Replication Data for: Using Multiple Pre-treatment Periods to Improve Difference-in-Differences and Staggered Adoption Designs

While a difference-in-differences (DID) design was originally developed with one pre- and one post-treatment period, data from additional pre-treatment periods are often available. How can researchers improve the DID design with such multiple pre-treatment periods under what conditions? We first use potential outcomes to clarify three benefits of multiple pre-treatment periods: (1) assessing the parallel trends assumption, (2) improving estimation accuracy, and (3) allowing for a more flexible parallel trends assumption. We then propose a new estimator, double DID, which combines all the benefits through the generalized method of moments and contains the two-way fixed effects regression as a special case. We show that the double DID requires a weaker assumption about outcome trends and is more efficient than existing DID estimators. We also generalize the double DID to the staggered adoption design where different units can receive the treatment in different time periods. We illustrate the proposed method with two empirical applications, covering both the basic DID and staggered adoption designs. We offer an open-source R package that implements the proposed methodologies.

双重差分（difference-in-differences, DID）方法最初仅设置单期事前与单期事后处理干预阶段，但实际研究中往往可获取多期事前处理阶段的数据。研究者应如何在何种条件下，借助多期事前阶段优化双重差分设计？首先，我们借助潜在结果（potential outcomes）框架阐明多期事前阶段的三大优势：其一，可检验平行趋势假设；其二，提升估计精度；其三，支持更具灵活性的平行趋势假设设定。随后，我们提出全新的双重双重差分（double DID）估计量，该估计量通过广义矩估计（generalized method of moments, GMM）整合上述全部优势，且将双向固定效应回归作为其特殊形式。我们证明，双重双重差分估计量对结果趋势的假设更为宽松，且相较于现有双重差分估计量具有更高的估计效率。此外，我们将双重双重差分估计量推广至渐进式采纳设计（staggered adoption design）场景，该场景中不同个体可于不同时点接受处理干预。我们通过两项实证应用对所提方法进行演示，涵盖基础双重差分与渐进式采纳设计两类场景。我们同步提供实现上述方法论的开源R软件包。