交错双重差分:处理效应异质性与估计方法选择

Staggered Difference-in-differences Method: Heterogeneous Treatment Effects and Choice of Estimation

双重差分法是社会科学中进行因果推断和政策评估时最广泛采用的研究手段。然而,近年来不断涌现的前沿文献发现,对于交错双重差分的情形,因存在处理效应异质性,采用传统双向固定效应模型可能会造成严重的估计偏误。为此,理论计量领域诞生了多种异质性—稳健的估计方法,但这也让应用者在实践中对如何选取合适的估计方法、如何验证前提假设产生困惑。本文阐释了处理效应异质性导致潜在偏误的根源,总结了三类异质性—稳健估计方法的经济学直觉。本文对比了这些方法的核心假设、应用场景和估计量性质,通过模拟数据检验了估计效果,并对验证“平行性趋势”假设进行了深入讨论。最后,针对国内当前的使用现状,本文结合应用案例和现有综述文章,为应用研究者提供了操作建议。

Difference-in-differences(DID) is one of the most popular methods in social sciences for estimating causal effects. However, recent econometrics research on staggered DID documents that the traditional two-way fixed effect estimator(TWFE) may not provide a valid estimation due to the existence of heterogeneous treatment effects. To solve such a problem, a variety of heterogeneity-robust estimators have been raised. This paper provides a literature review of new trends on staggered DID designs and gives practical suggestions for practitioners.We first survey a fast-growing literature and explain the reasons for the potential estimation bias of static/dynamic TWFE in a staggered DID setting. We then synthesize the intuition of three types of solutions for heterogeneity-robust estimation. Based on the simulation data, we apply these new methods and find that these alternative estimators helpful identifying the true treatment effects under their respective assumptions. We further discuss in detail how to conduct tests for “parallel trend” and how to choose base period in event study. In addition to traditional event-study plots, we also introduce the “Equivalence Test” provided by Liu et al.(2022) and “F-test” proposed by Borusyak et al.(2021). The origin of the pitfalls with TWFE in a staggered DID design is “the forbidden comparisons”, i.e. the previously treated groups compared to newly treated groups. Given this issue, several alternative heterogeneity-robust estimators have been proposed to capture ATT effectively. To compare the differences among various estimators, we further categorize them into three types according to their key ideas and then give application suggestions respectively.(1) We suggest researchers pay attention to three aspects before carrying on “CATT” methods: whether the sample size is large enough, whether the treatment has ever turned off and whether there exists never-treated samples.(2) We remind researchers that imputation estimators may rely on correct model specification, and if there are unobservable time-varying confounding factors, it is recommended that researchers use the IFEct or MC method proposed by Liu et al.(2022).(3) We recommend that researchers choose “stacked regression estimator” with caution since its statistical properties haven’t been rigorously proved and that data replication issues may arise. Our simulation results also support the suggestions above. We find the “CATT” estimators are similar but less efficiency. Imputation estimators can lead to more efficient estimate, but this is not always the case. Stacked regression estimator may lead to bias but researchers can use this method as robustness check.First, this paper reviews the recent advances in the econometrics of staggered DID and summarizes these theoretical works from an applied researcher’s perspective. Our discussion on these heterogeneity-robust estimators highlights the different applicable scenarios of each method and helps to clarify when and how to use these new approaches. Second, this paper explores the differences in the three types of heterogeneity-robust estimation methods from their core assumptions to statistical properties with numerical simulation results. This will help the applied researchers’ better understanding of the characteristics of each method, so as to make reasonable choices in their research.Commonly used TWFE DID specification is susceptible to biased estimates. This paper provides a guidance for applied researchers on how to select an appropriate heterogeneity-robust estimator in combination with the application scenarios, and how to understand and verify the corresponding premise assumptions.