Bequests and Social Security with Uncertain Lifetimes

The fact that consumers do not know in advance the dates at which they will die effects their individual consumption and portfolio decisions. In general, some consumers will end up leaving bequests at death, even if they have no bequest motive, simply because they happen to die at a time when they are holding wealth to provide for their own future consumption. In the model of this paper,consumers who are otherwise identical, die (randomly) at different ages and thus leave bequests of different sizes to their heirs. Therefore, there is intra-cohort variation in wealth and consumption even if all consumers have the same labor income, taxes, and social security benefits. This paper presents explicit steady state distributions for consumption and wealth. The introduction of an actuarially fair social security system reduces steady state private wealth by more than one-for-one so that, even in a fully funded system, national wealth falls. In addition, all central moments of the steady state distributions of consumption and wealth are reduced by actuarially fair social security