Synthetic controls with imperfect pretreatment fit

• 成果类型: Article
• 署名作者: Ferman, Bruno; Pinto, Cristine
• 署名单位: Getulio Vargas Foundation
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE1596
• 发表日期: 2021
• 页码: 1197-1221
• 关键词: Synthetic control; difference-in-differences; Policy Evaluation; linear factor model; C13; C21; C23

摘要

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.