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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. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 2000. "Avoiding Liquidity Traps," Departmental Working Papers, Rutgers University, Department of Economics 199925, Rutgers University, Department of Economics.
  2. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, Elsevier, vol. 120(1), pages 39-72, January.
  3. Athanasios Orphanides, 2001. "Monetary Policy Rules Based on Real-Time Data," American Economic Review, American Economic Association, American Economic Association, vol. 91(4), pages 964-985, September.
  4. 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, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 12026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 2003. "Backward-looking interest-rate rules, interest-rate smoothing, and macroeconomic instability," Working Papers 03-4, Federal Reserve Bank of Philadelphia.
  6. Michael Woodford, 1999. "Optimal Monetary Policy Inertia," NBER Working Papers 7261, National Bureau of Economic Research, Inc.
  7. Bill Dupor, 2000. "Investment and Interest Rate Policy," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0007, Econometric Society.
  8. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 115(1), pages 147-180, February.
  9. Gray, Malcolm R & Turnovsky, Stephen J, 1979. "Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models," Econometrica, Econometric Society, Econometric Society, vol. 47(6), pages 1457-74, November.
  10. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 1998. "Monetary policy and multiple equilibria," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 1998-29, Board of Governors of the Federal Reserve System (U.S.).
  11. Raouf Boucekkine & David de la Croix & Omar Licandro, . "Modelling vintage structures with DDEs: Principles and applications," Working Papers 2004-07, FEDEA.
  12. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers, European University Institute ECO2006/17, European University Institute.
  13. Charles T. Carlstrom & Timothy S. Fuerst, 2003. "Investment and interest rate policy: a discrete time analysis," Working Paper, Federal Reserve Bank of Cleveland 0320, Federal Reserve Bank of Cleveland.
  14. Stefano Eusepi, 2005. "Comparing forecast-based and backward-looking Taylor rules: a "global" analysis," Staff Reports, Federal Reserve Bank of New York 198, Federal Reserve Bank of New York.
  15. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00717412, HAL.
  16. Charles T. Carlstrom & Timothy S. Fuerst, 2001. "Timing and real indeterminacy in monetary models," Working Paper, Federal Reserve Bank of Cleveland 9910R, Federal Reserve Bank of Cleveland.
  17. 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, University of Chicago Press, vol. 83(2), pages 241-54, April.
  18. Leeper, Eric M., 1991. "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Elsevier, Elsevier, vol. 27(1), pages 129-147, February.
  19. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 36(1), pages 1-15, February.
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