MANAGING INEQUALITY OVER BUSINESS CYCLES: OPTIMAL POLICIES WITH HETEROGENEOUS AGENTS AND AGGREGATE SHOCKS

We present a projection theory on the space of idiosyncratic histories for heterogeneous-agents models. This allows solving for optimal Ramsey policies in heterogeneous-agent models with aggregate shocks, using a Lagrangian approach. In addition, it allows improving current simulation methods using perturbation techniques, by using more steady-state information. We apply this to study the optimal level distorting tax on labor and unemployment insurance over the business cycle in a production economy. In the quantitative exercise, the average optimal replacement rate is 10% higher than the one implies by a sufficient-statistics approach, due to saving distortions. Moreover, the optimal replacement rate is countercyclical.