Impact of Regression to the Mean on the Synthetic Control Method: Bias and Sensitivity Analysis

To make informed policy recommendations from observational panel data, researchers must consider the effects of confounding and temporal variability in outcome variables. Difference-in-difference methods allow for estimation of treatment effects under the parallel trends assumption. To justify this assumption, methods for matching based on covariates, outcome levels, and outcome trends-such as the synthetic control approach-have been proposed. While these tools can reduce bias and variability in some settings, we show that certain applications can introduce regression to the mean (RTM) bias into estimates of the treatment effect. Through simulations, we show RTM bias can lead to inflated type I error rates and bias toward the null in typical policy evaluation settings. We develop a novel correction for RTM bias that allows for valid inference and show how this correction can be used in a sensitivity analysis. We apply our proposed sensitivity analysis to reanalyze data concerning the effects of California's Proposition 99, a large-scale tobacco control program, on statewide smoking rates.