This issue is devoted to econometric models based on event counts where an event may be thought of as a realization of a point process. Count data models are relevant when the variables of interest are non-negative integer valued random variables, e.g. the number of patent registrations in a given year. In many research areas in economics event counts are not only readily observed but they are also the principal variables of interest. Such models have attracted increasing theoretical analysis and application in microeconometrics, especially since the publication in 1984 of two pathbreaking articles by Gourieroux, Monfort, and Trognon, and Hausman, Hall, and Griliches. Many new econometric models and methods for count data have been developed and applied variously in cross-section, time series, and panel data situations. This special issue brings together a representative selection of eight papers that were presented at various international conferences in 1995 and 1996. Each paper has its own independent motivation and story. However, collectively they involve many interconnected and overlapping themes. As a collection they should lead users to a better appreciation of models and methods for handling the diversity of data situations encountered in practice and of the currently predominant themes in this literature.
Count data may also be analysed within the framework of non-linear regression, without invoking distributional assumptions. The Poisson regression model is a leading example of a count data regression model. It is the oldest parametric count model with a tight distributional and parametric structure. However, in practical applications such a model is often found to inadequately account for the observed properties of data. Flexible models with reยฎnements and greater general applicability are model observed economic data. To accommodate many commonly occurring `non-Poisson' features of economic data sets new models, tools, and techniques continue to be developed. This special issue provides several examples of such endeavours.
A very pervasive feature of count data models is the presence of overdispersion ร this refers to actual variance exceeding nominal variance. This has motivated many generalizations of the Poisson. Many of these generalizations modify the variance function, but not the conditional mean. In contrast, Cameron and Johansson propose an approach that simultaneously aects the speciยฎcation of all conditional moments. They consider generalizations of the Poisson based on a squared polynomial series expansions, similar to that proposed by Gallant and his co-authors for the case of continuous data. Such a model permits a ยฏexible representation of the data-generating process (dgp) and ยฏexible modelling of conditional moments, allowing one to escape the restrictive framework of commonly used parametric count models. This work is a signiยฎcant