Bayesian Causal Synthesis for Supra-Inference on Heterogeneous Treatment Effects

We propose a novel Bayesian methodology to mitigate misspecification and improve estimating treatment effects. A plethora of methods to estimate -- particularly the heterogeneous -- treatment effect have been proposed with varying success. It is recognized, however, that the underlying data generating mechanism, or even the model specification, can drastically affect the performance of each method, without any way to compare its performance in real world applications. Using a foundational Bayesian framework, we develop Bayesian causal synthesis; a supra-inference method that synthesizes several causal estimates to improve inference. We provide a fast posterior computation algorithm and show that the proposed method provides consistent estimates of the heterogeneous treatment effect. Several simulations and an empirical study highlight the efficacy of the proposed approach compared to existing methodologies, providing improved point and density estimation of the heterogeneous treatment effect.