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Synthetic Controls with Imperfect Pre-Treatment Fit
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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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Correlated Synthetic Controls
Correlated Synthetic Controls, a weight-sharing synthetic control estimator for many treated units, is proposed and shown to have smaller estimation error than difference-in-differences under selection on unobservable...
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