Saddle cycles: Solving rational expectations models featuring limit cycles (or chaos) using perturbation methods

• 成果类型: Article
• 署名作者: Galizia, Dana
• 署名单位: Carleton University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE1491
• 发表日期: 2021
• 页码: 869-901
• 关键词: Dynamic equilibrium economies; computational methods; nonlinear solution methods; limit cycles; chaos; C63; C68; E37

摘要

Unlike linear ones, nonlinear business cycle models can generate sustained fluctuations even in the absence of shocks (e.g., via limit cycles/chaos). A popular approach to solving nonlinear models is perturbation methods. I show that, as typically implemented, these methods are incapable of finding solutions featuring limit cycles or chaos. Fundamentally, solutions are only required not to explode, while standard perturbation algorithms seek solutions that meet the stronger requirement of convergence to the steady state. I propose a modification to standard algorithms that does not impose this overly strong requirement.