The Utility of Zero-Inflated Models in the Estimation of the Number of Accidents in the Automobile Insurance Industry

The main purpose of the present paper is to provide an econometric model which estimates the number of automobile accidents that policyholders declare to their insurance companies, pointing out those variables that are significant in this process. Our empirical analysis is based on the data supplied by a private insurance company that operates in Spain, and on the zero-inflated count data models as methodology. We find a positive association between the levels of coverage and the accident rates, suggesting the existence of problems related to adverse selection and moral hazard. This result is one of the most important conclusions of our work and confirms the theoretical aspects pointed up by other empirical studies in the literature. Additionally, estimating the number of policyholders that suffered any accident but not declared, and how many these non-declared accidents are, could be very useful information for insurers to evaluate their risk planning. Our model attempts to reach this target as well.