IDEAS home Printed from https://ideas.repec.org/p/kob/dpaper/dp2016-22.html
   My bibliography  Save this paper

A Simple Optimality-Based No-Bubble Theorem for Deterministic Sequential Economies

Author

Listed:
  • Takashi Kamihigashi

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

Abstract

We establish a simple no-bubble theorem that applies to a wide range of deterministic sequential economies with infinitely lived agents. In particular, we show that asset bubbles never arise if at least one agent can reduce his asset holdings permanently from some period onward. Our no-bubble theorem is based on the optimal behavior of a single agent, requiring virtually no assumption beyond the strict monotonicity of preferences. The theorem is a substantial generalization of Kocherlakota's (1992, Journal of Economic Theory 57, 245-256) result on asset bubbles and short sales constraints.

Suggested Citation

  • 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.
  • Handle: RePEc:kob:dpaper:dp2016-22
    as

    Download full text from publisher

    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2016-22.pdf
    File Function: First version, 2016
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura, 2006. "Handbook on optimal growth (volume 1)," Post-Print halshs-00101345, HAL.
    2. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    3. Kocherlakota, Narayana R., 1992. "Bubbles and constraints on debt accumulation," Journal of Economic Theory, Elsevier, vol. 57(1), pages 245-256.
    4. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2014. "Intertemporal equilibrium with production: bubbles and efficiency," Documents de travail du Centre d'Economie de la Sorbonne 14043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Takashi Kamihigashi, 2002. "A simple proof of the necessity of the transversality condition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 427-433.
    6. 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.
    7. Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, March.
    8. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    9. Rose-Anne Dana & Cuong Le Van, 2006. "Optimal growth without discounting," Post-Print halshs-00101355, HAL.
    10. Takashi Kamihigashi, 2003. "Necessity of the Transversality Condition for Stochastic Models with CRRA Utility," Discussion Paper Series 137, Research Institute for Economics & Business Administration, Kobe University.
    11. Luigi Montrucchio, 2004. "Cass transversality condition and sequential asset bubbles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 645-663, October.
    12. Rose-Anne Dana & Cuong Le Van, 2006. "Optimal Growth Without Discounting," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 1, pages 1-17, Springer.
    13. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, October.
    14. repec:dau:papers:123456789/433 is not listed on IDEAS
    15. Rose-Anne Dana & Cuong Le Van, 2006. "Optimal growth without discounting," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101355, HAL.
    16. Obstfeld, Maurice & Rogoff, Kenneth, 1986. "Ruling out divergent speculative bubbles," Journal of Monetary Economics, Elsevier, vol. 17(3), pages 349-362, May.
    17. Kamihigashi, Takashi, 2005. "Necessity of the transversality condition for stochastic models with bounded or CRRA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1313-1329, August.
    18. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
    19. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 253-278.
    20. Wright, Randall D., 1987. "Market structure and competitive equilibrium in dynamic economic models," Journal of Economic Theory, Elsevier, vol. 41(1), pages 189-201, February.
    21. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    22. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    23. Werner, Jan, 2014. "Rational asset pricing bubbles and debt constraints," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 145-152.
    24. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem," Discussion Paper Series DP2015-03, Research Institute for Economics & Business Administration, Kobe University.
    5. Bosi, Stefano & Le Van, Cuong & Pham, Ngoc-Sang, 2017. "Asset bubbles and efficiency in a generalized two-sector model," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 37-48.
    6. Hirano, Tomohiro & Toda, Alexis Akira, 2024. "Bubble economics," LSE Research Online Documents on Economics 122042, London School of Economics and Political Science, LSE Library.
    7. Bosi, Stefano & Van, Cuong Le & Pham, Ngoc-Sang, 2018. "Intertemporal equilibrium with heterogeneous agents, endogenous dividends and collateral constraints," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 1-20.
    8. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
    9. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    10. 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.
    11. Bosi, Stefano & Le Van, Cuong & Pham, Ngoc-Sang, 2022. "Real indeterminacy and dynamics of asset price bubbles in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    12. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University.
    13. Marco Airaudo, 2017. "Complex stock price dynamics under Max Weber’s spirit of capitalism hypothesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 47-73, June.
    14. Cuong Le Van & Ngoc-Sang Pham, 2016. "Intertemporal equilibrium with financial asset and physical capital," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 155-199, June.
    15. Pham, Ngoc-Sang, 2017. "Assets with possibly negative dividends," MPRA Paper 78193, University Library of Munich, Germany.
    16. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2015. "Intertemporal equilibrium with heterogeneous agents, endogenous dividends, and borrowing constraints," Documents de recherche 15-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    17. Takashi Kamihigashi & Ryonghun Im, 2022. "Two Types of Asset Bubbles in a Small Open Economy," Discussion Paper Series DP2022-15, Research Institute for Economics & Business Administration, Kobe University.
    18. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research.
    19. Ravi Kashyap, 2016. "Solving the Equity Risk Premium Puzzle and Inching Towards a Theory of Everything," Papers 1604.04872, arXiv.org, revised Sep 2019.
    20. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2017. "Rational Land and Housing Bubbles in Infinite-Horizon Economies," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 203-230, Springer.

    More about this item

    Keywords

    Asset bubbles; No-bubble theorem; Sequential budget constraints; Optimality; Binary relation;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kob:dpaper:dp2016-22. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Office of Promoting Research Collaboration, Research Institute for Economics & Business Administration, Kobe University (email available below). General contact details of provider: https://edirc.repec.org/data/rikobjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.