Synthetic Controls with Imperfect Pre-Treatment Fit

Understand

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 substantially 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.