Optimal Unemployment Insurance with Private Insurance

I present a model of optimal contracts between firms and workers, under limited commitment and with worker savings. A central feature of the model is that firms can provide insurance against unemployment, by targeting a path of wages that encourages wealth accumulation. I provide an analytical expression for the scope of private insurance measured in the drop of consumption that the worker suffers when the match terminates. I then consider how government policy affects risk sharing through private markets. I find that unemployment benefits should be large and frontloaded. The government has the incentive to drive the allocation to the point where the firm’s participation constraint binds. At this point wages are equal to the match productivity in every period and thus private risk sharing is crowded out. However, the drop in consumption in unemployment is minimized. Moreover, the implications of the theory of optimal contracts are assessed relative to the standard model of heterogeneous households, whereby wealth is utilized for self-insurance purposes. I show that under the optimal UI policy, the contract model and the heterogeneous households model are equivalent.