Quantitative Economics, Volume 12, Issue 3 (July 2021)
Saddle cycles: Solving rational expectations models featuring limit cycles (or chaos) using perturbation methods
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.
Dynamic equilibrium economies computational methods nonlinear solution methods limit cycles chaos C63 C68 E37
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