On the role of the propensity score in efficient semiparametric estimation of average treatment effects

In this paper, the role of the propensity score in the efficient estimation of average treatment effects is examined. Under the assumption that the treatment is ignorable given some observed characteristics, it is shown that the propensity score is ancillary for estimation of the average treatment effects. The propensity score is not ancillary for estimation of average treatment effects on the treated. It is suggested that the marginal value of the propensity score lies entirely in the "dimension reduction." Efficient semiparametric estimators of average treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data completed by the nonparametric imputation method. It is shown that the projection on the propensity score is not necessary for efficient semiparametric estimation of average treatment effects on the treated even if the propensity score is known. An application to the experimental data reveals that conditioning on the propensity score may even result in a loss of efficiency.