Can model averaging improve propensity score based estimation of average treatment effects?

When drawing causal inferences from observational data, researchers often model the propensity score. To date, the literature on the estimation of propensity scores is vast, and includes covariate selection algorithms as well as super learners and model averaging procedures. The latter often tune the estimated scores to be either very accurate or to provide the best possible result in terms of covariate balance. This paper focuses on using inverse probability weighting to estimate average treatment effects, and makes the assertion that the context requires both accuracy and balance to yield suitable propensity scores. Using Monte Carlo simulation, the paper studies whether frequentist model averaging can be used to simultaneously account for both balance and accuracy in order to reduce the bias of estimated treatment effects. The candidate propensity scores are estimated using reproducing kernel Hilbert space regression, and the simulation results suggest that model averaging does not improve the performance of the individual estimators.