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Sunspot Fluctuations around a Steady State: The Case of Multidimensional, One-Step Forward Looking Economic Models

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  • Chiappori, Pierre-Andre
  • Geoffard, Pierre-Yves
  • Guesnerie, Roger

Abstract

The paper investigates the existence of stationary sunspot equilibria (SSE) in the vicinity of a steady state in a general, one-step forward looking economic model of dimension n. It is shown that, whenever the steady state is indeterminate, for the associated deterministic dynamics--i.e., there exists a continuum of perfect foresight paths converging to the steady state--then there exists a continuum of SSE of finite order in any neighborhood of the steady state. The proof relies upon bifurcation theory; it provides a characterization of the random processes for which SSE may appear and a description of the location of the support of the SSE close to the bifurcation. The results apply in particular to linear models. Copyright 1992 by The Econometric Society.

Suggested Citation

  • Chiappori, Pierre-Andre & Geoffard, Pierre-Yves & Guesnerie, Roger, 1992. "Sunspot Fluctuations around a Steady State: The Case of Multidimensional, One-Step Forward Looking Economic Models," Econometrica, Econometric Society, vol. 60(5), pages 1097-1126, September.
  • Handle: RePEc:ecm:emetrp:v:60:y:1992:i:5:p:1097-126
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    Cited by:

    1. Krebs, Tom, 1997. "Statistical Equilibrium in One-Step Forward Looking Economic Models," Journal of Economic Theory, Elsevier, vol. 73(2), pages 365-394, April.
    2. Roger Guesnerie, 2008. "Macroeconomic and monetary policies from the "eductive" viewpoint," Working Papers halshs-00586749, HAL.
    3. Gali Jordi, 1994. "Monopolistic Competition, Business Cycles, and the Composition of Aggregate Demand," Journal of Economic Theory, Elsevier, vol. 63(1), pages 73-96, June.
    4. Evans George W & Honkapohja Seppo M.S. & Marimon Ramon, 2007. "Stable Sunspot Equilibria in a Cash-in-Advance Economy," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-38, January.
    5. Evans, George W. & Honkapohja, Seppo, 2003. "Existence of adaptively stable sunspot equilibria near an indeterminate steady state," Journal of Economic Theory, Elsevier, vol. 111(1), pages 125-134, July.
    6. Fukuda, Shin-ichi, 1998. "Sunspot equilibria and periodic cycles under idiosyncratic uncertainty," Journal of Economic Behavior & Organization, Elsevier, vol. 36(1), pages 127-138, July.
    7. Davila, Julio, 2001. "Time and Uncertainty in Overlapping Generations Economies," Journal of Economic Theory, Elsevier, vol. 100(2), pages 356-386, October.
    8. Chiappori, P. A. & Davila, J., 1996. "Cycles and sunspot: The Poincare-Hopf approach," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 269-284.
    9. Dmitri Kolyuzhnov & Anna Bogomolova, 2004. "Escape Dynamics: A Continuous Time Approximation," Econometric Society 2004 Latin American Meetings 27, Econometric Society.
    10. Chao He & Randall Wright & Yu Zhu, 2015. "Housing and Liquidity," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(3), pages 435-455, July.
    11. Judd, Kenneth L., 1997. "Computational economics and economic theory: Substitutes or complements?," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 907-942, June.
    12. Ralf, Kirsten, 2001. "Do complementary factors lead to economic fluctuations?," Economics Letters, Elsevier, vol. 71(1), pages 97-103, April.
    13. Honkapohja, Seppo & Mitra, Kaushik, 2004. "Are non-fundamental equilibria learnable in models of monetary policy?," Journal of Monetary Economics, Elsevier, vol. 51(8), pages 1743-1770, November.
    14. Fukuda, Shin-ichi, 2004. "Extraneous shocks and international linkage of business cycles in a two-country monetary model," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 389-409, July.
    15. repec:sbe:breart:v:20:y:2000:i:2:a:2757 is not listed on IDEAS
    16. Evans, George W. & Honkapohja, Seppo, 2003. "Expectational stability of stationary sunspot equilibria in a forward-looking linear model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 171-181, October.
    17. Marimon, Ramon & Sunder, Shyam, 1995. "Does a constant money growth rule help stabilize inflation?: experimental evidence," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 111-156, December.
    18. Julio Dávila, "undated". "Reducing Overlapping Generations Economies to Finite Economies," Penn CARESS Working Papers 9819996a2b80f99a81bf1509c, Penn Economics Department.
    19. Antinolfi, Gaetano & Keister, Todd & Shell, Karl, 2001. "Growth Dynamics and Returns to Scale: Bifurcation Analysis," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 70-96, January.
    20. Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 127-157.
    21. Dmitri Kolyuzhnov & Anna Bogomolova, 2004. "Escape Dynamics: A Continuous Time Approximation," Econometric Society 2004 Far Eastern Meetings 557, Econometric Society.
    22. Gauthier, Stephane, 2004. "Determinacy in linear rational expectations models," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 815-830, November.
    23. Dmitri Kolyuzhnov & Anna Bogomolova, 2004. "Escape Dynamics: A Continuous Time Approximation," Computing in Economics and Finance 2004 190, Society for Computational Economics.

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