Automobile insurance contracts and risk of accident: An empirical test using French individual data

Insurance has for a long time been perceived as a way of transferring responsibility from insured agents to insurers and thus as potentially influencing insured agents' behavior. Two particular opportunistic behaviors have been analyzed. First, the theory of adverse selection predicts that high-risk agents are likely to demand more insurance than are low-risk agents. Second, the theory of moral hazard predicts that the wider the insurance coverage, the less agents will try to prevent accidents. Both theories thus conclude that agents who are totally insured should have a higher probability of accident than those with only partial insurance, ceteris paribus. Nevertheless, one of the aims of insurance rating systems is to control for these opportunistic behaviors. In this article, we use individual data to see if the French automobile insurance rating system has achieved this aim. We do this using a two-step maximum-likelihood method. First, we compute a probit model to estimate the probability of taking out comprehensive versus third-party insurance. We then calculate the generalized residual, which is included as an independent variable in a negative binomial model estimating the probability of having an accident. The coefficient of this variable is argued to represent adverse selection and ex-ante moral-hazard behavior.