, the sign of the adjustment term depends on the data generating process, and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small.