Before revision: We expand on Santos Silva and Tenreyro (2010)'s observation that estimates from Poisson models are not guaranteed to exist by documenting necessary and sufficient conditions for the existence of estimates for a wide class of generalized linear models (GLMs).
After revision: A fundamental problem with nonlinear estimation models is that estimates are not guaranteed to exist by documenting necessary and sufficient conditions for the existence of estimates for a wide class of generalized linear models (GLMs).