Synthetic Controls with Imperfect Pre-Treatment Fit

TL;DR

This paper examines the biases of Synthetic Control methods under imperfect pre-treatment fit, proposing a demeaned version that reduces bias and variance, along with a test for its validity, guiding empirical application.

Contribution

It introduces a demeaned Synthetic Control estimator that improves bias and variance properties under imperfect pre-treatment fit, with a new specification test.

Findings

Demeaned SC reduces bias compared to standard SC.

Demeaned SC outperforms difference-in-differences in variance.

Provides a practical test for the validity of the demeaned SC estimator.

Abstract

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. Given our theoretical results, we provide practical guidance for applied researchers on how to justify the use of such estimators in empirical applications.