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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.

Suggested Citation

  • Takashi Kamihigashi, 2010. "Recurrent Bubbles," Discussion Paper Series DP2010-27, Research Institute for Economics & Business Administration, Kobe University, revised Nov 2010.
    • Handle: RePEc:kob:dpaper:dp2010-27
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2010-27.pdf
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    1. Takatoshi Ito & Andrew K. Rose, 2006. "Introduction to EASE-15: Monetary Policy with Very Low Inflation in the Pacific Rim," NBER Chapters, in: Monetary Policy with Very Low Inflation in the Pacific Rim, pages 1-5, National Bureau of Economic Research, Inc.
    2. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    3. Charles P. Kindleberger & Robert Z. Aliber, 2005. "Manias, Panics and Crashes," Palgrave Macmillan Books, Palgrave Macmillan, edition 0, number 978-0-230-62804-5.
    4. William A. Branch & George W. Evans, 2011. "Learning about Risk and Return: A Simple Model of Bubbles and Crashes," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(3), pages 159-191, July.
    5. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    6. Carmen M. Reinhart & Kenneth S. Rogoff, 2014. "This Time is Different: A Panoramic View of Eight Centuries of Financial Crises," Annals of Economics and Finance, Society for AEF, vol. 15(2), pages 215-268, November.
    7. 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.
    8. Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October.
    9. 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.
    10. William A. Branch & George W. Evans, 2011. "Learning about Risk and Return: A Simple Model of Bubbles and Crashes," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(3), pages 159-191, July.
    11. 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, March.
    12. Carmen M. Reinhart & Kenneth S. Rogoff, 2009. "Varieties of Crises and Their Dates," Introductory Chapters, in: This Time Is Different: Eight Centuries of Financial Folly, Princeton University Press.
    13. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    14. Tim Robinson & Andrew Stone, 2006. "Monetary Policy, Asset-Price Bubbles, and the Zero Lower Bound," NBER Chapters, in: Monetary Policy with Very Low Inflation in the Pacific Rim, pages 43-84, National Bureau of Economic Research, Inc.
    15. 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.
    16. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    17. Kelly, Morgan, 1992. "On endogenous growth with productivity shocks," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 47-56, October.
    18. KevinJ. Lansing, 2010. "Rational and Near-Rational Bubbles Without Drift," Economic Journal, Royal Economic Society, vol. 120(549), pages 1149-1174, December.
    19. Takashi Kamihigashi, 2006. "Almost sure convergence to zero in stochastic growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 231-237, September.
    20. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
    21. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    22. 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.
    23. Froot, Kenneth A & Obstfeld, Maurice, 1991. "Intrinsic Bubbles: The Case of Stock Prices," American Economic Review, American Economic Association, vol. 81(5), pages 1189-1214, December.
    24. 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.
    25. 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.
    26. 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.
    27. Ito, Takatoshi & Rose, Andrew K. (ed.), 2006. "Monetary Policy with Very Low Inflation in the Pacific Rim," National Bureau of Economic Research Books, University of Chicago Press, number 9780226378978, December.
    28. Diba, Behzad T & Grossman, Herschel I, 1988. "The Theory of Rational Bubbles in Stock Prices," Economic Journal, Royal Economic Society, vol. 98(392), pages 746-754, September.
    29. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 103-122.
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    Cited by:

    1. Clain-Chamosset-Yvrard, Lise & Kamihigashi, Takashi, 2017. "International transmission of bubble crashes in a two-country overlapping generations model," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 115-126.
    2. Lise Clain-Chamosset-Yvrard & Takashi Kamihigashi, 2015. "International Transmission of Bubble Crashes in a Two-Country Overlapping Generations," Discussion Paper Series DP2015-43, Research Institute for Economics & Business Administration, Kobe University.
    3. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2015-38, Research Institute for Economics & Business Administration, Kobe University.
    4. Takashi Kamihigashi, 2016. "A Simple Optimality-Based No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2016-22, Research Institute for Economics & Business Administration, Kobe University.
    5. Lise Claini-Chamosset-Yvrard & Takashi Kamihigashi, 2015. "International Transmission of Bubble Crashes: Stationary Sunspot Equilibria in a Two-Country Overlapping Generations Model," Discussion Paper Series DP2015-21, Research Institute for Economics & Business Administration, Kobe University.
    6. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem," Discussion Paper Series DP2015-03, Research Institute for Economics & Business Administration, Kobe University.
    7. Kamihigashi, Takashi, 2018. "A Simple optimality-based no-bubble theorem for deterministic sequential economies with strictly monotone preferences," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 36-41.
    8. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Dynamic Economies," Discussion Paper Series DP2015-24, Research Institute for Economics & Business Administration, Kobe University.

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