Merging simulation and projection approaches to solve high-dimensional problems with an application to a New Keynesian model. (English) Zbl 1396.91539
Summary: 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 \(\varepsilon\)-distinguishable set method, and a locally-adaptive variant of the \(\varepsilon\)-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.
MSC:
| 91B64 | Macroeconomic theory (monetary models, models of taxation) |
Keywords:
ergodic set; \(\varepsilon\)-distinguishable set; clusters; adaptive grid; discrepancy; large-scale model; New Keynesian model; ZLB; stochastic simulationReferences:
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