🤖 AI Summary
The existence of maximum likelihood estimators (MLEs) in high-dimensional panel models with generalized linear models (GLMs) is frequently overlooked, yet its failure directly invalidates statistical inference. Method: We systematically characterize necessary and sufficient conditions for MLE existence in GLMs with multi-way fixed effects, integrating convex optimization, algebraic statistics, and the separating hyperplane theorem. We propose a computationally tractable existence-checking algorithm based on fixed-effect projection and dimension reduction. Contribution/Results: We establish the first unified existence criterion framework applicable across multiple GLM families—including logistic, Poisson, and negative binomial regression—demonstrating that even when the full MLE does not exist, certain structural parameters remain consistently estimable. This framework substantially enhances estimation reliability, robustness, and parameter interpretability in empirical high-dimensional panel analyses, particularly in fields such as international trade.
📝 Abstract
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
