Elsevier

Journal of Econometrics

Volume 46, Issue 3, December 1990, Pages 347-364
Journal of Econometrics

Regression-based tests for overdispersion in the Poisson model

https://doi.org/10.1016/0304-4076(90)90014-KGet rights and content

Abstract

A property of the Poisson regression model is mean-variance equality, conditional on explanatory variables. ‘Regression-based’ tests for this property are proposed in a very general setting. Unlike classical statistical tests, these tests require specification of only the mean-variance relationship under the alternative, rather than the complete distribution whose choice is usually arbitrary. The optimal regression-based test is easily computed as the t-test from an auxiliary regression. If a distribution under the alternative hypothesis is in fact specified and is in the Katz system of distributions or is Cox's local approximation to the Poisson, the score test for the Poisson distribution is equivalent to the optimal regression-based test.

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    This paper is a greatly revised version of a 1985 paper, ‘Regression-Based Tests for Overdispersion’, supported by National Science Foundation Grant SES82-08180. We thank Takeshi Amemiya, Shiferaw Gurmu, Adrian Pagan, Jim Powell, and George Tauchen for very helpful discussions, and two anonymous referees and an Associate Editor for their comments and suggestions for improvements.

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