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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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References

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  1. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-64, September.
  2. Ploeg, F. van der & Zeeuw, A.J. de, 1991. "Difference games and policy evaluation: A conceptual framework," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377519, Tilburg University.
  3. Aarle, B. van & Bovenberg, A.L. & Raith, M., 1995. "Monetary and fiscal policy interaction and government debt stabilization," Discussion Paper 1995-1, Tilburg University, Center for Economic Research.
  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. 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.
  6. Bas Aarle & Lans Bovenberg & Matthias Raith, 1995. "Monetary and fiscal policy interaction and government debt stabilization," Journal of Economics, Springer, vol. 62(2), pages 111-140, June.
  7. 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.
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Cited by:
  1. 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.
  2. Joseph Plasmans & Jacob Engwerda & Bas van Aarle & Tomasz Michalak & Giovanni Di Bartolomeo, 2006. "Macroeconomic Stabilization Policies In The Emu: Spillovers, Asymmetries And Institutions," Scottish Journal of Political Economy, Scottish Economic Society, vol. 53(4), pages 461-484, 09.
  3. 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.
  4. 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.

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