A Cluster-Grid Algorithm: Solving Problems With High Dimensionality∗

We develop a cluster-grid algorithm (CGA) that solves dynamic economic models on their ergodic sets and is tractable in problems with high dimensionality (hundreds of state variables) on a desktop computer. The key new feature is the use of methods from cluster analysis to approximate an ergodic set. CGA guesses a solution, simulates the model, partitions the simulated data into clusters and uses the centers of the clusters as a grid for solving the model. Thus, CGA avoids costs of finding the solution in areas of the state space that are never visited in equilibrium. In one example, we use CGA to solve a large-scale new Keynesian model that includes a Taylor rule with a zero lower bound on nominal interest rates.   : C61, C63, C68, E31, E52   : ergodic set; clusters; large-scale economy; new Keynesian model; ZLB; projection method; numerical method; stochastic simulation ∗This paper is a substantially revised version of an earlier version that circulated as NBER working paper 15965. We are indebted to the editor and three anonymous referees for many useful comments and suggestions, and in particular, for a suggestion to analyze a new Keynesian model. Errors are ours. Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution at Stanford University, Ivie, the Ministerio de Ciencia e Innovación and FEDER funds under the project SEJ-2007-62656 and the Generalitat Valenciana under the grants BEST/2011/283 and BEST/2011/282, respectively.