May 2007

Diagnosing and Treating Bifurcations in Perturbation Analysis of Dynamic Macro Models

Jinill Kim, Andrew T. Levin, and Tack Yun


In perturbation analysis of nonlinear dynamic systems, the presence of a bifurcation implies that the first-order behavior of the economy cannot be characterized solely in terms of the first-order derivatives of the model equations. In this paper, we use two simple examples to illustrate how to detect the existence of a bifurcation. Following the general approach of Judd (1998), we then show how to apply l'Hospital's rule to characterize the solution of each model in terms of its higher-order derivatives. We also show that in some cases the bifurcation can be eliminated through renormalization of model variables; furthermore, renormalization may yield a more accurate first-order solution than applying l'Hospital's rule to the original formulation.

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Keywords: Bifurcation, perturbation, relative price distortion, optimal monetary policy

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Last Update: October 19, 2020