Synthetic controls with imperfect pretreatment fit. Issue 4 (11th November 2021)

• Record Type: Journal Article
• Authors: Ferman, Bruno; Pinto, Cristine
• Is Part Of: Quantitative economics. Volume 12:Issue 4(2021)
• Page Start: 1197
• Page End: 1221
• Publication Date: 2021-11-11
• Subjects: Synthetic control -- difference‐in‐differences -- policy evaluation -- linear factor model; C13 -- C21 -- C23; Economics, Mathematical -- Periodicals; Econometrics -- Periodicals; Economics -- Periodicals; 330.0151
• DOI: 10.3982/QE1596
• Languages: English
• ISSNs: 1759-7323

Abstract

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 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.