Social insurance with competitive insurance markets and risk misperception

We examine the role of uniform and non-uniform social insurance to supplement a general income tax when neither public nor private insurers can observe individual risk, which is positively correlated with wages (e.g., for old age dependency). In the (private market) Rothschild and Stiglitz (1976) equilibrium low-wage/low-risk individuals are not fully insured. While social insurance provided to the poor has a negative incentive effect, it also increases their otherwise insufficient insurance coverage. Social insurance to the rich produces exactly the opposite effects. Whichever of these effects dominates, some social insurance is always desirable irrespective of the pattern of correlation. Finally, we introduce risk misperception which exacerbates the failure of private markets. Rather surprisingly, this does not necessarily strengthen the case for public insurance.