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

  • Engwerda, J. C.

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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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 22 (1998)
Issue (Month): 8-9 (August)
Pages: 1487-1506

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Handle: RePEc:eee:dyncon:v:22:y:1998:i:8-9:p:1487-1506
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  1. repec:ner:tilbur:urn:nbn:nl:ui:12-377519 is not listed on IDEAS
  2. Engwerda, J.C., 1998. "On the open-loop Nash equilibrium in LQ-games," Other publications TiSEM b0eba71b-2d15-471a-b057-4, Tilburg University, School of Economics and Management.
  3. de Zeeuw, A.J. & van der Ploeg, F., 1987. "Difference games and policy evaluation : A conceptual framework," Research Memorandum FEW 268, Tilburg University, School of Economics and Management.
  4. 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.
  5. van Aarle, B. & 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.
  6. 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.
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-80026 is not listed on IDEAS
  8. repec:dgr:kubcen:19951 is not listed on IDEAS
  9. 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.
  10. repec:ner:tilbur:urn:nbn:nl:ui:12-153069 is not listed on IDEAS
  11. 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.
  12. 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.
  13. 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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