叠加三差分
Stacked Triple Differences
AI总结：
本文提出叠加三差分方法，通过构建自包含的叠加结构，解决传统三差分在 staggered adoption 下的解释问题，并提供新的加权方案以提高因果估计的透明度和准确性。
摘要：
三差分（DDD）是应用经济学中常用的准实验设计。但在 staggered adoption 情况下，其传统三重固定效应（3WFE）实现继承了差分-in-差分文献中已知的解释问题。本文引入叠加 DDD，通过将叠加差分-in-差分方法扩展到 DDD 设置中，创建自包含的叠加结构，每个结构由事件窗口内的四个单元组成：处理组和清洁对照组，每组包含有资格和无资格的单位。将这些叠加结构附加在一起，形成一个统一的数据集以估计处理效应。证明在每个处理后事件时间点，对叠加数据集应用完全饱和的固定效应线性回归，可以识别出严格正的、基于单元大小加权的叠加层面条件平均处理效应的加权平均。基于这一特征，本文概述了替代的加权方案，以恢复具有清晰解释的因果估计量。叠加 DDD 通过以回归透明性换取效率，提供成对（而非全局）的平行变化趋势，以及对每个处理单位的对照组和聚合权重的直接控制，补充了最近的GMM和插补框架。本文提供了两个实证示例，其中叠加 DDD 得到了与现有方法显著不同的定量结论。
英文摘要：
Triple differences (DDD) is a workhorse quasi-experimental design in applied economics. But, under staggered adoption, its conventional three-way fixed-effects (3WFE) implementation inherits the interpretation issues now well understood in the difference-in-differences literature. I introduce stacked DDD. I extend the stacked difference-in-differences approach to the DDD setting by creating self-contained stacks, each consisting of four cells over an event window: treated and clean comparison cohorts, each with treatment-eligible and treatment-ineligible units. Appending these stacks yields a unified dataset for estimating treatment effects. I prove that, at each post-treatment event-time, a linear regression with fully saturated fixed-effects applied to the stacked dataset identifies a strictly positive, cell-size-weighted average of stack-level conditional average treatment effects, with stack weights proportional to stack-level cell sizes. Building on this characterization, I outline alternative weighting schemes that recover causal estimands with clear interpretations. Stacked DDD complements recent GMM and imputation-based frameworks by trading efficiency for regression-based transparency, pairwise (rather than global) parallel changes-in-trends, and direct control over both the comparison group for each treated unit and the aggregation weights. I provide two empirical illustrations where stacked DDD yields substantially different quantitative conclusions compared to existing procedures.
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