A fundamental problem with nonlinear estimation models is that  estimates are not guaranteed to exist. However, while non-existence is a well-studied issue for binary choice models , it presents significant challenges for other models as well and is not as well understood in more general settings. These challenges are only magnified for models that feature many fixed effects and other high-dimensional parameters. We address the current ambiguity surrounding this topic by studying the conditions that govern 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 estimates of at least some of the linear parameters 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
A fundamental problem with nonlinear models is that maximum likelihood estimates are not guaranteed to exist. Though nonexistence is a well known problem in the binary choice literature , it presents significant challenges for other models as well and is not as well understood in more general settings. These challenges are only magnified for models that feature many fixed effects and other high-dimensional parameters. We address the current ambiguity surrounding this topic by studying the conditions that govern the existence of estimates for (pseudo-)maximum likelihood estimators used to estimate a wide class of generalized linear models (GLMs). We show that some, but not all, of these GLM estimators can still deliver consistent estimates of at least some of the linear parameters when these conditions fail to hold. We also demonstrate how to verify these conditions in models with high-dimensional parameters, such as panel data models with multiple levels of fixed effects.
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estimation
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maximum likelihood
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However, while non-existence is a well-studied issue for binary choice models
Though nonexistence is a well known problem in the binary choice literature
A
(pseudo-)maximum likelihood estimators used to estimate
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GLMs
of these GLM estimators
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the presence of
models with
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fixed effects, as are often recommended in the international trade literature and in other common panel settings
parameters, such as panel data models with multiple levels of fixed effects.