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The Unique Minimum State Variable RE Solution is E-Stable in All Well Formulated Linear Models

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  • Bennett T. McCallum

Abstract

This paper explores the relationship between the closely linked concepts of E-stability and least-squares learnability, featured in recent work by Evans and Honkapohja (1999, 2001), and the minimum-state-variable (MSV) solution defined by McCallum (1983) and used by many researchers for rational expectations (RE) analysis. It is shown that the MSV solution, which is unique by construction, is E-stable--and therefore LS learnable when nonexplosive--in all linear RE models that satisfy conditions for being well formulated.' The latter property involves two requirements. The first is that values of the model's parameters are restricted so as to avoid any infinite discontinuity, of the steady state values of endogenous variables, in response to small changes in these parameters. (It is expressed in terms of the eigenvalues of a matrix that is the sum of those attached to the one-period-ahead and one-period-lagged values of the endogenous variables in a first-order vector formulation of the model.) The second, which is needed infrequently, is that the parameters are restricted to prevent any infinite discontinuities in the MSV response coefficients.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9960.

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Date of creation: Sep 2003
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Publication status: published as McCallum, Bennett T. "On The Relationship Between Determinate And CSV Solutions In Linear Re Models," Economics Letters, 2004, v84(1,Jul), 55-60.
Handle: RePEc:nbr:nberwo:9960

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  1. Robert G. King, 2000. "The new IS-LM model : language, logic, and limits," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 45-103.
  2. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
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  7. Evans, George, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, MIT Press, vol. 100(4), pages 1217-33, November.
  8. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics 9415, Faculty of Economics, University of Cambridge.
  9. DeCanio, Stephen J, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 47-57, February.
  10. Robert A. Driskill, 2002. "A Proposal for a Selection Criterion in a Class of Dynamic Rational Expectations Models with Multiple Equilibria," Vanderbilt University Department of Economics Working Papers 0210, Vanderbilt University Department of Economics.
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  13. Desgranges, G. & Gauthier, S., 1999. "On the Uniqueness of the Bubble-Free Solution in Linear Rational Expectations Models," G.R.E.Q.A.M. 99a45, Universite Aix-Marseille III.
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  16. Michael Woodford, 1994. "Nonstandard Indicators for Monetary Policy: Can Their Usefulness Be Judged from Forecasting Regressions?," NBER Chapters, in: Monetary Policy, pages 95-115 National Bureau of Economic Research, Inc.
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  23. Evans, George W & Honkapohja, Seppo, 1992. "On the Robustness of Bubbles in Linear RE Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 1-14, February.
  24. Bennett T. McCallum, 1981. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc.
  25. Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
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Cited by:
  1. Fanelli, Luca, 2007. "Evaluating the New Keynesian Phillips Curve under VAR-based learning," MPRA Paper 1616, University Library of Munich, Germany.
  2. Bianchi, Francesco, 2008. "Regime switches, Agents’ Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," MPRA Paper 24251, University Library of Munich, Germany, revised 19 Jan 2010.
  3. Ellison, Martin & Pearlman, Joseph, 2011. "Saddlepath learning," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1500-1519, July.
  4. Joseph Pearlman, 2007. "Is There More than One Way to be E-Stable?," CDMA Working Paper Series 200701, Centre for Dynamic Macroeconomic Analysis.
  5. Kimura, Takeshi & Kurozumi, Takushi, 2007. "Optimal monetary policy in a micro-founded model with parameter uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 399-431, February.
  6. Eusepi, Stefano, 2007. "Learnability and monetary policy: A global perspective," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1115-1131, May.
  7. Heinz-Peter Spahn, 2004. "Learning in Macroeconomics and Monetary Policy: The Case of an Open Economy," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 236/2004, Department of Economics, University of Hohenheim, Germany.
  8. repec:nbr:nberwo:14164 is not listed on IDEAS

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