Optimal Regional Insurance Provision under Privately Observable Shocks

We study the design and implementation of optimal regional insurance provision against privately observable shocks to the degree of intergenerational externality (DIE) induced by, or the degree of technological progress (DTP) for producing, intergenerational public goods (IPGs). We obtain four main results. First, the intertemporal allocation is not distorted only at the endpoints of type distribution, and insurance is incomplete. Second, if the grant to bottom type is distorted upward, then its debt must be distorted downward, and vice versa; the direction of distortion is qualitatively reversed between top and bottom types. Third, for all but the endpoints, there is a grant scheme, which is nonlinear and monotonic in debt, that decentralizes welfare optimum. For the endpoints, however, the implementation grant scheme is independent of debt. Fourth, when regions differ in DIE in the course of implementation, grant and debt are complementary in insurance provision; when regions differ in DTP, they are complementary with observable output of, but are substitutive with observable expenditure on, the IPGs.