Synthetic Control with Time Varying Coefficients A State Space Approach with Bayesian Shrinkage

Abstract

Synthetic control methods are a popular tool for measuring the effects of policy interventions on a single treated unit. In practice, researchers create a counterfactual using a linear combination of untreated units that closely mimic the treated unit. Oftentimes, creating a synthetic control is not possible due to untreated units’ dynamic characteristics such as integrated processes or a time varying relationship. These are cases in which viewing the counterfactual estimation problem as a cross-sectional one fails. In this article, I investigate a new approach to estimate the synthetic control counterfactual incorporating time varying parameters to handle such situations. This is done using a state space framework and Bayesian shrinkage. The dynamics allow for a closer pretreatment fit leading to a more accurate counterfactual estimate. Monte Carlo simulations are performed showcasing the usefulness of the proposed model in a synthetic control setting. I then compare the proposed model to existing approaches in a classic synthetic control case study.