The Relative Performance of Poisson and Negative Binomial Regression Estimators
| Date | 01 August 2015 |
| DOI | http://doi.org/10.1111/obes.12074 |
| Author | Mckinley L. Blackburn |
| Published date | 01 August 2015 |
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©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 77, 4 (2015) 0305–9049
doi: 10.1111/obes.12074
The Relative Performance of Poisson and Negative
Binomial Regression Estimators
Mckinley L. Blackburn*
*Department of Economics, University of South Carolina, Columbia, SC 29208, USA
(e-mail: blackbrn@moore.sc.edu)
Abstract
Negative binomial estimators are commonly used in estimating models with count-data
dependent variables. In this paper, sampling experiments are used to evaluate the per-
formance of these estimators relative to the simpler Poisson estimator in finite-sample
situations. The results do not suggest a clear preference for negative binomial estimators
in situations in which the underlying dependent variables are overdispersed, unless the
researcher is comfortable in assumptions about the precise form of the overdispersion.
I. Introduction
A constant concern in the regression modelling of count-data dependent variables through
Poisson-regression methods has been the frequent suggestion of overdispersion in most
applications – that is, situations in which the variance of the dependent variableexceeds its
mean. Twodifferent negative binomial estimators have commonly been used as alternatives
to the Poisson, each built on a different assumption about how overdispersion in the data
relates to the mean. If one’s primary interest is in estimating and testing coefficients (rather
than predicting probabilities), it is not obvious that there is any added benefit to using
negative binomial estimators. The Poisson estimator is consistent under the assumptions
used to motivate the alternative estimators, and asymptotically robust inference is possible
(see Wooldridge, 2010).
In what follows, I use sampling experiments to consider the relative merits of the
Poisson and negative binomial estimators in situations in which dependent variables are
overdispersed.Very little prior evidencehas used this type of approach for examining finite-
sample performance for count-data models. Breslow (1990) evaluated the performance of
the Poisson estimator relative to a weighted quasi-likelihood estimator similar to the type
2 negative binomial,1demonstrating little suggestion of bias in either estimator and the
efficiency of the negative binomial estimator when overdispersion was present. Allison
and Waterman (2002) compared the Poisson and type 2 negative binomial estimators in
JEL Classification numbers: C12, C25
1The estimator used a two-step approach, estimating the overdispersionparameter then the coefficients by ML. It
is customary in recent applications of the negative binomial to use a full ML estimator.
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