A Semi-Nonparametric Approach to Model Panel Count Data

Abstract

In count data models, overdispersion of the dependent variable can be incorporated into the model if a heterogeneity term is added into the mean parameter of the Poisson distribution. We use a nonparametric estimation for the heterogeneity density based on a squared Kth-order polynomial expansion, that we generalize for panel data. A numerical illustration using an insurance dataset is discussed. Even if some statistical analyses showed no clear differences between these new models and the standard Poisson with gamma random effects, we show that the choice of the random effects distribution has a significant influence for interpreting our results.

Keywords:

• A posteriori distribution
• Heterogeneity
• Poisson model
• Polynomial expansion
• Semiparametric models

Mathematics Subject Classification:

• 62G08
• 62P05
• 62F03
• 62J12

Acknowledgments

The authors would like to thank two anonymous referees and Catalina Bolancé for her useful advice. Jean-Philippe Boucher would like to thank the Université du Québec ontréal and the Natural Sciences and Engineering Research Concil of Canada for financial support. Montserrat Guillén would like to acknowledge the Spanish Ministry of Education and Science SEJ2007-63298.