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

  • Bennett McCallum

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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File URL: https://student-3k.tepper.cmu.edu/gsiadoc/wp/2003-E78.pdf
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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
Contact details of provider: 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. Barro, Robert J., 1989. "Interest-rate targeting," Journal of Monetary Economics, Elsevier, vol. 23(1), pages 3-30, January.
  2. 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.
  3. 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.
  4. 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.
  5. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
  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. repec:dgr:kubcen:199597 is not listed on IDEAS
  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. Stéphane Gauthier, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Post-Print hal-00731065, HAL.
  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. 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. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  14. Stéphane Gauthier, 2003. "Dynamic equivalence principle in linear rational expectations models," Post-Print halshs-00069499, HAL.
  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. 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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