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On the relationship between determinate and MSV solutions in linear RE models

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  • McCallum, Bennett T.

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 yt = AEtyt+1 + Cyt-1 + ut 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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Bibliographic Info

Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 84 (2004)
Issue (Month): 1 (July)
Pages: 55-60

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Handle: RePEc:eee:ecolet:v:84:y:2004:i:1:p:55-60

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  1. Stéphane Gauthier, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Post-Print hal-00731065, HAL.
  2. 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.
  3. Uhlig, H., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
  4. 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.
  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. 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.
  7. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  8. 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.
  9. Bennett T. McCallum, 1998. "Solutions to Linear Rational Expectations Models: A Compact Exposition," NBER Technical Working Papers 0232, National Bureau of Economic Research, Inc.
  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, . "Role of the minimal state variable criterion in rational expectations models," GSIA Working Papers 1999-13, Carnegie Mellon University, Tepper School of Business.
  12. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
  13. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  14. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January.
  15. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
  16. 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.
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Cited by:
  1. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
  2. Andreas Schabert, 2005. "Discretionary Policy, Multiple Equilibria, and Monetary Instruments," Tinbergen Institute Discussion Papers 05-098/2, Tinbergen Institute.
  3. Miguel Casares & Antonio Moreno & Jesús Vázquez, 2012. "Wage stickiness and unemployment fluctuations: an alternative approach," SERIEs, Spanish Economic Association, vol. 3(3), pages 395-422, September.
  4. McCallum, Bennett T., 2007. "E-stability vis-a-vis determinacy results for a broad class of linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1376-1391, April.
  5. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.
  6. 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.
  7. Bennett T. Mccallum, 2011. "Causality, Structure And The Uniqueness Of Rational Expectations Equilibria," Manchester School, University of Manchester, vol. 79(s1), pages 551-566, 06.
  8. Schabert, Andreas, 2005. "Money Supply and the Implementation of Interest Rate Targets," CEPR Discussion Papers 5094, C.E.P.R. Discussion Papers.
  9. repec:nbr:nberwo:14164 is not listed on IDEAS
  10. Cho, Seonghoon & Moreno, Antonio, 2011. "The forward method as a solution refinement in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 257-272, March.

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