A0482
Title: Semiparametric Bayesian difference-in-differences
Authors: Christoph Breunig - University of Bonn (Germany)
Ruixuan Liu - Chinese University of Hong Kong (Hong Kong)
Zhengfei Yu - University of Tsukuba (Japan) [presenting]
Abstract: Semiparametric Bayesian inference is studied for the average treatment effect on the treated (ATT) within the difference-in-differences research design. Two new Bayesian methods are proposed with frequentist validity. The first one places a standard Gaussian process prior on the conditional mean function of the control group. Asymptotic equivalence of the Bayesian estimator and an efficient frequentist estimator is obtained by establishing a semiparametric Bernstein-von Mises (BvM) theorem. The second method is a double-robust Bayesian procedure that adjusts the prior distribution of the conditional mean function and subsequently corrects the posterior distribution of the resulting ATT. A semiparametric BvM result is established under double robust smoothness conditions; i.e., the lack of smoothness of conditional mean functions can be compensated by the high regularity of the propensity score, and vice versa. Monte Carlo simulations and an empirical application demonstrate that the proposed Bayesian DiD methods exhibit strong finite-sample performance compared to existing frequentist methods. Finally, an extension is outlined to difference-in-differences with multiple periods and staggered entry
