A0297
Title: Doubly robust Bayesian Difference-in-Differences estimators
Authors: Christoph Breunig - University of Bonn (Germany) [presenting]
Abstract: A double robust Bayesian inference procedure is proposed for estimating the average treatment effect on the treated (ATT) within the difference-in-differences research design. Our robustification of the Bayesian procedure involves two important modifications: first, adjusting the prior distributions of the conditional mean function, and second, correcting the posterior distribution of the resulting ATT. We prove the asymptotic equivalence between our Bayesian estimator and efficient frequentist estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness. That is, the lack of smoothness in conditional mean functions can be compensated for by the regularity of the propensity score and vice versa. Consequently, the Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our robust Bayesian procedure leads to a significant reduction in bias for point estimation and accurate coverage of confidence intervals, especially when the dimensionality of covariates is large relative to the sample size and the underlying functions become complex.
