Congratulations to Professor Dana Galizia! His paper titled “Saddle Cycles: Solving Rational Expectations Models Featuring Limit Cycles (or Chaos) Using Perturbation Methods” has been accepted for publication in Quantitative Economics – a leading peer-reviewed economics journal aimed at empirical research that is rigorously informed by econometrics and/or economic theory.
Unlike linear ones, non-linear business cycle models can generate sustained fluctuations even in the absence of shocks (e.g., via limit cycles/chaos). A popular approach to solving non-linear 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.