Working Paper

Diagnosing and treating bifurcations in perturbation analysis of dynamic macro models

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.

Keywords: Bifurcation theory; Perturbation (Mathematics);

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Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2007

Number: 2007-14