Optimal unemployment insurance and redistribution

We characterize optimal income taxation and unemployment insurance in a search-matching framework where both voluntary and involuntary unemployment are endogenous and Nash bargaining determines wages. Individuals decide whether to participate as job seekers and if so, how much search effort to exert. Unemployment insurance trades off insurance versus search and participation incentives. We also allow for different productivity types so there is a redistributive role for the income tax and show that a piecewise linear wage tax internalizes the macro effects arising from endogenous wages. Type-specific lump-sum taxes and transfers can then redistribute between individuals of differing skills and employment states. Our analysis embeds optimal unemployment insurance into an extensive-margin optimal redistribution framework where transfers to the involuntarily and voluntarily unemployed can differ, and nests several standard models in the literature.