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

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  • Bennett McCallum

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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Paper provided by Carnegie Mellon University, Tepper School of Business in its series GSIA Working Papers with number 2003-E78.

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Handle: RePEc:cmu:gsiawp:1362627550

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Postal: Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890
Web page: http://www.tepper.cmu.edu/

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  1. Uhlig, H., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
  2. 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.
  3. Stéphane Gauthier, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Post-Print hal-00731065, HAL.
  4. Kaushik Mitra & James Bullard, . "Learning About Monetary Policy Rules," Discussion Papers 00/41, Department of Economics, University of York.
  5. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  6. 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.
  7. 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.
  8. Bennett T. McCallum, 1998. "Solutions to Linear Rational Expectations Models: A Compact Exposition," NBER Technical Working Papers 0232, National Bureau of Economic Research, Inc.
  9. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
  10. Svensson, Lars E.O. & Faust, John, 1998. "Transparency and Credibility: Monetary Policy with Unobservable Goals," Seminar Papers 636, Stockholm University, Institute for International Economic Studies.
  11. 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.
  12. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  13. 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.
  14. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January.
  15. 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.
  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, 2005. "Generalizing the Taylor principle," Research Working Paper RWP 05-13, Federal Reserve Bank of Kansas City.
  2. 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.
  3. 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.
  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.).
  5. Schabert, Andreas, 2005. "Money supply and the implementation of interest rate targets," Working Paper Series 0483, European Central Bank.
  6. Schabert, Andreas, 2005. "Discretionary policy, multiple equilibria, and monetary instruments," Working Paper Series 0533, European Central Bank.
  7. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.
  8. Miguel Casares & Antonio Moreno & Jesús Vázquez, 2009. "Wage Stickiness and Unemployment Fluctuations: An Alternative Approach," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0902, Departamento de Economía - Universidad Pública de Navarra.
  9. 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.
  10. repec:nbr:nberwo:14164 is not listed on IDEAS

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