Count data models have found a wide variety of applications not only in applied economics and finance but also in diverse fields ranging from biometrics to political science. Poisson and negative binomial (NB) models have been extensively used in count data analysis. Two particular NB model specifications, NBI and NBII, have been especially popular. However, these models impose arbitrary restrictions on the relation between the conditional mean and variance of the dependent variable, limiting their generality. This study proposes tests for selection among the Poisson and NB models by formally demonstrating that the log likelihood function (LLF) of a general NB model parametrically nests the LLF of the Poisson, NBI and NBII as testable special cases. It also proposes estimation of the general NB model since it allows greater flexibility in the relationship between the mean and variance of the dependent variable than NBI and NBII. The empirical application, which uses micro-level data on recreational boating, provides support for the paper’s main theme. Tests clearly reject not only the Poisson, but also NBI and NBII, in favor of a different NB model, underscoring the importance of the general model specification.

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“Estimating Nested Count Data Models,” A. Saha, D. Dong, Oxford Bulletin of Economics and Statistics, 59 (3) (1997), 423–430