Functional Form and Heterogeneity in Models for Count Data

William Greene

Foundations and Trends(R) in Econometrics, 2007, vol. 1, issue 2, 113-218

Abstract: 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 analyze 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 briefly present some alternative approaches to modeling heterogeneity.) We also resolve some features in Hausman, Hall and Griliches (1984, Economic models for count data with an application to the patents–R&D relationship, Econometrica 52 , 909–938) 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 (search for similar items in EconPapers)
Date: 2007
References: Add references at CitEc
Citations: View citations in EconPapers (32)

Downloads: (external link)
http://dx.doi.org/10.1561/0800000008 (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:now:fnteco:0800000008

Access Statistics for this article

More articles in Foundations and Trends(R) in Econometrics from now publishers
Bibliographic data for series maintained by Lucy Wiseman ().