Beyond Pretrends: A Discordance-Based Sensitivity Analysis for Difference-in-Differences
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超越预趋势：基于反事实填补不一致性的双重差分敏感性分析
- 研究问题
- 当平行趋势填补与替代反事实填补给出不同结果时，仅依据预趋势的敏感性分析是否会遗漏处理后对照组变化所带来的风险？
- 方法与思路
- 作者建立基于填补不一致性的敏感性模型，用不同假设下平均处理效应的加权预期距离解释模型，并给出最坏不一致性的决策论依据。
- 材料陈述的贡献
- 摘要称，新模型将平行预趋势视为低敏感性的必要但非充分条件，并在南非劳动供给冲击应用中展示与预趋势方法不同的结论。
- 阅读关注点
- 应核对替代填补及假设可信度权重的定义、敏感性参数的标定方式，以及不一致性如何转换为处理效应的敏感性结论。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或接收；摘要未说明权重与参数的具体构造，填补一致也不能直接证明平行趋势成立。
原文摘要
In the canonical Difference-in-Differences design, the control group's post-treatment change serves as an imputation of the treated group's counterfactual change in the same period, an imputation justified by parallel trends. However, differences in group composition can produce between-group differences in how outcomes would evolve over time, rendering this imputation vulnerable to confounding. An alternative imputation -- such as one based on the treated group's pre-treatment change -- avoids such between-group confounding but introduces the risk of confounding from within-group temporal shifts. Ideally, both imputations, each vulnerable to different sources of confounding, would have concordant values, thereby yielding the same causal conclusions. When the imputations are discordant, conclusions under parallel trends hinge more critically on that assumption since alternative imputations would point to different results. Yet in these scenarios, existing pretrends-based sensitivity analyses can show low sensitivity because they ignore post-treatment deviations from pretrends in the control group. This paper therefore proposes a discordance-based sensitivity model in which parallel pretrends are necessary but not sufficient for low sensitivity. I formally justify this model in terms of the expected distance between the ATT under parallel trends and under alternative assumptions, weighted by the joint plausibility of those assumptions. I then provide a decision-theoretic rationale for benchmarking violations of parallel trends using the worst-case discordance between the parallel trends imputation and alternative imputations. Finally, I apply both pretrends- and discordance-based sensitivity models to assess how a labor supply shock influenced electoral support for apartheid-era policies in South Africa, showing how the two approaches yield different results.