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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.
Markus Frölich (Mon,) studied this question.