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To make informed policy recommendations from observational data, we must beable to discern true treatment effects from random noise and effects due toconfounding. Difference-in-Difference techniques which match treated units tocontrol units based on pre-treatment outcomes, such as the synthetic controlapproach have been presented as principled methods to account for confounding.However, we show that use of synthetic controls or other matching procedurescan introduce regression to the mean (RTM) bias into estimates of the averagetreatment effect on the treated. Through simulations, we show RTM bias can leadto inflated type I error rates as well as decreased power in typical policyevaluation settings. Further, we provide a novel correction for RTM bias whichcan reduce bias and attain appropriate type I error rates. This correction canbe used to perform a sensitivity analysis which determines how results may beaffected by RTM. We use our proposed correction and sensitivity analysis toreanalyze data concerning the effects of California's Proposition 99, alarge-scale tobacco control program, on statewide smoking rates.

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