Assessing Synthetic Control Estimation of Treatment Effects in Linear Panel Data Models with Multifactor Errors

I study bias reduction properties of Synthetic Control (SC) estimators in settings in which both time fixed effects estimation and difference-in-differences estimation are biased. I assume a multifactor error model in which the treatment assignment depends on unobserved unit-specific characteristics. I show how the SC estimator (Abadie, Diamond, and Hainmueller, 2010) and the demeaned SC estimator (Ferman and Pinto, 2019) reduce the bias under balancing conditions on the confounding characteristics. Monte Carlo evidence suggests that their finite sample performance depends on sufficient penalization of the weight estimation. I revisit the study on the effect of the German reunification (Abadie, Diamond, and Hainmueller, 2015) as an empirical application.