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.