Estimation of average marginal effects in multiplicative unobserved effects panel models

- I show consistency of some fixed effects averages in the F.E. Poisson setting.
- This implies average marginal effects are estimable in levels, not just proportions.
- I derive the asymptotic variance for this class of estimators.

In multiplicative unobserved effects panel models for nonnegative dependent variables, estimation of average marginal effects would seem problematic with a large cross section and few time periods due to the incidental parameters problem. While fixed effects Poisson consistently estimates the slope parameters of the conditional mean function, marginal effects generally depend on the unobserved heterogeneity. However, I show that a class of fixed effects averages is consistent and asymptotically normal with only the cross section growing. This implies researchers can estimate average treatment effects in levels as opposed to settling for average proportional effects.