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). We show that some, but not all, GLMs can still deliver consistent, uniquely-identified maximum likelihood estimates of at least some of the linear parameters at the boundary of the parameter space when these conditions fail to hold. We also demonstrate how to verify this condition in the presence of high-dimensional fixed effects, which are often recommended in the international trade literature and in other common panel settings.
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). We show that some, but not all, GLMs can still deliver consistent, uniquely-identified maximum likelihood estimates of at least some of the linear parameters at the boundary of the parameter space when these conditions fail to hold. We also demonstrate how to verify these conditions in the presence of high-dimensional fixed effects, as are often recommended in the international trade literature and in other common panel settings.
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