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Recurrent Bubbles

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

We study rational bubbles in a standard linear asset price model. We first consider a class of bubble processes driven by multiplicative iid shocks. We show that a bubble process in this class either diverges to infinity with probability one, converges to zero with probability one, or keeps fluctuating forever with probability one, depending on investors' "con dence" in expected bubble growth. We call a bubble process having the last property "recurrent." We develop sufficient conditions for a bubble process to be recurrent when it is driven by non-iid shocks, when the risk-free interest rate is not constant, and when the process is driven by non-iid shocks and the risk-free interest rate is not constant. In the last case we demonstrate via simulation that there can be a prolonged period in which both the bubble and the interest rate stay close to zero.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2010-27.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number DP2010-27.

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Length: 44 pages
Date of creation: Oct 2010
Date of revision: Nov 2010
Handle: RePEc:kob:dpaper:dp2010-27

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  1. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  2. Dean Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Levine's Bibliography 843644000000000095, UCLA Department of Economics.
  3. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  4. Takashi Kamihigashi, 2003. "Almost sure convergence to zero in stochastic growth models," Discussion Paper Series 170, Research Institute for Economics & Business Administration, Kobe University, revised May 2005.
  5. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September.
  6. Kenneth A. Froot & Maurice Obstfeld, 1992. "Intrinsic Bubbles: The Case of Stock Prices," NBER Working Papers 3091, National Bureau of Economic Research, Inc.
  7. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
  8. Turnovsky, Stephen J & Weintraub, E Roy, 1971. "Stochastic Stability of a General Equilibrium System under Adaptive Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(1), pages 71-86, February.
  9. Diba, Behzad T & Grossman, Herschel I, 1988. "The Theory of Rational Bubbles in Stock Prices," Economic Journal, Royal Economic Society, vol. 98(392), pages 746-54, September.
  10. Charemza, Wojciech W. & Deadman, Derek F., 1995. "Speculative bubbles with stochastic explosive roots: The failure of unit root testing," Journal of Empirical Finance, Elsevier, vol. 2(2), pages 153-163, June.
  11. Wilson, Charles A., 1981. "Equilibrium in dynamic models with an infinity of agents," Journal of Economic Theory, Elsevier, vol. 24(1), pages 95-111, February.
  12. Kiernan, E & Madan, Dilip B, 1989. "Stochastic Stability in Macro Models," Economica, London School of Economics and Political Science, vol. 56(221), pages 97-108, February.
  13. Takashi Kamihigashi, 2008. "The spirit of capitalism, stock market bubbles and output fluctuations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 3-28.
  14. Flood, Robert P & Hodrick, Robert J, 1990. "On Testing for Speculative Bubbles," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 85-101, Spring.
  15. Carmen M. Reinhart & Kenneth S. Rogoff, 2009. "This Time Is Different: Eight Centuries of Financial Folly," Economics Books, Princeton University Press, edition 1, volume 1, number 8973.
  16. Tim Robinson & Andrew Stone, 2006. "Monetary Policy, Asset-Price Bubbles, and the Zero Lower Bound," NBER Chapters, in: Monetary Policy under Very Low Inflation in the Pacific Rim, NBER-EASE, Volume 15, pages 43-90 National Bureau of Economic Research, Inc.
  17. Kelly, Morgan, 1992. "On endogenous growth with productivity shocks," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 47-56, October.
  18. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer, vol. 12(1), pages 103-122.
  19. Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October.
  20. Ikeda, Shinsuke & Shibata, Akihisa, 1995. "Fundamentals uncertainty, bubbles, and exchange rate dynamics," Journal of International Economics, Elsevier, vol. 38(3-4), pages 199-222, May.
  21. George A. Akerlof, 2009. "How Human Psychology Drives the Economy and Why It Matters," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(5), pages 1175-1175.
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