Optimal Policies with Heterogeneous Agents : Truncation and Transitions

We compare methods to solve for optimal policies in heterogeneous agent-models with and without aggregate shocks, considering the optimal provision of a public good in a heterogeneous-agent economy. We first use a method based on transitions that we modify to neutralize the effect of the initial distribution. Second, we consider a truncation method combining a Lagrangian approach and an improved truncation procedure that takes advantage of the restrictions imposed by the first-order conditions of the Ramsey problem. The truncation method provides quantitatively accurate estimates of the value of the planner’s instruments, whereas a time-inconsistency issue affects the transition method. We also report a number of quantitative checks, both in time-0 and timeless perspectives, and both with and without aggregate risk