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Synthetic Controls with Imperfect Pre-Treatment Fit

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  • Bruno Ferman
  • Cristine Pinto
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.

Suggested Citation

  • Bruno Ferman & Cristine Pinto, 2019. "Synthetic Controls with Imperfect Pre-Treatment Fit," Papers 1911.08521, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:1911.08521
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