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, su ch as civil liability or health and workers' injuries, must be fully i nsured or at least covered for a specific amount. We examine in this p aper conditions under which a reduction in the constrained level of in surance for one risk increases the demand of insurance for another ind ependent risk. We show that it is necessary to sign the fourth derivat ive of the utility function to obtain an unambiguous spillover effect. Three different sufficient conditions are derived if the expected val ue of the exogenous risk is zero. The first condition is that risk ave rsion be standard-that is, that absolute risk aversion and absolute pr udence be decreasing. The second condition is that absolute risk avers ion be decreasing and convex. The third condition is that both the thi rd 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 absol ute risk aversion is decreasing.