Discussion Papers in Economics Optimal Unemployment Insurance with Human Capital Depreciation and Duration Dependence

This paper studies the effect of human capital depreciation and duration dependence on the design of an optimal unemployment insurance (UI) scheme. Our results partially confirm those obtained in most previous studies: benefits should decrease with unemployment duration. The optimal program also generates two main novel features, which are not present in stationary models. First, if human capital depreciates rapidly enough during unemployment, UI transfers are bounded below by a minimal “assistance” level that arises endogenously in the efficient program. Second, we study the optimality of imposing a history contingent wage tax after reemployment. Our numerical simulations based on the Spanish and US economies show that the wage tax should decrease with the length of worker’s previous unemployment spell, and become a wage subsidy for long-term unemployed workers. As a by-product of our study, we develop a systematic approach suitable for studying recursively a wide range of dynamic moral-hazard problems, and other models with similar characteristics. JEL Classification: C61, D63, D82, D83, J24, J31, J38, J64, J65.