Unlike their linear counterparts, non-linear models of the business cycle can generate sustained economic fluctuations even in the absence of shocks (e.g., via limit cycles or chaos). A popular approach to solving non-linear models is the use of perturbation methods. I show that, as typically implemented, these methods are generally incapable of finding solutions that feature limit cycles or chaos, a fact that does not appear to be recognized in the existing literature. Standard algorithms only seek solutions that feature converge to the steady state, which is stronger than the standard definitional requirement that a solution simply cannot explode. Because of this, in estimation exercises any parameterization that involves limit cycles would typically (and incorrectly) be discarded. I propose a modification to standard algorithms that does not impose the overly strong requirement that solutions involve convergence.

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Department of Economics
Carleton Economics Working Papers (CEWP)
Department of Economics

Galizia, D. (2018). Saddle Cycles: Solving Rational Expectations Models Featuring Limit Cycles (or Chaos) Using Perturbation Methods (No. CEP 18-11). Carleton Economics Working Papers (CEWP). Department of Economics.