Propensity score matching is widely used in treatment evaluation to estimate average treatment effects. Nevertheless, the role of the propensity score is still controversial. Since the propensity score is usually unknown and has to be estimated, the efficiency loss arising from not knowing the true propensity score is examined. Hahn (1998) derived the asymptotic variance bounds for known and unknown propensity scores. Whereas the variance of the average treatment effect is unaffected by knowledge of the propensity score, the bound for the treatment effect on the treated changes if the propensity score is known. However, the reasons for this remain unclear. In this paper it is shown that knowledge of the propensity score does not lead to a 'dimension reduction'. Instead, it enables a more efficient estimation of the distribution of the confounding variables.
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Find related papers by JEL classification: C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
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