Semiparametric estimation of heterogeneous count data models

Unobserved heterogeneity in a stochastic model is usually represented by a mixing distribution. In this paper a semiparametric estimator is adapted to over-dispersed Poisson regression models. No assumptions are needed about the estimated mixing distribution. The parameters of included explanatory variables are estimated at the same time. The applicability and promising properties of the method are illustrated. Empirically the estimator is applied to a coffee purchase model and to a business travel frequency model subject to zero truncation. The approach is useful, e.g., in marketing research where socio-demographic variables as well as marketing instruments can be included as explanatory variables.