A Cluster-Grid Projection Method: Solving Problems with High Dimensionality
We develop a projection method that can solve dynamic economic models with a large number of state variables. A distinctive feature of our method is that it operates on the ergodic set realized in equilibrium: we simulate a model, distinguish clusters on simulated series and use the clusters' centers as a grid for projections. Making the grid endogenous to the model allows us to avoid costs associated with finding a solution in areas of state space that are never visited in equilibrium. On a standard desktop computer, we calculate linear and quadratic solutions to a multi-country growth model with up to 400 and 80 state variables, respectively. Our solutions are global, and their accuracy does not rapidly decline away from steady state.
Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution at Stanford University, the Ivie, the Ministerio de Ciencia e Innovación and FEDER funds under the project SEJ-2007-62656 and the Generalitat Valenciana under the grants BEST/2010/142 and BEST/2010/141, respectively. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.