Synthetic controls with imperfect pretreatment fit

By Bruno Ferman, Cristine Pinto. Quantitative Economics, 2016

198 citations recorded by the source corpus.

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 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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e58d3b6d259c2b9ea68b8354e8489ef4e324cf2f

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Citations in the corpus

On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls (2019, methodology): “However, when the perfect pretreatment fit condition is relaxed and the number of control units is fixed, Ferman and Pinto (2021) showed that the SC estimator is generally biased when there are unobserved confounders.”
Synthetic Difference In Differences (2018, unknown): “Ferman and Pinto ( 2019 ) analyze the performance of SC estimator using essentially the same model as we do.”
On the role of covariates in the synthetic control method (2019, background): “9See Ferman and Pinto (2018) for the implications of relaxing the perfect balance assumption on pretreatment outcomes.”
Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects (2021, background): “Similarly, one could measure outcomes in differences with respect to pre-intervention means, Ỹjt = Yjt − (1/T0) ∑T0 h=1 Yjh (Ferman and Pinto, 2018).”