Fixed and Random Effects Models for Count Data

14 Pages Posted: 13 Oct 2008

See all articles by William H. Greene

William H. Greene

New York University Stern School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: May 2007


The most familiar fixed effects (FE) and random effects (RE) panel data treatments for count data were proposed by Hausman, Hall and Griliches (HHG) (1984). The Poisson FE model is particularly simple and is one of a small few known models in which the incidental parameters problem is, in fact, not a problem. The same is not true of the negative binomial (NB) model. Researchers are sometimes surprised to find that the HHG formulation of the FENB model allows an overall constant a quirk that has also been documented elsewhere. We resolve the source of the ambiguity, and consider the difference between the HHG FENB model and a true FENB model that appears in the familiar index function form.The familiar RE Poisson model using a log gamma heterogeneity term produces the NB model. The HHG RE NB model is also unlike what might seem the natural application in which the heterogeneity term appears as an additive common effect in the conditional mean. We consider the lognormal model as an alternative RENB model in which the common effect appears in a natural index function form.

Keywords: Poisson regression, Negative binomial, Panel data, Heterogeneity;, Lognormal;, Fixed effects, Random effects

Suggested Citation

Greene, William H., Fixed and Random Effects Models for Count Data (May 2007). NYU Working Paper No. 2451/26046, Available at SSRN:

William H. Greene (Contact Author)

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