A Note on the Role of the Propensity Score for Estimating Average Treatment Effects
解释了为何已知倾向得分能提高平均处理效应估计效率，指出其通过改善混杂变量分布估计来实现，而非仅因降维。
Abstract Hahn [Hahn, J. (1998). On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica 66:315–331] derived the semiparametric efficiency bounds for estimating the average treatment effect (ATE) and the average treatment effect on the treated (ATET). The variance of ATET depends on whether the propensity score is known or unknown. Hahn attributes this to “dimension reduction.” In this paper, an alternative explanation is given: Knowledge of the propensity score improves upon the estimation of the distribution of the confounding variables.