Bayesian Synthetic Control Methods

43 Pages Posted: 9 Jun 2019

See all articles by Sungjin Kim

Sungjin Kim

Cornell University, Samuel Curtis Johnson Graduate School of Management

Clarence Lee

Cornell University - Samuel Curtis Johnson Graduate School of Management

Sachin Gupta

Cornell University - Samuel Curtis Johnson Graduate School of Management

Date Written: January 27, 2019

Abstract

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

Kim, Sungjin and Lee, Clarence and Gupta, Sachin, Bayesian Synthetic Control Methods (January 27, 2019). Available at SSRN: https://ssrn.com/abstract=3382359 or http://dx.doi.org/10.2139/ssrn.3382359

Sungjin Kim (Contact Author)

Cornell University, Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY
United States

Clarence Lee

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY 14853
United States

HOME PAGE: http://https://www.johnson.cornell.edu/Faculty-And-Research/Profile?id=cl2278

Sachin Gupta

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY 14853
United States

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