Event studies often conflate direct treatment effects with indirect effects operating through endogenous covariate adjustment. We develop a dynamic panel event study framework that separates these effects. The framework allows for persistent outcomes and treatment effects and for covariates that respond to past outcomes and treatment exposure. Under sequential exogeneity and homogeneous feedback, we establish point identification of common parameters governing outcome and treatment effect dynamics, the distribution of heterogeneous treatment effects, and the covariate feedback process. We propose an algorithm for dynamic decomposition that enables researchers to assess the relative importance of each effect in driving treatment effect dynamics.
Botosaru et al. (Fri,) studied this question.