Finance and Economics Discussion Series (FEDS)
May 2007
Diagnosing and Treating Bifurcations in Perturbation Analysis of Dynamic Macro Models
Jinill Kim, Andrew T. Levin, and Tack Yun
Abstract:
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.
Full Paper (Screen Reader Version)Keywords: Bifurcation, perturbation, relative price distortion, optimal monetary policy
PDF: Full Paper
Disclaimer: The economic research that is linked from this page represents the views of the authors and does not indicate concurrence either by other members of the Board's staff or by the Board of Governors. The economic research and their conclusions are often preliminary and are circulated to stimulate discussion and critical comment. The Board values having a staff that conducts research on a wide range of economic topics and that explores a diverse array of perspectives on those topics. The resulting conversations in academia, the economic policy community, and the broader public are important to sharpening our collective thinking.