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Computational aspects of the open-loop Nash equilibrium in linear quadratic games

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  • Engwerda, J.C.

    (Tilburg University)

Abstract

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

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-75998.

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Date of creation: 1998
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Publication status: Published in Journal of Economic Dynamics and Control (1998) v.22, p.1487-1506
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-75998

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Web page: http://www.tilburguniversity.edu/

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  1. Brociner, Andrew & Levine, Paul L, 1992. "Fiscal Policy Coordination and EMU: A Dynamic Game Approach," CEPR Discussion Papers 639, C.E.P.R. Discussion Papers.
  2. Bovenberg, A.L. & Aarle , B. van & Raith, M., 1995. "Monetary and fiscal policy interaction and government debt stabilization," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153069, Tilburg University.
  3. Zeeuw, A.J. de & Ploeg, F. van der, 1987. "Difference games and policy evaluation: A conceptual framework," Research Memorandum 268, Tilburg University, Faculty of Economics and Business Administration.
  4. Engwerda, Jacob C., 1998. "On the open-loop Nash equilibrium in LQ-games," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 729-762, May.
  5. Reinhard Neck & Engelbert Dockner, 1995. "Commitment and coordination in a dynamic game model of international economic policy-making," Open Economies Review, Springer, vol. 6(1), pages 5-28, January.
  6. Petit, Maria Luisa, 1989. "Fiscal and Monetary Policy Co-ordination: A Differential Game Approac h," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(2), pages 161-79, April-Jun.
  7. Tabellini, Guido, 1986. "Money, debt and deficits in a dynamic game," Journal of Economic Dynamics and Control, Elsevier, vol. 10(4), pages 427-442, December.
  8. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-64, September.
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Cited by:
  1. Nicola Acocella & Giovanni Di Bartolomeo, 2005. "Non-neutrality of economic policy: An application of the Tinbergen-Theil's approach to a strategic context," Working Papers 82, University of Rome La Sapienza, Department of Public Economics.
  2. Yeh, Kuo-chun & Ho, Tai-kuang, 2010. "Will Japan, Taiwan or the US be isolated by China? A macroeconomic game approach," Japan and the World Economy, Elsevier, vol. 22(1), pages 59-68, January.
  3. DI BARTOLOMEO, Giovanni & ENGWERDA, Jacob & PLASMANS, Joseph & VAN AARLE, Bas, 2003. "Macroeconomic stabilisation policies in the EMU: Spillovers, asymmetries and institutions," Working Papers 2003019, University of Antwerp, Faculty of Applied Economics.
  4. Yeh, Kuo-chun, 2012. "Renminbi in the future international monetary system," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 106-114.
  5. Yeh Kuo-chun, 2009. "Will a Taiwan-China Monetary Union be Feasible? Lessons from Europe," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 14(3), pages 1-36, March.
  6. N. Acocella & G. Bartolomeo & Andrew Hallett, 2006. "Controllability in Policy Games: Policy Neutrality and the Theory of Economic Policy Revisited," Computational Economics, Society for Computational Economics, vol. 28(2), pages 91-112, September.
  7. Yeh, Kuo-chun & Ho, Tai-kuang, 2011. "ERM crisis in retrospect: What if a European central bank had been in existence before 1992?," Economic Modelling, Elsevier, vol. 28(4), pages 1526-1535, July.

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