Verifying the Existence of Maximum Likelihood Estimates in Generalized Linear Models

There has been considerable ambiguity over how to verify whether estimates from nonlinear models "exist" and what can be done if they do not. This is the so-called ``separation'' problem. We characterize the problem in detail across a wide range of generalized linear models and introduce a novel method for dealing with it in the presence of high-dimensional fixed effects, as are often recommended for gravity models of international trade and in other common panel data settings. We have included these methods in a new Stata command for HDFE-Poisson estimation called ``PPMLHDFE''. We have also created a suite of test cases developers may use in the future for testing whether their estimation packages are correctly identifying instances of separation. These projects are joint with Sergio Correia and Paulo Guimaraes. We have written two papers related to these topics and also created a website with example code and data illustrating the separation issue and how we solve it. Please see our github for more details: https://github.com/sergiocorreia/ppmlhdfe/