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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.

Suggested Citation

  • Bennett McCallum, "undated". "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," GSIA Working Papers 2003-E78, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:1362627550
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    2. Pablo Cuba-Borda & Sanjay R. Singh, 2024. "Understanding Persistent ZLB: Theory and Assessment," American Economic Journal: Macroeconomics, American Economic Association, vol. 16(3), pages 389-416, July.
    3. 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.
    4. Miguel Casares & Antonio Moreno & Jesús Vázquez, 2012. "Wage stickiness and unemployment fluctuations: an alternative approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(3), pages 395-422, September.
    5. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.
    6. Bennett T. McCallum, 2012. "A Continuity Refinement for Rational Expectations Solutions," NBER Working Papers 18323, National Bureau of Economic Research, Inc.
    7. Nakagawa, Ryuichi, 2015. "Learnability of an equilibrium with private information," Journal of Economic Dynamics and Control, Elsevier, vol. 59(C), pages 58-74.
    8. Bennett T. Mccallum, 2011. "Causality, Structure And The Uniqueness Of Rational Expectations Equilibria," Manchester School, University of Manchester, vol. 79(s1), pages 551-566, June.
    9. Seonghoon Cho & Antonio Moreno, 2007. "The Forward Solution for Linear Rational Expectations Models," Faculty Working Papers 07/07, School of Economics and Business Administration, University of Navarra.
    10. Schabert, Andreas, 2005. "Discretionary Policy, Multiple Equilibria, and Monetary Instruments," CEPR Discussion Papers 5400, C.E.P.R. Discussion Papers.
    11. 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.
    12. John Y. Campbell & Carolin Pflueger & Luis M. Viceira, 2020. "Macroeconomic Drivers of Bond and Equity Risks," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3148-3185.
    13. Kimura, Takeshi & Kurozumi, Takushi, 2007. "Optimal monetary policy in a micro-founded model with parameter uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 399-431, February.
    14. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    15. Giuseppe Ferrero & Alessandro Secchi, 2010. "Central banks' macroeconomic projections and learning," Temi di discussione (Economic working papers) 782, Bank of Italy, Economic Research and International Relations Area.
    16. Schabert, Andreas, 2005. "Money Supply and the Implementation of Interest Rate Targets," CEPR Discussion Papers 5094, C.E.P.R. Discussion Papers.
    17. Minseong Kim, 2019. "Time-consistent decisions and rational expectation equilibrium existence in DSGE models," Papers 1909.10915, arXiv.org, revised May 2020.
    18. Roberta CARDANI, 2008. "Optimal Monetary Policy with Wealth Effect and Cost Channel," EcoMod2008 23800021, EcoMod.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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