Synthetic Controls with Imperfect Pre-Treatment Fit

Bruno Ferman; Cristine Pinto

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arXiv · 1911.08521

Synthetic Controls with Imperfect Pre-Treatment Fit

Bruno Ferman·Cristine Pinto

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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.

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Bruno Ferman, Cristine Pinto. 2021-01-12. Synthetic Controls with Imperfect Pre-Treatment Fit. https://arxiv.org/abs/1911.08521

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