Optimal Disability Insurance and Unemployment Insurance With Cyclical Fluctuations

This paper studies the optimal joint design of disability insurance and unemployment insurance in an environment with moral hazard, when health status is private information, and cyclical fluctuations. I show how disability benefits and unemployment benefits vary with aggregate economic conditions in an optimal contract. In a special case of the model, I first show the optimal contract can be solved explicitly up to a system of non-linear equations. I then demonstrate that the optimal joint insurance system can be implemented by allowing workers to save or borrow using a bond and by providing flow payments and lump-sum transfers (or payments), where the interest rates and the amounts paid (transferred) depend on the employment or health status of the agent and the state of the economy. Finally, I consider a calibrated version of the full model and study the quantitative implications of both the current system and the optimal system. In the optimal system, disability benefits are designed such that the system punishes workers who stay unemployed for a long time. I consider . The cost savings incurred from incentive problems are substantial, and the unemployment rate will be reduced by roughly 40 percent.