Maliar, L., and S. Maliar
Quantitative Economics – 6(1), 1-47

Keywords: ergodic set; ε-distinguishable set; clusters; adaptive grid; discrepancy; large-scale model; new Keynesian model; ZLB; stochastic simulation

Abstract: We introduce a numerical 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 cover the support of the constructed ergodic measure with a fixed grid, and we use projection techniques to accurately solve the model on that grid. The construction of the grid is the key novel piece of our analysis: we replace a large cloud of simulated points with a small set of “representative” points. We present three alternative techniques for constructing representative points: a clustering method, an epsilon-distinguishable set method, and a locally-adaptive variant of the epsilon-distinguishable set method. As an illustration, we solve one- and multi-agent neoclassical growth models and a large-scale new Keynesian model with a zero lower bound on nominal interest rates. The proposed solution algorithm is tractable in problems with high dimensionality (hundreds of state variables) on a desktop computer.