Functional Form and Heterogeneity in Models for Count Data

By William H. Greene. 2007

192 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/9a3fed42c33447f3daaff376f366f59d5ae7acb4

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Citations in the corpus

Models for count data with endogenous participation (2009, background): “The sample selection model appears in Terza (1995, 1998) and in Greene (1997, 2006, 2007a) , and is included here for completenessandtodeveloptheplatformfortheothertwo.TheZIPandZINBmodels are also established, e.g., by Heilbron (1992), Lambert (1994) andGreene(1994).”
Fixed and Random Effects Models for Count Data (2007, methodology): “However, Greene (2004) provides a solution to this problem that enables the computation even with large N.”
Audit quality, debt financing, and earnings management: Evidence from Jordan (2017, methodology): “The Hausman analysis was employed to examine if there is an endogeneity bias of the independent variables (Greene, 2007). The result of the Hausman analysis shows non-significant evidence of endogeneity bias at the level of 5% (w2 1⁄4 3.136, p=0.21), which has two imperative imputations. Firstly, co”
Discrete Choice Modeling (2007, methodology): “[See Hensher and Greene (2006) and Greene (2007) for discussion.]”