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刻画倾向得分在平均处理效应有效估计中的作用。
The role of propensity score in the efficient estimation of the average treatment effects is examined. If the treatment is ignorable given some observed characteristics, it is shown that the propensity score is ancillary for estimation of the average treatment effects but not for estimation of average treatment effects on the treated. Efficient semiparametric estimators take the form of relevant sample averages of the data completed by the nonparametric imputation method. Projection on the propensity score is not necessary for efficient semiparametric estimation of the average treatment effects on the treated even if the propensity score is known.