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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. Bennett McCallum, 1999. "Role of the Minimal State Variable Criterion in Rational Expectations Models," International Tax and Public Finance, Springer, vol. 6(4), pages 621-639, November.
  2. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 102(2), pages 354-374, February.
  3. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  4. Stéphane Gauthier, 2003. "Dynamic equivalence principle in linear rational expectations models," Post-Print halshs-00069499, HAL.
  5. McCallum, Bennett T., 1998. "Solutions to linear rational expectations models: a compact exposition," Economics Letters, Elsevier, vol. 61(2), pages 143-147, November.
  6. 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.
  7. Kaushik Mitra & James Bullard, . "Learning About Monetary Policy Rules," Discussion Papers 00/41, Department of Economics, University of York.
  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. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
  10. Uhlig, H., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
  11. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
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Citations

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Cited by:
  1. Bennett T. McCallum, 2009. "Causality, Structure, and the Uniqueness of Rational Expectations Equilibria," NBER Working Papers 15234, National Bureau of Economic Research, Inc.
  2. 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.).
  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. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor Principle," NBER Working Papers 11874, National Bureau of Economic Research, Inc.
  5. 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.
  6. repec:nbr:nberwo:14164 is not listed on IDEAS
  7. Miguel Casares & Antonio Moreno & Jesús Vázquez, 2009. "Wage Stickiness and Unemployment Fluctuations: An Alternative Approach," Faculty Working Papers 04/09, School of Economics and Business Administration, University of Navarra.
  8. Schabert, Andreas, 2005. "Discretionary Policy, Multiple Equilibria, and Monetary Instruments," CEPR Discussion Papers 5400, C.E.P.R. Discussion Papers.
  9. Schabert, Andreas, 2005. "Money supply and the implementation of interest rate targets," Working Paper Series 0483, European Central Bank.
  10. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.

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