Generalized Synthetic Control Method with State-Space Model

Synthetic control method (SCM) is a widely used approach to assess the treatment effect of a point-wise intervention for cross-sectional time-series data. The goal of SCM is to approximate the counterfactual outcomes of the treated unit as a combination of the control units' observed outcomes. Many studies propose a linear factor model as a parametric justification for the SCM that assumes the synthetic control weights are invariant across time. However, such an assumption does not always hold in practice. We propose a generalized SCM with time-varying weights based on state-space model (GSC-SSM), allowing for a more flexible and accurate construction of counterfactual series. GSC-SSM recovers the classic SCM when the hidden weights are specified as constant. It applies Bayesian shrinkage for a two-way sparsity of the estimated weights across both the donor pool and the time. On the basis of our method, we shed light on the role of auxiliary covariates, on nonlinear and non-Guassian state-space model, and on the prediction interval based on time-series forecasting. We apply GSC-SSM to investigate the impact of German reunification and a mandatory certificate on COVID-19 vaccine compliance.