Bifurcation in Perturbation Analysis:Calvo Pricing Examples

Jinill Kim, Andrew T. Levin, Tack Yun

Research output: Contribution to journalArticlepeer-review


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
Issue number3
Publication statusPublished - 2011 Mar

Bibliographical note

Funding Information:
Acknowledgements We have benefited from the comments by the referee and discussion with Gary Anderson, Jean Boivin, Chris Sims, and participants at the 2006 Canadian Macroeconomics Study Group meeting and the 2007 Society of Computational Economics conference. The first author thanks the support by a Korea University grant. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System.


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

ASJC Scopus subject areas

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


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