Modeling Inflated Count Data

This paper extends standard regression models for count data in two ways. The first involves allowing for excess numbers of counts (count inflation) simultaneously at several values other than the zero value. The second involves broadening the class of discrete distributions by considering the Hermite distribution (Kemp and Kemp, 1965). This distribution has not been used previously in the econometrics literature, and when it has been used elsewhere, no consideration has been given to introducing covariates into the model. Two particularly appealing features of the Hermite distribution are its abilities to model multi-modal count data without any modification, and to allow for over-dispersion in the sample. We pursue these extensions of the standard count data models both separately and jointly, and provide several empirical applications that illustrate some of their merits. Our results to date suggest that the Hermite distribution, parameterized to incorporate covariates, offers considerable potential in the modeling of discrete economic data.