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

  • Bennett McCallum

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
Date of revision:
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:nberte:0297
Note: TWP
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  1. Gauthier, S., 1999. "Determinacy and Stability under Learning of Rational Expectations Equilibria," DELTA Working Papers 1999-22, DELTA (Ecole normale supérieure).
  2. 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.
  3. Jon Faust & Lars E. O. Svensson, 1998. "Transparency and Credibility: Monetary Policy with Unobservable Goals," NBER Working Papers 6452, National Bureau of Economic Research, Inc.
  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.
  5. 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.
  6. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January.
  7. James B. Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers 2000-001, Federal Reserve Bank of St. Louis.
  8. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  9. Bennett T. McCallum, . "Role of the minimal state variable criterion in rational expectations models," GSIA Working Papers 1999-13, Carnegie Mellon University, Tepper School of Business.
  10. G. Desgranges & Stéphane Gauthier, 2003. "Uniqueness of bubble-free solution in linear rational expectations models," Post-Print halshs-00069498, HAL.
  11. Bennett T. McCallum, 1998. "Solutions to Linear Rational Expectations Models: A Compact Exposition," NBER Technical Working Papers 0232, National Bureau of Economic Research, Inc.
  12. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  13. 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.
  14. 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.
  15. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
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