Econometric Models of Accident Distributions

Abstract

This paper deals with the econometrics of car accidents, that is, the estimation of the relative importance or significance of the factors explaining the number of accidents in a given period on an individual basis. The number of car accidents is a discrete variable and, therefore, represents a count process: the dependent variable takes only nonnegative integer values. Hence, the observed dependent variable is the number of accidents an individual i had in the period considered. The individual characteristics are considered exogenous or predetermined and may or may not be significant factors in explaining the number of accidents. We have estimated four categorical models (linear probability, probit, logit, and multinomial logit) and four count data models (Poisson and negative binomial models with and without individual characteristics in the regression component). It is difficult to compare the econometric results of the different models since some of these models are not nested. However, it is shown that the negative binomial model with a regression component produces a reasonable approximation of the true distribution of accidents. Different statistical tests reject the Poisson models (with and without a regression component) and the negative binomial model without individual characteristics. It is also observed that all estimated models provide the same qualitative results (essentially the same significant variables), but differ when predictions of either the probabilities of accident or the expected number of accidents were made. For quantitative predictions, it is important to select the appropriate model. Moreover, it is shown that, in all models, the individual’s past driving experience is a good predictor of risk. Finally, we apply the statistical results to a model of insurance rating in the presence of moral hazard.