Bayesian Predictive Synthetic Control Methods

We study Bayesian model synthesis for synthetic control methods (SCMs). SCMs have garnered significant attention as an indispensable tool for comparative case studies. The fundamental concept underlying SCMs involves the prediction of counterfactual outcomes for a treated unit by a weighted summation of observed outcomes from untreated units. In this study, we reinterpret the untreated outcomes as predictors for the treated outcomes and employ Bayesian predictive synthesis (BPS) to synthesize these forecasts. We refer to our novel approach as Bayesian Predictive SCM (BPSCM). The BPSCM represents a comprehensive, and foundational framework encompassing diverse statistical models, including dynamic linear models and mixture models, and generalizes SCMs significantly. Moreover, our proposal possesses the capability to synthesize a range of predictive models utilizing covariates, such as random forests. From a statistical decision-making perspective, our method can be interpreted as a Bayesian approach aimed at minimizing regrets in the prediction of counterfactual outcomes. Additionally, Bayesian approaches can effectively address challenges encountered in frequentist SCMs, such as statistical inference with finite sample sizes, timevarying parameters, and model misspecification. Through the utilization of simulation examples and empirical analysis, we substantiate the robustness of our proposed BPSCM.