NA-DiD: Extending Difference-in-Differences with Capabilities

TL;DR

This paper presents NA-DiD, a novel econometric framework that extends traditional Difference-in-Differences by incorporating non-additive measures via the Choquet integral, improving impact estimation accuracy in complex treatment scenarios.

Contribution

It introduces the NA-DiD framework, extending classical DiD with non-additive measures, and provides theoretical properties and practical implementation for impact evaluation.

Findings

NA-DiD offers more accurate effect estimates than classical DiD.

Classical DiD can overestimate effects due to non-linear treatment dynamics.

NA-DiD effectively captures non-linear aggregation in impact assessment.

Abstract

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.