Title: NA-DiD: Extending Difference-in-Differences with capabilities Authors:  Stanislaw Halkiewicz - AGH University of Cracow (Poland) [presenting]
Abstract: A novel reinterpretation is proposed for the classical Difference-in-Differences (DiD) estimator as an integral operator, where treatment effects are aggregated over time using an underlying measure. In the standard framework, the DiD coefficient can be expressed as a Lebesgue integral, which implicitly assumes linearity and additivity in the contribution of treatment periods. Building on this insight, we introduce the Non-Additive Difference-in-Differences (NA-DiD) framework, which generalises the aggregation scheme by replacing the additive measure with a capacity and employing the Choquet integral. This generalisation allows for modelling non-linear aggregation patterns, including synergies, diminishing returns, and threshold effects, which are often observed in real-world interventions but cannot be accommodated within the classical model. The NA-DiD estimator preserves the structure of DiD while relaxing its restrictive assumptions, and coincides with the classical form under additivity. We demonstrate the usefulness of the approach using a simulated intervention with time-varying treatment intensity, where NA-DiD yields more conservative and temporally nuanced estimates than its classical counterpart. The proposed framework provides a flexible and theoretically coherent extension of DiD, particularly well-suited for evaluating interventions with dynamic or non-monotonic effects that challenge the assumptions of standard causal inference methods.