Dynamic Synthetic Controls: Accounting for Varying Speeds in Comparative Case Studies

Synthetic controls (SCs) are widely used to estimate the causal effect of a treatment. However, they do not account for the different speeds at which units respond to changes. Reactions may be inelastic or “sticky” and thus slower due to varying regulatory, institutional, or political environments. We show that these different reaction speeds can lead to biased estimates of causal effects. We therefore introduce a dynamic SC approach that accommodates varying speeds in time series, resulting in improved SC estimates. We apply our method to re-estimate the effects of terrorism on income (Abadie and Gardeazabal [2003, American Economic Review 93, 113–132]), tobacco laws on consumption (Abadie, Diamond, and Hainmueller [2010, Journal of the American Statistical Association 105, 493–505]), and German reunification on GDP (Abadie, Diamond, and Hainmueller [2015, American Journal of Political Science 59, 495–510]). We also assess the method’s performance using Monte Carlo simulations. We find that it reduces errors in the estimates of true treatment effects by up to 70% compared to traditional SCs, improving our ability to make robust inferences. An open-source R package, dsc, is made available for easy implementation.