Paradox in Propensity Score Matching Estimation and the Average Treatment Effect on the Treated

Paradox in Propensity Score Matching Estimation and the Average Treatment Effect on the Treated

In the study we examine the existence of the paradox that using the true propensity scores makes the propensity score matching estimator worse than using the estimated propensity scores in the estimation of the average treatment effect on the treated (ATT). Using a parametric specification of propensity score and standard GMM framework, we show that a variant of the paradox exists in the estimation of ATT as well. We also compare using the average treatment and using the average propensity in intuitive infeasible estimation of ATT and show that nothing dominates the other.