Extend the de Chaisemartin et al. equivalence result to recurrent-event settings

Establish whether the equivalence between the relevant imputation and regression-based estimators can be achieved in the more general time-varying-treatment framework of de Chaisemartin et al. when treatment is represented by recurrent events.

Background

The paper shows that the equivalence result of Wooldridge can be generalized to recurrent-event settings, allowing sufficiently flexible TWFE specifications to recover average total treatment-trajectory effects. It also observes that recurrent events can be embedded in the more general framework of de Chaisemartin et al., which accommodates trajectories of continuous treatment intensity.

The unresolved issue is whether the same equivalence between the regression and imputation approaches can be established directly within that more general framework. The problem concerns extending the methodological equivalence beyond the structured recurrent-event environment analyzed in the paper.

References

That the same can be achieved in the more general environment of \citet{de_chaisemartin_did_2024} is a conjecture I leave for future work.

— First as Tragedy? Second as What? Estimating Dynamic Effects of Recurrent Events  (2609.30007 - Keiller, 24 Sep 2026) in Section 2, subsection discussing identification limits of conventional difference-in-differences assumptions

Conditional inference procedures of the kind developed for pre-trend testing could in principle be adapted to the present setting, and I leave this to future work.

— First as Tragedy? Second as What? Estimating Dynamic Effects of Recurrent Events  (2609.30007 - Keiller, 24 Sep 2026) in Section 3.3, subsection “Diagnostic Test of Effect-Growth Selection”