Optimal Policies with Heterogeneous Agents: Truncation and Transitions

We study the optimal provision of a public good in an heterogeneous-agent economy, with and without aggregate shocks. We rely on a method combining a Lagrangian approach and a truncation procedure that takes advantage of the restrictions imposed by the first-order conditions of the Ramsey problem. We compare these outcomes with those of other solution techniques considering transitions, as usually done in the literature. We have two main results. First, we find that the optimal Ramsey policy faces a time-inconsistency problem specific to incomplete-market economies, which is due to the non-optimality of private savings. This issue affects the solution based on the computation of transitions. Second, we find that the truncation approach provides quantitatively accurate estimates of the value of planner's instruments, both at the steady-state and during the dynamics. We also report a number of quantitative checks.