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Uniqueness Of Bubble-Free Solution In Linear Rational Expectations Models

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  • Desgranges, Gabriel
  • Gauthier, Stéphane

Abstract

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

  • Desgranges, Gabriel & Gauthier, Stéphane, 2003. "Uniqueness Of Bubble-Free Solution In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(2), pages 171-191, April.
    • Handle: RePEc:cup:macdyn:v:7:y:2003:i:02:p:171-191_01
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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.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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