A. Colin Cameron and Pravin K. Trivedi
"Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests "
Journal of Applied Econometrics, 1986, Vol. 1(1), pp.29-54.
This paper deals with specification, estimation and tests of single equation
reduced form type equations in which the dependent variable takes only non-negative
integer values. Beginning with Poisson and compound Poisson models, which
involve strong assumptions, a variety of stochastic models and their implications
are discussed. A number of estimators including maximum likelihood
(MLE), pseudo maximum likelihood (PMLE) and quasi generalised pseudo maximum
likelihood (QGPMLE) and their properties are considered in the light of uncertainty
about the data generation process. The paper also considers the role of tests
in sequential revision of the model specification beginning with the Poisson
case and provides a detailed application of the estimators and tests to a
model of the number of doctor consultations.