NA-DiD：扩展双重差分法的能力框架 (NA-DiD: Extending Difference-in-Differences with Capabilities)

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This paper introduces the Non-Additive Difference-in-Differences (NA-DiD) framework, which extends classical DiD by incorporating non-additive measures the Choquet integral for effect aggregation. It serves as a novel econometric tool for impact evaluation, particularly in settings with non-additive treatment effects. First, we introduce the integral representation of the classial DiD model, and then extend it to non-additive measures, therefore deriving the formulae for NA-DiD estimation. Then, we give its theoretical properties. Applying NA-DiD to a simulated hospital hygiene intervention, we find that classical DiD can overestimate treatment effects, f.e. failing to account for compliance erosion. In contrast, NA-DiD provides a more accurate estimate by incorporating non-linear aggregation. The Julia implementation of the techniques used and introduced in this article is provided in the appendices.

翻译：本文介绍了非可加双重差分（NA-DiD）框架，该框架通过引入非可加测度——Choquet积分进行效应聚合，从而扩展了经典双重差分法。这一框架为影响评估提供了一种新颖的计量经济学工具，尤其适用于处理效应非可加的场景。首先，我们给出经典双重差分模型的积分表示形式，进而将其推广至非可加测度，由此推导出NA-DiD的估计公式。随后，我们阐述了其理论性质。通过将NA-DiD应用于模拟的医院卫生干预案例，我们发现经典双重差分法可能高估处理效应，例如未能考虑依从性衰减问题。相比之下，NA-DiD通过纳入非线性聚合机制，能够提供更准确的估计结果。本文所使用及提出的相关技术已通过Julia语言实现，代码详见附录。