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

• 成果类型: Article
• 署名作者: Maliar, Lilia; Maliar, Serguei
• 署名单位: Stanford University; Santa Clara University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE364
• 发表日期: 2015
• 页码: 1-47
• 关键词: Ergodic set; epsilon-distinguishable set; clusters; adaptive grid; discrepancy; large-scale model; new Keynesian model; ZLB; stochastic simulation; C61; C63; C68; E31; E52

摘要

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 epsilon-distinguishable set method, and a locally-adaptive variant of the epsilon-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.