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.