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Endogenous Cycles in Optimal Monetary Policywith a Nonlinear Phillips Curve

  • Orlando Gomes

    ()

    (Instituto Politécnico de Lisboa - Escola Superior de Comunicação Social and UNIDE-ERC)

  • Diana A. Mendes

    ()

    (ISCTE - Department of Quantitative Methods and UNIDE-StatMath)

  • Vivaldo M. Mendes

    ()

    (ISCTE - Department of Economics and UNIDE-ERC)

  • José Sousa Ramos

    (Technical University of Lisbon, IST, Department of Mathematics)

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 with sticky prices a la Calvo and forward looking behavior. In this paper we extend this standard model by introducing nonlinearity into the Phillips curve. As the linear Phillips curve may be questioned on theoretical grounds and seems not to be favoured by empirical evidence, a similar procedure has already been undertaken in a series papers over the last few years, e.g., Schaling (1999), Semmler and Zhang (2004), Nobay and Peel (2000), Tambakis (1999), and Dolado et al. (2004). However, these papers were mainly concerned with the analysis of the problem of inflation bias, by deriving an interest rate rule which is nonlinear, leaving the issues of stability and the possible existence of endogenous cycles in such a framework mostly overlooked. Under the specific form of nonlinearity proposed in our paper (which allows for both convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into a fully deterministic structure of the standard model produces significant changes to the major conclusions regarding stability and the efficiency of monetary policy in the standard model. We should 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 and chaotic fixed points (endogenous cycles); (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 interesting. Firstly, when the Central Bank pays attention essentially to ination targeting, the inflation rate may have a lower mean and is certainly less volatile; secondly, for changes in the degree of price stickiness the results are not are clear cut as in the previous case, however, we can also observe that when such stickiness is high the inflation rate tends to display a somewhat larger mean and also higher volatility; and thirdly, it shows that the target values for ination and the output gap, both crucially aect the dynamics of the economy in terms of average values and volatility of the endogenous variables – e.g., the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility – while in the linear case only the inflation rate does so (obviously, only affecting in this case the level of the endogenous variables). Moreover, the existence of endogenous cycles due to chaotic motion may raise serious questions about whether the old dictum of monetary policy (that the Central Bank should conduct policy with discretion instead of commitment) is not still very much in the business of monetary policy.

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File URL: http://bru-unide.iscte.pt/RePEc/pdfs/ERCwp1508.pdf
File Function: Second draft, 2006
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Paper provided by ISCTE-IUL, Business Research Unit (BRU-IUL) in its series Working Papers Series 1 with number ercwp1508.

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Length: 37 pages
Date of creation: 15 Jan 2006
Date of revision:
Handle: RePEc:isc:iscwp1:ercwp1508
Contact details of provider: Web page: http://bru-unide.iscte.pt/Email:


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  1. Henry Siu, 2005. "Time Consistent Monetary Policy with Endogenous Price Rigidity," 2005 Meeting Papers 821, Society for Economic Dynamics.
  2. Andrew J. Filardo, 1998. "New evidence on the output cost of fighting inflation," Economic Review, Federal Reserve Bank of Kansas City, issue Q III.
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  4. 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.
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  12. Michael Woodford, 1999. "Optimal Monetary Policy Inertia," NBER Working Papers 7261, National Bureau of Economic Research, Inc.
  13. Marvin Goodfriend & Robert G. King, 1998. "The new neoclassical synthesis and the role of monetary policy," Working Paper 98-05, Federal Reserve Bank of Richmond.
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  16. Guy Debelle & Douglas Laxton, 1997. "Is the Phillips Curve Really a Curve? Some Evidence for Canada, the United Kingdom, and the United States," IMF Staff Papers, Palgrave Macmillan, vol. 44(2), pages 249-282, June.
  17. Paolo Surico, 2002. "Inflation Targeting and Nonlinear Policy Rules: the Case of Asymmetric Preferences," Macroeconomics 0210002, EconWPA, revised 09 Dec 2003.
  18. Gordon, Robert J, 1996. "The Time-varying NAIRU and its Implications for Economic Policy," CEPR Discussion Papers 1492, C.E.P.R. Discussion Papers.
  19. Douglas Laxton & Peter B. Clark & David Rose, 1995. "Asymmetry in the U.S. Output-Inflation Nexus; Issues and Evidence," IMF Working Papers 95/76, International Monetary Fund.
  20. Demosthenes N. Tambakis, 1998. "Monetary Policy with a Convex Phillips Curve and Asymmetric Loss," IMF Working Papers 98/21, International Monetary Fund.
  21. Eric Schaling, 1999. "The non-linear Phillips curve and inflation forecast targeting," Bank of England working papers 98, Bank of England.
  22. Peersman, Gert & Smets, Frank, 2001. "Are the effects of monetary policy in the euro area greater in recessions than in booms?," Working Paper Series 0052, European Central Bank.
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  25. Cover, James Peery, 1992. "Asymmetric Effects of Positive and Negative Money-Supply Shocks," The Quarterly Journal of Economics, MIT Press, vol. 107(4), pages 1261-82, November.
  26. 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.
  27. Tommy Sveen & Lutz Weinke, 2004. "Pitfalls in the Modelling of Forward-Looking Price Setting and Inverstment Behavior," Working Paper 2004/01, Norges Bank.
  28. Kaushik Mitra & Seppo Honkapohja, 2004. "Performance of Monetary Policy with Internal Central Bank Forecasting," Royal Holloway, University of London: Discussion Papers in Economics 04/18, Department of Economics, Royal Holloway University of London, revised Jul 2004.
  29. 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.
  30. Karras, Georgios, 1996. "Why are the effects of money-supply shocks asymmetric? Convex aggregate supply or "pushing on a string"?," Journal of Macroeconomics, Elsevier, vol. 18(4), pages 605-619.
  31. Eliasson, Ann-Charlotte, 2001. "Is the Short-run Phillips Curve Nonlinear? Empirical Evidence for Australia, Sweden and the United States," Working Paper Series 124, Sveriges Riksbank (Central Bank of Sweden).
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