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Chaotic dynamics in optimal monetary policy

  • O. Gomes


  • V. M. Mendes


  • D. A. Mendes


  • J. Sousa Ramos


There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King [NBER Macroeconomics Annual 1997 edited by B. Bernanke and J. Rotemberg (Cambridge, Mass.: MIT Press, 1997), pp. 231–282], Clarida et al. [J. Econ. Lit. 37, 1661 (1999)], Svensson [J. Mon. Econ. 43, 607 (1999)] and Woodford [Interest and Prices: Foundations of a Theory of Monetary Policy (Princeton, New Jersey, Princeton University Press, 2003)]. In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle-path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

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Article provided by Springer in its journal The European Physical Journal B.

Volume (Year): 57 (2007)
Issue (Month): 2 (05)
Pages: 195-199

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Handle: RePEc:spr:eurphb:v:57:y:2007:i:2:p:195-199
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  1. J. J. Dolado & R. Maria-Dolores & F. J. Ruge-Murcia, 2002. "Nonlinear Monetary Policy Rules: Some New Evidence For The Us," Economics Working Papers we022910, Universidad Carlos III, Departamento de Economía.
  2. Svensson, Lars E.O., 1998. "Inflation Targeting as a Monetary Policy Rule," Seminar Papers 646, Stockholm University, Institute for International Economic Studies.
  3. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "The science of monetary policy: A new Keynesian perspective," Economics Working Papers 356, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 1999.
  4. Tambakis Demosthenes N., 1999. "Monetary Policy with a Nonlinear Phillips Curve and Asymmetric Loss," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-17, January.
  5. Marvin Goodfriend & Robert King, 1997. "The New Neoclassical Synthesis and the Role of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 231-296 National Bureau of Economic Research, Inc.
  6. Zhang, Wenlang & Semmler, Willi, 2005. "Monetary Policy Rules Under Uncertainty: Empirical Evidence, Adaptive Learning, And Robust Control," Macroeconomic Dynamics, Cambridge University Press, vol. 9(05), pages 651-681, November.
  7. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
  8. Eric Schaling, 1999. "The non-linear Phillips curve and inflation forecast targeting," Bank of England working papers 98, Bank of England.
  9. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
  10. Willi SEMMLER & Wenlang ZHANG, . "Monetary Policy Rules with Nonlinear Philips Curve and Endogenous Nairu," EcoMod2004 330600128, EcoMod.
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