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Bifurcation in Perturbation Analysis:Calvo Pricing Examples

Authors
Kim, JinillLevin, Andrew T.Yun, Tack
Issue Date
3월-2011
Publisher
SPRINGER
Keywords
Bifurcation; Perturbation; Relative price distortion; Relative price dispersion
Citation
COMPUTATIONAL ECONOMICS, v.37, no.3, pp.221 - 236
Indexed
SCIE
SSCI
SCOPUS
Journal Title
COMPUTATIONAL ECONOMICS
Volume
37
Number
3
Start Page
221
End Page
236
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/112951
DOI
10.1007/s10614-010-9251-x
ISSN
0927-7099
Abstract
In recent macro models with staggered price and wage settings, the presence of variables such as relative price and wage dispersion is prevalent, which leads to the source of bifurcations. In this paper, we illustrate how to detect the existence of a bifurcation in stylized macroeconomic models with Calvo (J Monet Econ 12(3):383-398, 1983) pricing. Following the general approach of Judd (Numerical methods in economics, 1998), we employ l'Hospital's rule to characterize the first-order dynamics of relative price distortion in terms of its higher-order derivatives. We also show that, as in the usual practice in the literature, the bifurcation can be eliminated through renormalization of model variables. Furthermore, we demonstrate that the second-order approximate solutions under this renormalization and under bifurcations can differ significantly.
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