Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/247557 
Year of Publication: 
2020
Citation: 
[Journal:] Econometrics [ISSN:] 2225-1146 [Volume:] 8 [Issue:] 1 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-36
Publisher: 
MDPI, Basel
Abstract: 
The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of "Poisson-ness" with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context.
Subjects: 
binomial distribution
Hellinger distance
Katz family of distributions
negative binomial distribution
point optimal test
regression
score test
JEL: 
C12
C25
C46
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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