This paper examines the effect of restricting the elderly’s driver’s licenses or encouraging elderly drivers to forfeit their licenses on reducing the number of traffic accidents. Considering the pedestrians and drivers who participate in compulsory automobile liability insurance and voluntary insurance we model a traffic accident scenario that incorporates the number of elderly, the insurance rates, population density, income, and pavement extensions by prefecture in Japan. Furthermore, we model a simultaneous equation that considers the occurrence of traffic accident and insurance participation. The study found that when strict liability is applied to a driver, drivers are not likely to avoid accidents beforehand. Notably, it is possible that elderly people possessing a driver's license induce more traffic accidents. It is difficult to expect the effect of deterring an accident in the insurance market unless there is a mechanism to give pedestrians incentives to avoid accidents.