IDEAS home Printed from https://ideas.repec.org/a/cup/macdyn/v7y2003i01p63-88_01.html
   My bibliography  Save this article

Dynamic Equivalence Principle In Linear Rational Expectations Models

Author

Listed:
  • Gauthier, St phane

Abstract

Linear models with infinite horizon generally admit infinitely many rational expectations solutions. Consequently, some additional selection devices are needed to narrow the set of relevant solutions. The viewpoint of this paper is that a solution will be more likely to arise if it is locally determinate (i.e., locally isolated), locally immune to sunspots, and locally stable under learning. These three criteria are applied to solutions of linear univariate models along which the level of the state variable evolves through time. In such models the equilibrium behavior of the level of the state variable is described by a linear recursive equation characterized by the set of its coefficients. The main innovation of this paper is to define new perfect-foresight dynamics whose fixed points are these sets of coefficients, thus allowing us to study the property of determinacy of these sets, or, equivalently, of the associated solutions. It is shown that only one solution is locally determinate in the new dynamics. It is also locally immune to sunspots and locally stable under myopic learning. This solution corresponds to the saddle path in the saddle-point case.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  • Handle: RePEc:cup:macdyn:v:7:y:2003:i:01:p:63-88_01
    as

    Download full text from publisher

    File URL: http://journals.cambridge.org/abstract_S1365100502010301
    File Function: link to article abstract page
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Evans George W. & Guesnerie Roger, 1993. "Rationalizability, Strong Rationality, and Expectational Stability," Games and Economic Behavior, Elsevier, pages 632-646.
    2. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
    3. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    4. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
    5. Marimon, R. & Spear, S. & Sunder, S., 1991. "Expectationally-Driven Market Volatility: An Experimental Study," GSIA Working Papers 1991-3, Carnegie Mellon University, Tepper School of Business.
    6. Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 297-317, March.
    7. Roger Guesnerie & Costas Azariadis, 1982. "Prophéties créatrices et persistance des théories," Revue Économique, Programme National Persée, vol. 33(5), pages 787-806.
    8. Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, pages 354-374.
    9. Townsend, Robert M, 1978. "Market Anticipations, Rational Expectations, and Bayesian Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 481-494, June.
    10. Herbert Dawid, 1996. "Learning of cycles and sunspot equilibria by Genetic Algorithms (*)," Journal of Evolutionary Economics, Springer, pages 361-373.
    11. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    12. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, pages 439-480.
    13. Guesnerie, Roger, 1992. "An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis," American Economic Review, American Economic Association, pages 1254-1278.
    14. Marimon Ramon & Spear Stephen E. & Sunder Shyam, 1993. "Expectationally Driven Market Volatility: An Experimental Study," Journal of Economic Theory, Elsevier, vol. 61(1), pages 74-103, October.
    15. Frank Heinemann, 1997. "Rationalizable expectations and sunspot equilibria in an overlapping-generations economy," Journal of Economics, Springer, pages 257-277.
    16. Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
    17. Guesnerie, Roger, 1993. "Theoretical tests of the rational expectations hypothesis in economic dynamical models," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 847-864.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
    2. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
    3. George W. Evans & Seppo Honkapohja, 2007. "The E-Correspondence Principle," Economica, London School of Economics and Political Science, pages 33-50.
    4. Evans, George W. & Guesnerie, Roger, 2005. "Coordination on saddle-path solutions: the eductive viewpoint--linear multivariate models," Journal of Economic Theory, Elsevier, pages 202-229.
    5. McCallum, Bennett T & Nelson, Edward, 1999. "An Optimizing IS-LM Specification for Monetary Policy and Business Cycle Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 296-316, August.
    6. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:macdyn:v:7:y:2003:i:01:p:63-88_01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters). General contact details of provider: http://journals.cambridge.org/jid_MDY .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.