Insurance as a Giffen Good under a Bonus-Malus System and its Effect on Adverse Selection

A bonus-malus system (BMS) serves not only as a fair rating system but also as a mechanism to avoid adverse selection by developing an applied premium based on the claim experience of a policy. This paper analyzes how a BMS could work for these two concepts: achieving fairness among policies and mitigating adverse selection. The purpose is to understand how the transition rules, the number of classes, and the premium scale affect the behavior of a consumer’s insurance purchase. By utilizing the mean asymptotic premium and the elasticity (Loimaranta (1972), Lemaire (1995, 1998)), this article defines the asymptotic critical value characterizing automobile insurance as a good and the condition for the slope of insurance demand curve under a bonus-malus system. As an empirical analysis, current and past Japanese bonus-malus systems are introduced in chronological order, and it is shown that no negative slope could be found for any combination of systems and claim frequency. This implies that promoting fairness in the way of lower premiums for good drivers and assigning higher penalties for bad drivers might increase the occurrence of adverse selection, contrary to the expected result.