Hidden overconfidence and advantageous selection

Theories of adverse selection and moral hazard predict the occurrence of the risk and the coverage of the insurance should be positively correlated, whereas empirical researches find little support of it. This paper provides a theoretical model of hidden overconfidence and demonstrates that a competitive insurance market may settle on separating equilibrium with advantageous selection predicting a negative relationship between risk and coverage. By assuming heterogeneity in risk perception and hidden action on self-protection, we find that, in equilibrium, the rational type of individual takes precautions to reduce the loss probability, whereas the overconfident type of individual will not make any effort. In the separating equilibrium, the insurer provides a product with high coverage to attract rational type of individual (low risk), and a product with low coverage for overconfident type of individual (high risk). In addition, other types of equilibrium such as adverse selection or linear premium rate are also found.