Bayesian Synthetic Control Methods
43 Pages Posted: 9 Jun 2019
Date Written: January 27, 2019
We 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 and a natural mechanism to deal with the “large p, small n” and sparsity problems through Markov Chain Monte Carlo (MCMC) procedures. We find via simulations that for a variety of data generating processes, the proposed BSCMs almost always provide better predictive accuracy than extant SCMs. We demonstrate an application of the proposed BSCMs to real-world data of a tax imposed on sales of soda in Washington state in 2010. As in the simulations, the proposed models show good in-sample fit in the pre-treatment periods and better predictive accuracy than extant models. We find that the tax led to an increase of 5.7% in retail price and a decrease of 5.5~5.8% in sales. We also find that retailers in Washington over-shifted the tax to consumers, leading to a pass-through rate of about 121%.
Keywords: Synthetic Control, Treatment Effect, Bayesian Estimation, Soda Tax
JEL Classification: C10, C11
Suggested Citation: Suggested Citation