In a treatment effect model with unconfoundedness, treatment assignments are not only independent of potential outcomes given the covariates, but also given the propensity score alone. Despite this powerful dimension reduction property, adjusting for the propensity score is known to lead to an...

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...