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This paper develops a model of equilibrium unemployment with duration-dependent unemployment insurance (UI) payments. As the government does not observe job offers, there is a moral hazard problem because the option of receiving further UI payments raises the job-seeker's value of remaining unemployment. Extending the duration of UI payments while reducing the level of payments, to hold total generosity constant, results in higher negotiated wages. Simulations suggest that a generosity neutral switch from a six-month UI scheme to a one-year scheme has small effects, but a switch to an indefinite scheme has a large impact on wages and unemployment.