Functional Form and Heterogeneity in Models for Count Data

Leonard N. Stern Economics Working Papers

63 Pages Posted: 17 May 2007

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: April 1, 2007


This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well known variants of the negative binomial model (the NB1 and NB2 forms). We then propose some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these models. The lognormal model provides a versatile alternative specification that is more flexible (and more natural) than the log gamma form, and provides a platform for several "two part" extensions, including zero inflation, hurdle and sample selection models. We also resolve some features in Hausman, Hall and Griliches's (1984) widely used panel data treatments for the Poisson and negative binomial models that appear to conflict with more familiar models of fixed and random effects. Finally, we consider a bivariate Poisson model that is also based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed methods using the data employed in one of the two aforementioned bivariate Poisson studies.

Keywords: Poisson regression, Negative binomial, Panel data, Heterogeneity, Lognormal, Bivariate Poisson, Zero inflation, Two part model, Hurdle model

JEL Classification: C14, C23, C25

Suggested Citation

Greene, William H., Functional Form and Heterogeneity in Models for Count Data (April 1, 2007). Leonard N. Stern Economics Working Papers, Available at SSRN: or

William H. Greene (Contact Author)

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