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 estim ation of average treatment effects is examined. Under the assumption t hat 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 suggeste d that the marginal value of the propensity score lies entirely in the ''dimension reduction.'' Efficient semiparametric estimators of avera ge treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data complet ed by the nonparametric imputation method. It is shown that the projec tion on the propensity score is not necessary for efficient semiparame tric estimation of average treatment effects on the treated even if th e propensity score is known. An application to the experimental data r eveals that conditioning on the propensity score may even result in a loss of efficiency.