Bifurcation in Perturbation Analysis:Calvo Pricing Examples

Jinill Kim, Andrew T. Levin, Tack Yun

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)221-236
Number of pages16
JournalComputational Economics
Volume37
Issue number3
DOIs
Publication statusPublished - 2011 Mar

Keywords

  • Bifurcation
  • Perturbation
  • Relative price dispersion
  • Relative price distortion

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)
  • Computer Science Applications

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