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Backward- versus Forward-Looking Feedback Interest Rate Rules

  • Hippolyte D'Albis


    (Axe Macroéconomie - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

  • Emmanuelle Augeraud-Véron


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

  • Hermen Jan Hupkes


    (University of Missouri - Columbia - Mathematics Department)

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
Date of revision:
Publication status: Published in Documents de travail du Centre d'Economie de la Sorbonne 2012.51 - ISSN : 1955-611X. 2012
Handle: RePEc:hal:cesptp:halshs-00721289
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  1. Benhabib, Jess & Schmitt-Grohé, Stephanie & Uribe, Martín, 1999. "Monetary Policy and Multiple Equilibria," CEPR Discussion Papers 2316, C.E.P.R. Discussion Papers.
  2. 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.).
  3. 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.
  4. Charles T. Carlstrom & Timothy S. Fuerst, 2003. "Investment and interest rate policy: a discrete time analysis," Working Paper 0320, Federal Reserve Bank of Cleveland.
  5. Woodford, Michael, 2000. "Optimal Monetary Policy Inertia," Seminar Papers 666, Stockholm University, Institute for International Economic Studies.
  6. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 1999. "Vintage Capital and the Dynamics of the AK Model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  7. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 2003. "Backward-looking interest-rate rules, interest-rate smoothing, and macroeconomic instability," Proceedings, Federal Reserve Bank of Cleveland, pages 1379-1423.
  8. Bill Dupor, 2000. "Investment and Interest Rate Policy," Econometric Society World Congress 2000 Contributed Papers 0007, Econometric Society.
  9. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Venditti, Alain, 2010. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," LERNA Working Papers 10.13.319, LERNA, University of Toulouse.
  10. 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.
  11. 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.
  12. BOUCEKKINE, RAOUF & de la CROIX, David & LICANDRO, Omar, 2004. "Modelling vintage structures with DDEs : principles and applications," CORE Discussion Papers 2004047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
  14. Benhabib, Jess & Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Avoiding Liquidity Traps," CEPR Discussion Papers 2948, C.E.P.R. Discussion Papers.
  15. Carlstrom, Charles T. & Fuerst, Timothy S., 2001. "Timing and real indeterminacy in monetary models," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 285-298, April.
  16. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  17. 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.
  18. 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) halshs-00717412, HAL.
  19. repec:fda:fdaddt:2004-07 is not listed on IDEAS
  20. Stefano Eusepi, 2005. "Comparing forecast-based and backward-looking Taylor rules: a "global" analysis," Staff Reports 198, Federal Reserve Bank of New York.
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