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E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models

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Bennett T. McCallum

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Abstract

It is argued that learnability/E-stability is a necessary condition for a RE solution to be plausible. A class of linear models considered by Evans and Honkapohja (2001) is shown to include all models of the form used by King and Watson (1998) and Klein (2000), which permits any number of lags, leads, and lags of leads. For this broad class it is shown that, if current-period information is available in the learning process, determinacy is a sufficient condition for E-stability. It is not a necessary condition, however; there exist cases with more than one stable solution in which the solution based on the decreasing-modulus ordering of the system’s eigenvalues is E-stable. If in such a case the other stable solution(s) are not E-stable, then the condition of indeterminacy may not be important for practical issues.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12441.

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Date of creation: Aug 2006
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Handle: RePEc:nbr:nberwo:12441

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
E00 - Macroeconomics and Monetary Economics - - General - - - General

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  4. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September. [Downloadable!] (restricted)
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  6. Sims, Christopher A, 1994. "A Simple Model for Study of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy," Economic Theory, Springer, vol. 4(3), pages 381-99.
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  11. George W. Evans & Roger Guesnerie, 2003. "Coordination on Saddle-Path Solutions: the Eductive Viewpoint - Linear Multivariate Models," DELTA Working Papers 2003-28, DELTA (Ecole normale supérieure). [Downloadable!]
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  12. Bennett McCallum, 2004. "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," NBER Technical Working Papers 0297, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  13. Bennett T. McCallum, 1983. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Klaus Adam & George W. Evans & Seppo Honkapohja, 2004. "Are Stationary Hyperinflation Paths Learnable?," CFS Working Paper Series 2004/15, Center for Financial Studies. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Bask, Mikael, 2007. "Optimal monetary policy in a hybrid New Keynesian model with a cost channel," Research Discussion Papers 24/2007, Bank of Finland. [Downloadable!]
  2. Bennett T. McCallum, 2009. "Causality, Structure, and the Uniqueness of Rational Expectations Equilibria," NBER Working Papers 15234, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Evans, George W & Honkapohja, Seppo, 2008. "Expectations, Learning and Monetary Policy: An Overview of Recent Rersearch," CEPR Discussion Papers 6640, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  4. Seonghoon Cho & Antonio Moreno, 2006. "Expectational Stability in Multivariate Models," Faculty Working Papers WP06/08, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  5. Llosa Gonzalo & Tuesta Vicente, 2007. "Learning about Monetary Policy Rules when the Cost Channel Matters," Working Papers 2007-014, Banco Central de Reserva del Perú. [Downloadable!]
    Other versions:
  6. Bennett T. McCallum, 2008. "Determinacy, Learnability, and Plausibility in Monetary Policy Analysis: Additional Results," NBER Working Papers 14164, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  7. James B. Bullard & Stefano Eusepi, 2009. "When does determinacy imply expectational stability?," Working Papers 2008-007, Federal Reserve Bank of St. Louis. [Downloadable!]
  8. Bennett T. McCallum, 2009. "Indeterminancy from inflation forecast targeting : problem or pseudo-problem?," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 25-51. [Downloadable!]
  9. Bennett T. McCallum, 2009. "The Role of "Determinacy" in Monetary Policy Analysis," IMES Discussion Paper Series 09-E-17, Institute for Monetary and Economic Studies, Bank of Japan. [Downloadable!]
  10. Bask, Mikael, 2007. "Optimal monetary policy under heterogeneity in currency trade," Research Discussion Papers 21/2007, Bank of Finland. [Downloadable!]
  11. Bask, Mikael, 2007. "Instrument rules in monetary policy under heterogeneity in currency trade," Research Discussion Papers 22/2007, Bank of Finland. [Downloadable!]
    Other versions:
  12. Joseph Pearlman, 2007. " Is There More than One Way to be E-Stable?," CDMA Working Paper Series 0701, Centre for Dynamic Macroeconomic Analysis. [Downloadable!]
  13. Bask, Mikael, 2009. "Monetary Policy, Stock Price Misalignments and Macroeconomic Instability," Working Papers 540, Hanken School of Economics. [Downloadable!]
  14. George W. Evans & Seppo Honkapohja, 2008. "Learning and Macroeconomics," University of Oregon Economics Department Working Papers 2008-3, University of Oregon Economics Department. [Downloadable!]
  15. Bask, Mikael, 2007. "A case for interest rate smoothing," Research Discussion Papers 25/2007, Bank of Finland. [Downloadable!]
  16. Carceles-Poveda, Eva & Giannitsarou, Chryssi, 2006. "Adaptive Learning in Practice," CEPR Discussion Papers 5627, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  17. Ichiro Muto, 2008. "Monetary Policy and Learning from the Central Bank's Forecast," IMES Discussion Paper Series 08-E-01, Institute for Monetary and Economic Studies, Bank of Japan. [Downloadable!]
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