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On the Relationship Between Determinate and MSV Solutions in Linear RE Models

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Bennett McCallum

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Abstract

This paper considers the possibility that, in linear rational expectations (RE) models, all determinate (uniquely non-explosive) solutions coincide with the minimum state variable (MSV) solution, which is unique by construction. In univariate specifications of the form y(t) = AE(t)y(t+1) + Cy(t-1) + u(t) that result holds: if a RE solution is unique and non-explosive, then it is the same as the MSV solution. Also, this result holds for multivariate versions if the A and C matrices commute and a certain regularity condition holds. More generally, however, there are models of this form that possess unique non-explosive solutions that differ from their MSV solutions. Examples are provided and a strategy for easily constructing others is outlined.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0297.

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Date of creation: Jul 2004
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Handle: RePEc:nbr:nberte:0297

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C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming

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  1. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September. [Downloadable!] (restricted)
  2. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  3. James Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers 2000-001, Federal Reserve Bank of St. Louis. [Downloadable!]
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  4. 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.
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  5. Uhlig, H., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 97, Tilburg University, Center for Economic Research. [Downloadable!]
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  6. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  7. Desgranges, Gabriel & Gauthier, St phane, 2003. "Uniqueness Of Bubble-Free Solution In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(02), pages 171-191, April. [Downloadable!]
  8. 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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  9. Faust, Jon & Svensson, Lars E O, 2001. "Transparency and Credibility: Monetary Policy with Unobservable Goals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 369-97, May.
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  10. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 102(2), pages 354-374, February. [Downloadable!] (restricted)
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  11. Leitemo, Kai, 2003. " Targeting Inflation by Constant-Interest-Rate Forecasts," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(4), pages 609-26, August.
  12. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July. [Downloadable!] (restricted)
  13. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January. [Downloadable!] (restricted)
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Cited by:
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  1. Andreas Schabert, 2005. "Money Supply and the Implementation of Interest Rate Targets," Tinbergen Institute Discussion Papers 05-059/2, Tinbergen Institute. [Downloadable!]
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  2. Schabert, Andreas, 2005. "Discretionary Policy, Multiple Equilibria, and Monetary Instruments," CEPR Discussion Papers 5400, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  3. 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)
  4. Takeshi Kimura & Takushi Kurozumi, 2003. "Optimal monetary policy in a micro-founded model with parameter uncertainty," Finance and Economics Discussion Series 2003-67, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  5. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor Principle," NBER Working Papers 11874, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    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. Bennett T. McCallum, 2006. "E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models," NBER Working Papers 12441, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
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