Merging simulation and projection approaches to solve high-dimensional problems with an application to a new Keynesian model

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 ε-distinguishable set method, and a locally-adaptive variant of the ε-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.Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution and the Department of Economics at Stanford University, Santa Clara University, University of Alicante, Ivie, MECD, and FEDER funds under the project ECO2012-36719