A Bayesian Fix for Synthetic Control: Better Counterfactuals in Small-N Studies

🔍 What the Method Does

Presents a Bayesian alternative to the synthetic control method for comparative case studies with one or multiple treated units. Adopts a Bayesian posterior predictive approach to Rubin's causal model, which yields empirical posterior distributions for counterfactuals and enables inference about both individual and average treatment effects on treated observations.

📊 How Counterfactuals Are Built

• Uses a dynamic multilevel prediction model with a latent factor term to correct biases from unit-specific time trends.
• Allows heterogeneous and dynamic relationships between covariates and the outcome, improving precision of causal estimates.
• Applies a Bayesian shrinkage procedure for model searching and factor selection to reduce model dependence.

🔬 What Simulations Show

Monte Carlo exercises demonstrate that this Bayesian approach:

• Produces more precise causal estimates than existing methods.
• Achieves correct frequentist coverage rates even when sample sizes are small and rich heterogeneities are present in the data.

✍️ Empirical Demonstrations

The method is illustrated with two empirical examples drawn from political economy, showing practical application to real comparative case studies.

⚖️ Why It Matters

Provides a flexible, principled way to estimate counterfactuals and treatment effects in small-N comparative settings, addressing unit-specific trends and heterogeneous relationships while reducing model-selection risk.