Yiqing Xu and Xun Pang: A Bayesian Alternative to Synthetic Control for Comparative Case Studies

"A Bayesian Alternative to Synthetic Control for Comparative Case Studies: A Dynamic Multilevel Latent Factor Model with Hierarchical Shrinkage" Yiqing Xu (Stanford) and Xun Pang (Tsinghua University) Discussant: Dmitry Arkhangelsky, CEMFI, Madrid Abstract: This paper proposes a Bayesian alternative to the synthetic control method (SCM) for comparative case studies based on a posterior predictive approach to Rubin's causal model. Our counterfactual imputation method generalizes the SCM by assigning observation-specific parameters to covariates of treated units and exploiting high-order relationships between treated and control time series. The model includes a dynamic latent factor term to correct biases induced by unit-specific time trends and other unobserved time-varying confounders. To reduce model dependence, we develop a Bayesian hierarchical shrinkage strategy for factor selection and model specification search. It allows researchers to make causal inferences about both individual and average treatment effects based on empirical posterior distributions of treated counterfactuals. We apply this method to simulated data and two empirical examples and show that, compared to existing approaches, our method has smaller biases, higher efficiency, and more flexibility. July 21, 2020