This paper considers the design of an optimal unemployment insurance s
ystem. The problem is modeled as a repeated principal-agent problem in
volving a risk-averse agent-the unemployed worker-and a risk-neutral p
rincipal, which cannot monitor the agent's search effort. The optimal
long-term contract subject to the associated incentive constraints is
characterized, This contract involves a replacement ratio that decreas
es throughout the unemployment spell and a wage tax after reemployment
that, under some mild regularity conditions, increases with the lengt
h of the unemployment spell. Some numerical results are presented that
suggest that the gains from switching to this optimal unemployment in
surance scheme could be quite large. The performance of this optimal c
ontract is also compared to alternative liquidity provision mechanisms
.