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

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