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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. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
  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. 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.
  5. 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.
  6. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  7. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
  8. McCallum, Bennett T., 1998. "Solutions to linear rational expectations models: a compact exposition," Economics Letters, Elsevier, vol. 61(2), pages 143-147, November.
  9. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  10. 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.
  11. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 102(2), pages 354-374, February.
  12. 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.
  13. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
  14. 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.
  15. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
  16. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January.
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Citations

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Cited by:
  1. Schabert, Andreas, 2005. "Discretionary Policy, Multiple Equilibria, and Monetary Instruments," CEPR Discussion Papers 5400, C.E.P.R. Discussion Papers.
  2. Schabert, Andreas, 2005. "Money supply and the implementation of interest rate targets," Working Paper Series 0483, European Central Bank.
  3. 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.
  4. 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.
  5. 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.
  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.
  7. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor principle," Research Working Paper RWP 05-13, Federal Reserve Bank of Kansas City.
  8. 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.
  9. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.
  10. 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.).

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