Synthetic controls with imperfect pretreatment fit - Bruno Ferman; Cristine Campos de Xavier Pinto (Quantitative Economics, 2021)
We analyze the properties of the Synthetic Control (SC) and related estimators when the pre-treatment fit is imperfect. In this framework, we show that these estimators are generally biased if treatment assignment is correlated with unobserved confounders, even when the number of pre-treatment periods goes to infinity. Still, we show that a demeaned version of the SC method can improve in terms of bias and variance relative to the difference-in-difference estimator. We also derive a specification test for the demeaned SC estimator in this setting with imperfect pre-treatment fit. Given our theoretical results, we provide practical guidance for applied researchers on how to justify the use of such estimators in empirical applications.
Keywords: C13; C21; C23; 330; Synthetic control; difference-in-differences; policy evaluation; linearfactor model