Econometric Reviews· 2026Q2
Verifying the existence of maximum likelihood estimates for generalized linear models
- 40citations
- Q2SCImago
- 2026year
Short summary
New methods verify conditions for the existence of maximum likelihood estimates in generalized linear models (GLMs), especially those with high-dimensional parameters, showing some estimators remain consistent even when conditions fail.
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Key points
- Establishes conditions for the existence of maximum likelihood estimators in a wide class of generalized linear models (GLMs).
- Demonstrates that some GLM estimators can provide consistent estimates for linear parameters even when existence conditions fail.
- Provides a method to verify existence conditions in models with high-dimensional parameters, like panel data models with multiple fixed effects.
- Shows that failing to detect nonexistence can result in misleading numerical estimates, as illustrated with a gravity model.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 response model literature, it presents significant challenges for other models 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. Applying our methods to a gravity model with heterogeneous free trade agreement effects, we show that failing to detect nonexistence can produce misleading numerical estimates.
The authors' abstract, as published at the source. Econometric Reviews, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics