Merging Simulation and Projection Approaches to Solve High-Dimensional Problems

We introduce an algorithm for solving dynamic economic models that merges stochastic simulation and projection approaches: we use simulation to approximate the ergodic measure of the solution, we construct a fixed grid covering the support of the constructed ergodic measure, and we use projection techniques to accurately solve the model on that grid. The grid construction is the key novel piece of our analysis: we select an ε-distinguishable subset of simulated points that covers the support of the ergodic measure roughly uniformly. The proposed algorithm is tractable in problems with high dimensionality (hundreds of state variables) on a desktop computer. As an illustration, we solve one- and multicountry neoclassical growth models and a large-scale new Keynesian model with a zero lower bound on nominal interest rates