The Value of Knowing the Propensity Score for Estimating Average Treatment Effects

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 estimator of the average treatment effect with lower asymptotic efficiency than one based on adjusting for all covariates. Moreover, knowledge of the propensity score does not change the efficiency bound for estimating average treatment effects, and many empirical strategies are more efficient when an estimate of the propensity score is used instead of its true value. Here, we resolve this "propensity score paradox" by demonstrating the value of knowledge of the propensity score. We show that by exploiting such knowledge properly, it is possible to construct an efficient treatment effect estimator that is not affected by the "curse of dimensionality", which yields desirable second order asymptotic properties and finite sample performance. The method combines knowledge of the propensity score with a nonparametric adjustment for covariates, building on ideas from the literature on double robust estimation. It is straightforward to implement, and performs well in simulations. We also show that confidence intervals based on our estimator and a simple variance estimate have remarkably robust coverage properties with respect to the implementation details of the nonparametric adjustment step.