Public versus private risk sharing

Can public income insurance through progressive income taxation improve the allocation of risk in an economy where private risk sharing is incomplete? The answer depends crucially on the fundamental friction that limits private risk sharing in the first place. If risk sharing is limited because insurance markets are missing for model-exogenous reasons (as in Bewley (1986) [8]) publicly provided risk sharing improves on the allocation of risk. If instead private insurance markets exist but their use is limited by limited enforcement (as in Kehoe and Levine (1993) [23]) then the provision of public insurance interacts with equilibrium private insurance, as, by providing risk sharing, the government affects the value of exclusion from private insurance markets and thus the enforcement mechanism of these contracts. We characterize consumption allocations in an economy with limited enforcement and a continuum of agents facing plausible income risk and tax systems with various degrees of progressivity (public risk sharing). We provide conditions under which more publicly provided insurance actually reduces total insurance for agents (excess crowding-out), or under which more public insurance increases total insurance (partial crowding-out).