How should unemployment insurance vary over the business cycle?

We study optimal unemployment insurance (UI) over the business cycle using a heterogeneous agent job search model with aggregate risk and incomplete markets. We validate the model-implied micro and macro labor market elasticities to changes in UI generosity against existing estimates, and provide an explanation for divergent empirical findings. We show that generating the observed demographic differences between UI recipients and non-recipients is critical in determining the magnitudes of these elasticities. We find that the optimal policy features countercyclical replacement rates with average generosity close to current U.S. policy but adopts longer payment durations reminiscent of European policies