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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 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
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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

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  1. G. Desgranges & Stéphane Gauthier, 2003. "Uniqueness of bubble-free solution in linear rational expectations models," Post-Print, HAL halshs-00069498, HAL.
  2. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  3. Faust, Jon & Svensson, Lars E O, 2001. "Transparency and Credibility: Monetary Policy with Unobservable Goals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 369-97, May.
  4. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(2), pages 354-374, February.
  5. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, Elsevier, vol. 11(2), pages 139-168.
  6. James Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers, Federal Reserve Bank of St. Louis 2000-001, Federal Reserve Bank of St. Louis.
  7. Leitemo, Kai, 2003. " Targeting Inflation by Constant-Interest-Rate Forecasts," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 35(4), pages 609-26, August.
  8. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1305-11, July.
  9. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 7(01), pages 63-88, February.
  10. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9415, Faculty of Economics, University of Cambridge.
  11. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, Elsevier, vol. 18(2), pages 147-157, September.
  12. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis 101, Federal Reserve Bank of Minneapolis.
  13. Bennett T. McCallum, . "Role of the minimal state variable criterion in rational expectations models," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 1999-13, Carnegie Mellon University, Tepper School of Business.
  14. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  15. Bennett T. McCallum, 1998. "Solutions to Linear Rational Expectations Models: A Compact Exposition," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0232, National Bureau of Economic Research, Inc.
  16. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, Elsevier, vol. 23(1), pages 3-30, January.
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Cited by:
  1. Schabert, Andreas, 2005. "Money supply and the implementation of interest rate targets," Working Paper Series, European Central Bank 0483, European Central Bank.
  2. Schabert, Andreas, 2005. "Discretionary policy, multiple equilibria, and monetary instruments," Working Paper Series, European Central Bank 0533, European Central Bank.
  3. Troy Davig & Eric M. Leeper, 2005. "Generalizing the Taylor principle," Research Working Paper, Federal Reserve Bank of Kansas City RWP 05-13, Federal Reserve Bank of Kansas City.
  4. 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, Departamento de Economía - Universidad Pública de Navarra 0902, Departamento de Economía - Universidad Pública de Navarra.
  5. Cho, Seonghoon & Moreno, Antonio, 2011. "The forward method as a solution refinement in rational expectations models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(3), pages 257-272, March.
  6. Bennett T. Mccallum, 2011. "Causality, Structure And The Uniqueness Of Rational Expectations Equilibria," Manchester School, University of Manchester, University of Manchester, vol. 79(s1), pages 551-566, 06.
  7. repec:nbr:nberwo:14164 is not listed on IDEAS
  8. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(10), pages 3203-3227, October.
  9. 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, Elsevier, vol. 31(4), pages 1376-1391, April.
  10. Takeshi Kimura & Takushi Kurozumi, 2003. "Optimal monetary policy in a micro-founded model with parameter uncertainty," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2003-67, Board of Governors of the Federal Reserve System (U.S.).

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