Forced Saving, Redistribution, and Nonlinear Social Security Schemes

This paper studies the design of nonlinear social security schemes when individuals differ in productivity and in their degree of myopia. Myopic individuals may not save "enough" for their retirement. The welfare function is paternalistic: The rate of time preference of the farsighted is used for both types. We show that the solution does not necessarily imply forced savings for the myopics: Paternalistic considerations are mitigated by incentive effects. Numerical results suggest that as the proportion of myopic individuals increases, there is less redistribution and more forced saving, and the desirability of social security increases.