A Bayesian synthetic control method via horseshoe priors

This paper provides a novel Bayesian synthetic control method (BSCM) that integrates a horseshoe prior (H-BSCM) with a panel interactive fixed effects model for policy evaluation involving multiple treated units and staggered treatment timing. Counterfactual posterior distributions are constructed within a Bayesian panel interactive fixed effects framework, with horseshoe priors added to address sparsity in panel data. The new H-BSCM naturally quantifies heterogeneous policy effects while enabling effective variable selection. We further discuss an extension that incorporates hierarchical group structures. Monte Carlo simulations reveal that H-BSCM outperforms existing methods in uncertainty estimation and signal identification. Additional empirical applications across different fields confirm the method’s adaptability. An application to China’s Sulfur Dioxide Emissions Trading Pilot Scheme indicates that the policy significantly reduced industrial SO2 emissions, with effects that vary across regions and over time. Overall, the results highlight the effectiveness and practical applicability of the proposed methodology for policy evaluation.