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The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models

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  • Bennett T. McCallum

Abstract

This paper explores the relationship between the closely linked concepts of E-stability and least-squares learnability, featured in important recent work by Evans and Honkapohja (1999, 2001), and the minimum-state-variable (MSV) solution concept introduced by McCallum (1983) and used by many researchers for rational expectations (RE) analysis. It is shown that the MSV solution, which is unique by construction, is E-stable—and therefore LS learnable if nonexplosive—in all linear RE models that satisfy conditions for being “well formulated.” The latter property, introduced in the paper, consists of two requirements. The first is that a model’s structural parameters are restricted so as to avoid any infinite discontinuity, of the steady state values of endogenous variables, in response to small changes in these parameters. (It can be expressed cleanly in terms of the eigenvalues of a matrix that is the sum of those attached to the one period ahead and one period lagged values of the endogenous variables in a first-order vector formulation of the model.) The second, which is needed infrequently, is that the parameters are restricted to prevent any infinite discontinuities in the MSV solution response coefficients.

Suggested Citation

  • Bennett T. McCallum, 2002. "The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models," GSIA Working Papers 2003-25, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:906654633
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    3. Heinz-Peter Spahn, 2004. "Learning in Macroeconomics and Monetary Policy: The Case of an Open Economy," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 236/2004, Department of Economics, University of Hohenheim, Germany.
    4. Leitemo, Kai, 2006. "Targeting inflation by forecast feedback rules in small open economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 393-413, March.
    5. Audzei, Volha & Slobodyan, Sergey, 2022. "Sparse restricted perceptions equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    6. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2011. "Minimal state variable solutions to Markov-switching rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2150-2166.
    7. Eusepi, Stefano, 2007. "Learnability and monetary policy: A global perspective," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1115-1131, May.
    8. Juan Paez-Farrell, 2008. "Assessing sticky price models using the Burns and Mitchell approach," Applied Economics, Taylor & Francis Journals, vol. 40(11), pages 1387-1397.
    9. Bennett T. Mccallum, 2003. "Is The Fiscal Theory of the Price Level Learnable?," Scottish Journal of Political Economy, Scottish Economic Society, vol. 50(5), pages 634-649, November.
    10. Ellison, Martin & Pearlman, Joseph, 2011. "Saddlepath learning," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1500-1519, July.
    11. 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.
    12. Fanelli, Luca, 2008. "Evaluating New Keynesian Phillips Curve under VAR-Based Learning," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-24.
    13. Joseph Pearlman, 2007. "Is There More than One Way to be E-Stable?," CDMA Working Paper Series 200701, Centre for Dynamic Macroeconomic Analysis.

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    JEL classification:

    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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