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Uniqueness of bubble-free solution in linear rational expectations models


  • G. Desgranges

    (THEMA - Théorie économique, modélisation et applications - Université de Cergy Pontoise - CNRS - Centre National de la Recherche Scientifique)

  • Stéphane Gauthier

    () (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - CNRS - Centre National de la Recherche Scientifique, CREST-INSEE - Centre de Recherche en Economie et en Statistique - Institut national de la statistique et des études économiques (INSEE), ERMES - Equipe de recherche sur les marches, l'emploi et la simulation - UP2 - Université Panthéon-Assas - M.E.N.E.S.R. - Ministère de l'Éducation nationale, de l’Enseignement supérieur et de la Recherche - CNRS - Centre National de la Recherche Scientifique)


One usually identifies bubble solutions to linear rational expectations models by extra components (irrelevant lags) arising in addition to market fundamentals. Although there are still many solutions relying on a minimal set of state variables, i.e., relating in equilibrium the current state of the economic system to as many lags as initial conditions, there is a conventional wisdom that the bubble-free (fundamentals) solution should be unique. This paper examines the existence of endogenous stochastic sunspot fluctuations close to solutions relying on a minimal set of state variables, which provides a natural test for identifying bubble and bubble-free solutions. It turns out that only one solution is locally immune to sunspots, independently of the stability properties of the perfect-foresight dynamics. In the standard saddle-point configuration for these dynamics, this solution corresponds to the so-called saddle stable path.

Suggested Citation

  • G. Desgranges & Stéphane Gauthier, 2003. "Uniqueness of bubble-free solution in linear rational expectations models," Post-Print halshs-00069498, HAL.
  • Handle: RePEc:hal:journl:halshs-00069498
    DOI: 10.1017/S1365100501010264
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    References listed on IDEAS

    1. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    2. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1991. "Speculative Dynamics," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 529-546.
    3. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    4. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
    5. Costas Azariadis & Shankha Chakraborty, 1998. "Asset price volatility in a nonconvex general equilibrium model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(3), pages 649-665.
    6. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    7. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
    8. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
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    Cited by:

    1. 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.
    2. Roger Guesnerie, 2009. "Macroeconomic and Monetary Policies from the Eductive Viewpoint," Central Banking, Analysis, and Economic Policies Book Series,in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.), Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 6, pages 171-202 Central Bank of Chile.
    3. 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.
    4. Gauthier, Stephane, 2004. "Determinacy in linear rational expectations models," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 815-830, November.


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