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In this paper, I consider the problem of optimal unemployment insurance in a world in which the unemployed agent's job-finding effort is unobservable and his level of savings is unobservable. I show that the first-order approach is not always valid for this problem, and I argue that the available recursive procedures are not currently computationally feasible. Nonetheless, for the case in which the disutility of effort is linear, I am able to provide a complete characterization of the optimal contract: the agent's consumption is constant while he is unemployed, and jumps up to a higher constant and history-independent level of consumption when he finds a job. (Copyright: Elsevier)