Sustainable Intergenerational Insurance

This paper studies the dynamic and steady state properties of optimal intergenerational insurance when enforcement is limited. It considers a pure exchange and stochastic overlapping generations economy. The optimal allocation is chosen by a benevolent government whose welfare function values the initial old and places a positive, but vanishing weight on the welfare of future generations. The optimal allocation is constrained to be self-enforceable. That is, generations must have no incentive to default on the consumption allocation at any history of states. We show that the optimal intergenerational insurance when enforcement is limited takes the form of a history-dependent pension plan payable by the young to the old generation. In a simple two-state example we show how the degree of insurance depends on the history of states, in particular, insurance falls with more consecutive good states for the young but reverts whenever the bad state occurs. Finally, we solve for the optimal time-dependent and stationary contracts and numerically compare the welfare loss of these schemes relative to the fully optimal history-dependent scheme.