Optimal Unemployment Insurance in a THANK Model

A Tractable HANK (THANK) model with three agents, incomplete markets, unemployment and sticky prices and wages, is used to analyze the dynamics, welfare and distributional effects of Ramsey-optimal unemployment insurance (UI) policies. First, the optimal transition from a steady state that replicates several empirical regularities of the European labor market to the Ramsey steady state is analyzed. In the long run, the vacancy creation motive dominates, as the replacement rate falls, lowering the unemployment rate. In the short run however, the insurance motive dominates until unemployment falls enough to generate larger welfare gains from a lower unemployment rate. Over the business cycle around the Ramseyoptimal steady state, we nd that the optimal changes in the replacement rate depend (i) on the nature of the shock and (ii) on the presence of price and wage rigidities. After productivity shocks, the vacancy creation motive dominates. After separation shocks, the planner has almost no traction over vacancy creations. Only the insurance and aggregate demand stabilization motives remain, and both point to a counter-cyclical UI policy.