Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

TLDR

When treatment assignment is exogenous, adjusting for covariates via the propensity score removes bias in average treatment comparisons, but this adjustment can reduce efficiency. The study seeks to estimate the average effect of a binary treatment on a scalar outcome. By weighting observations with the inverse of a nonparametric propensity score estimate, the authors obtain an efficient average treatment effect estimator that can be viewed as an empirical likelihood estimator incorporating propensity score information.

Abstract

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is exogenous or unconfounded, that is, independent of the potential outcomes given covariates, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the covariates. Rosenbaum and Rubin (1983) show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates. Although adjusting for differences in the propensity score removes all the bias, this can come at the expense of efficiency, as shown by Hahn (1998), Heckman, Ichimura, and Todd (1998), and Robins, Mark, and Newey (1992). We show that weighting by the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the average treatment effect. We provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score.