Pain, Precautions and Present-biased Preferences: A Theory of Health Insurance

We develop an insurance market model where consumers (i) exhibit present-biased preferences, and (ii) suffer from physical pain in case of (health-) damage. They can exert preventive effort to reduce the probability of damage. Sophisticated consumers correctly anticipate their effort and purchase full insurance. Naive consumers overestimate their future effort, purchase no insurance and end up with less effort than sophisticated ones. We allow consumers to differ in their wealth and risk preferences. Our model can explain why in some insurance markets there is a negative correlation between risk and insurance and a positive correlation between insurance and wealth.