Conclusion
This paper has revisited the role of social insurance to supplement a general income tax. We have assumed that neither public nor private insurers can observe an individual’s risk type. Instead, the private insurance market suffers from asymmetric information, a RS equilibrium emerges and low-risk individuals are only partly insured. We have concentrated on the case of positive correlation between loss probability and productivity, which is relevant for the old-age dependency risk. This is the interesting case from our perspective, because it implies that social insurance, whether uniform or not, is not desirable when private insurance markets are fair. We have shown that with adverse selection in the insurance market social insurance does have a role to play. When there is no concern for redistribution it can achieve a first-best outcome by completing the market insurance coverage provided to the poor. In the general case, when redistribution is accounted for by adopting a strictly concave welfare function, the solution is second-best. Extending benefits to the poor, or on a universal basis, does have adverse incentive effects, but it also corrects a market failure and enhances insurance coverage of the previously underinsured. Uniform coverage was shown to be desirable only when the insurance benefits outweigh the incentive cost. A properly designed non-uniform insurance schedule, on the other hand, is always desirable irrespective of the pattern of correlation between productivity and risk. Under positive correlation, insurance benefits need to be targeted to one of the types only, and quite surprisingly this may be the productive individuals.
