Proportional Treatment Effects in Staggered Settings: An Approach for Poisson Pseudo-Maximum Likelihood

I propose a counterfactual approach to measure proportional treatment effects for staggered multiplicative difference-in-differences (DiD) models with Poisson Pseudo-Maximum Likelihood (PPML). Two-way fixed effect (TWFE) linear estimators do not recover DiD estimates in the presence of a staggered treatment. I show that the wrong comparisons problem extends to TWFE PPML. I provide evidence that robust estimators for the linear case do not naturally extend to PPML, as aggregation of lower-level effects is challenging in the non-linear case. In these settings, my proposed estimator recovers a quantity analogous to that in the canonical 2-by-2 TWFE PPML model: the percent change of the average.