Synthetic Controls with Imperfect Pre-Treatment Fit

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 also show that a modified version of the SC method can substantially improve in terms of bias and variance relative to standard methods. We also consider the properties of these estimators in settings with non-stationary common factors