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Backward- versus Forward-Looking Feedback Interest Rate Rules

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  • Hippolyte D'Albis

    ()
    (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Emmanuelle Augeraud-Véron

    ()
    (MIA - Mathématiques, Image et Applications - Université de La Rochelle : EA3165)

  • Hermen Jan Hupkes

    ()
    (University of Missouri - Columbia - Mathematics Department)

Abstract

This paper proposes conditions for the existence and uniqueness of solutions to systems of differential equations with delays or advances in which some variables are non-predetermined. An application to the issue of optimal interest rate policy is then develop in a flexible-price model where money enters the utility function. Central banks have the choice between a rule that depends on past inflation rates or one that depends on predicted interest rates. When inflation rates are selected over a bounded time interval, the problem is characterized by a system of delay or advanced differential equations. We then prove that if the central bank's forecast horizon is not too long, an active and forward-looking monetary policy is not too destabilizing : the equilibrium trajectory is unique and monotonic.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00721289.

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Date of creation: Jun 2012
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Handle: RePEc:hal:cesptp:halshs-00721289

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Keywords: Interest rate rules; indeterminacy; functionnal differential equations;

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  1. Raouf BOUCEKKINE & David DE LA CROIX & Omar LICANDRO, 2004. "Modelling vintage structures with DDEs: principles and applications," Economics Working Papers ECO2004/06, European University Institute.
  2. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 1998. "Monetary policy and multiple equilibria," Finance and Economics Discussion Series 1998-29, Board of Governors of the Federal Reserve System (U.S.).
  3. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, . "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
  4. Athanasios Orphanides, 1998. "Monetary policy rules based on real-time data," Finance and Economics Discussion Series 1998-03, Board of Governors of the Federal Reserve System (U.S.).
  5. Charles T. Carlstrom & Timothy S. Fuerst, 2001. "Timing and real indeterminacy in monetary models," Working Paper 9910R, Federal Reserve Bank of Cleveland.
  6. Jess Benhabib & Stephanie Schitt-Grohe & Martin Uribe, 2002. "Backward-Looking Interest-Rate Rules, Interest-Rate Smoothing, and Macroeconomic Instability," PIER Working Paper Archive 03-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 14 Feb 2003.
  7. Bill Dupor, 2000. "Investment and Interest Rate Policy," Econometric Society World Congress 2000 Contributed Papers 0007, Econometric Society.
  8. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(1), pages 1-15, February.
  9. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Documents de travail du Centre d'Economie de la Sorbonne 12026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  10. Benhabib, Jess & Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Avoiding Liquidity Traps," CEPR Discussion Papers 2948, C.E.P.R. Discussion Papers.
  11. Charles T. Carlstrom & Timothy S. Fuerst, 2003. "Investment and interest rate policy: a discrete time analysis," Working Paper 0320, Federal Reserve Bank of Cleveland.
  12. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February.
  13. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  14. Gray, Malcolm R & Turnovsky, Stephen J, 1979. "Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models," Econometrica, Econometric Society, vol. 47(6), pages 1457-74, November.
  15. Woodford, Michael, 1999. "Optimal monetary policy inertia," CFS Working Paper Series 1999/09, Center for Financial Studies (CFS).
  16. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Functional Differential-Algebraic Equations of Mixed Type," Documents de travail du Centre d'Economie de la Sorbonne 12043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  17. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717198, HAL.
  18. Sargent, Thomas J & Wallace, Neil, 1975. ""Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 241-54, April.
  19. Leeper, Eric M., 1991. "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 129-147, February.
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