The Spillover Effect of Compulsory Insurance

The assumption usually made in the insurance literature that risks are always insurable at the desired level does not hold in the real world: some risks are not—or are only partially—insurable, while others, such as civil liability or health and workers' injuries, must be fully insured or at least covered for a specific amount. We examine in this paper conditions under which a reduction in the constrained level of insurance for one risk increases the demand of insurance for another independent risk. We show that it is necessary to sign the fourth derivative of the utility function to obtain an unambiguous spillover effect. Three different sufficient conditions are derived if the expected value of the exogenous risk is zero. The first condition is that risk aversion be standard—that is, that absolute risk aversion and absolute prudence be decreasing. The second condition is that absolute risk aversion be decreasing and convex. The third condition is that both the third and the fourth derivatives of the utility function be negative. If the expected value of the exogenous risk is positive, a wealth effect is added to the picture, which goes in the opposite direction if absolute risk aversion is decreasing.