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Synthetic Controls with Imperfect Pre-Treatment Fit

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Document pages: 41 pages

Abstract: We analyze the properties of the Synthetic Control (SC) and relatedestimators when the pre-treatment fit is imperfect. In this framework, we showthat these estimators are generally biased if treatment assignment iscorrelated with unobserved confounders, even when the number of pre-treatmentperiods goes to infinity. Still, we show that a demeaned version of the SCmethod can substantially improve in terms of bias and variance relative to thedifference-in-difference estimator. We also derive a specification test for thedemeaned SC estimator in this setting with imperfect pre-treatment fit. Givenour theoretical results, we provide practical guidance for applied researcherson how to justify the use of such estimators in empirical applications.

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