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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.

Suggested Citation

  • Bennett McCallum, 2004. "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," NBER Technical Working Papers 0297, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0297
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    3. 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.
    4. Schabert, Andreas, 2005. "Discretionary Policy, Multiple Equilibria, and Monetary Instruments," CEPR Discussion Papers 5400, C.E.P.R. Discussion Papers.
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    8. Giuseppe Ferrero & Alessandro Secchi, 2010. "Central bank’s macroeconomic projections and learning," NBP Working Papers 72, Narodowy Bank Polski.
    9. Schabert, Andreas, 2005. "Money supply and the implementation of interest rate targets," Working Paper Series 483, European Central Bank.
    10. Minseong Kim, 2019. "Time-consistent decisions and rational expectation equilibrium existence in DSGE models," Papers 1909.10915, arXiv.org, revised May 2020.
    11. Roberta CARDANI, 2008. "Optimal Monetary Policy with Wealth Effect and Cost Channel," EcoMod2008 23800021, EcoMod.
    12. 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.
    13. 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.
    14. Bennett T. McCallum, 2012. "A Continuity Refinement for Rational Expectations Solutions," NBER Working Papers 18323, National Bureau of Economic Research, Inc.
    15. Nakagawa, Ryuichi, 2015. "Learnability of an equilibrium with private information," Journal of Economic Dynamics and Control, Elsevier, vol. 59(C), pages 58-74.
    16. 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.
    17. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.

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

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