多时间段的双重差分法
Difference-in-Differences with Multiple Time Periods
摘要：
在这篇文章中，我们考虑使用双重差分法（DiD）的处理效应参数的识别，估计和推断程序（i）多个时间段，（ii）治疗时间的变化，以及（iii）当“平行趋势假设“可能仅在对观察到的协变量进行调节后才成立。我们发现，一个家庭的因果效应参数被确定在交错的DiD设置，即使观察到的特征的差异创建组之间的非平行的结果动态。我们的识别结果允许一个使用结果回归，逆概率加权，或双鲁棒被估量。我们还提出了不同的汇总方案，可用于突出不同维度的处理效应异质性，以及总结参与治疗的总体效果。我们建立的估计量的渐近性质，并证明了有效的计算方便的引导程序进行渐近有效的同时（而不是逐点）的推断。最后，我们通过分析2001- 2007年最低工资对青少年就业的影响来说明我们提出的工具的相关性。开源软件可用于实现所提出的方法。
英文摘要：
In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create non-parallel outcome dynamics between groups. Our identification results allow one to use outcome regression, inverse probability weighting, or doubly-robust estimands. We also propose different aggregation schemes that can be used to highlight treatment effect heterogeneity across different dimensions as well as to summarize the overall effect of participating in the treatment. We establish the asymptotic properties of the proposed estimators and prove the validity of a computationally convenient bootstrap procedure to conduct asymptotically valid simultaneous (instead of pointwise) inference. Finally, we illustrate the relevance of our proposed tools by analyzing the effect of the minimum wage on teen employment from 2001--2007. Open-source software is available for implementing the proposed methods.
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