Misspecified Exponential Regressions: Estimation, Interpretation, and Average Marginal Effects

Exponential regressions are frequently used when outcomes are non-negative. They are attractive because they are easy to interpret and to estimate, using pseudo maximum likelihood (PML). However, the validity of these methods depends on the correct specification of the conditional expectation, and little is known regarding their properties when the conditional expectation is misspecified. We show that PML estimators of misspecified exponential models provide optimal approximations to the conditional expectation, in a weighted mean squared error sense, and we give conditions under which their Poisson PML estimator identifies average marginal effects.