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Recurrent Bubbles

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  • TAKASHI KAMIHIGASHI

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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Suggested Citation

  • Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, March.
    • Handle: RePEc:bla:jecrev:v:62:y:2011:i:1:p:27-62
    DOI: j.1468-5876.2010.00527.x
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem," Discussion Paper Series DP2015-03, Research Institute for Economics & Business Administration, Kobe University.

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