Estimating Nested Count Data Models
DOI | http://doi.org/10.1111/1468-0084.00074 |
Date | 01 August 1997 |
Author | Diansheng Dong,Atanu Saha |
Published date | 01 August 1997 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 59, 3 (1997)
0305-9049
PRACTITIONERS CORNER
Estimating Nested Count Data Models
Atanu Saha and Diansheng Dong*
I. INTRODUCTION
In count data models the endogenous variable takes only non-negative
integer values corresponding to the number of events occurring in a given
interval of time or space. Examples of count data model applications
include number of patents applied for by firms (Hausman, Hall, and
Griliches, 1984), number of visits to physicians (Cameron and Trivedi,
1986), number of trips to a recreational area (Hellerstein, 1991), number
of defective products in a manufacturing process (Lambert, 1992), and
number of takeover bids received by a target firm after an initial bid
(Jaggia and Thosar, 1993). Gurmu and Trivedi (1994) provide an excel-
lent survey of the relevant literature.
The benchmark model for count data is the Poisson model. In the
Poisson regression model, however, the conditional mean of the endogen-
ous variable given the exogenous variables is equal to its conditional
variance. To overcome this limitation several generalizations have been
proposed. Among these, negative binomial (NB) models, in which the
conditional variance can exceed the conditional mean (i.e., allow over-
dispersion), have been widely used. Within NB models, specifications
differ in their implied relationship between the conditional mean and
variance of the dependent variable. The purpose of this study is (a) to
propose tests for selection among the Poisson and NB models by formally
demonstrating that the loglikelihood function (LLF) of the general NB
model nests the LLF of the Poisson and the two most widely used
NB models as special cases, and (b) to propose estimation of the general
NB model since it allows greater flexibility in the relationship between the
mean and variance of the dependent variable than the widely used NB
specifications. An application to micro-level data on the number of recre-
ational boating trips illustrates the results.
*The authors thank Teofilo Ozuna for providing the data set used in this study.
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© Blackwell Publishers Ltd, 1997. Published by Blackwell Publishers, 108 Cowley Road, Oxford
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