Bayesian Synthetic Control Methods

Abstract

The authors propose a new Bayesian synthetic control framework to overcome limitations of extant synthetic control methods (SCMs). The proposed Bayesian synthetic control methods (BSCMs) do not impose any restrictive constraints on the parameter space a priori. Moreover, they provide statistical inference in a straightforward manner as well as a natural mechanism to deal with the “large p, small n” and sparsity problems through Markov chain Monte Carlo procedures. Using simulations, the authors find that for a variety of data-generating processes, the proposed BSCMs almost always provide better predictive accuracy and parameter precision than extant SCMs. They demonstrate an application of the proposed BSCMs to a real-world context of a tax imposed on soda sales in Washington state in 2010. As in the simulations, the proposed models outperform extant models, as measured by predictive accuracy in the posttreatment periods. The authors find that the tax led to an increase of 5.7% in retail price and a decrease of 5.5%∼5.8% in sales. They also find that retailers in Washington overshifted the tax to consumers, leading to a pass-through rate of approximately 121%.