IDEAS home Printed from
   My bibliography  Save this paper

Steady-State Distributions for Models of Bubbles: their Existence and Econometric Implications


  • John Knight

    (University of Western Ontario)

  • Stephen Satchell

    (Department of Economics, Mathematics & Statistics, Birkbeck
    University of Sydney)

  • Nandini Srivastava

    (Christ's College, University of Cambridge)


The purpose of this paper is to examine the properties of bubbles in the light of steady state results for threshold auto-regressive (TAR) models recently derived by Knight and Satchell (2011). We assert that this will have implications for econometrics. We study the conditions under which we can obtain a steady state distribution of asset prices using our simple model of bubbles based on our particular definition of a bubble. We derive general results and further extend the analysis by considering the steady state distribution in three cases of a (I) a normally distributed error process, (II) a non normally (exponentially) distributed steady-state process and (III) a switching random walk with a fairly general i.i.d error process We then examine the issues related to unit root testing for the presence of bubbles using standard econometric procedures. We illustrate as an example, the market for art, which shows distinctly bubble-like characteristics. Our results shed light on the ubiquitous finding of no bubbles in the econometric literature.

Suggested Citation

  • John Knight & Stephen Satchell & Nandini Srivastava, 2012. "Steady-State Distributions for Models of Bubbles: their Existence and Econometric Implications," Birkbeck Working Papers in Economics and Finance 1208, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:1208

    Download full text from publisher

    File URL:
    File Function: First version, 2012
    Download Restriction: no

    References listed on IDEAS

    1. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
    2. Simon van Norden & Huntley Schaller, 2002. "Fads or bubbles?," Empirical Economics, Springer, vol. 27(2), pages 335-362.
    3. Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
    4. William Branch & George Evans, 2011. "Monetary policy and heterogeneous expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 365-393, June.
    5. Kenneth D. West, 1987. "A Specification Test for Speculative Bubbles," The Quarterly Journal of Economics, Oxford University Press, vol. 102(3), pages 553-580.
    6. KevinJ. Lansing, 2010. "Rational and Near-Rational Bubbles Without Drift," Economic Journal, Royal Economic Society, vol. 120(549), pages 1149-1174, December.
    7. Behzad T. Diba & Herschel I. Grossman, 1984. "Rational Bubbles in the Price of Gold," NBER Working Papers 1300, National Bureau of Economic Research, Inc.
    8. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
    9. Harrison Hong & José Scheinkman & Wei Xiong, 2006. "Asset Float and Speculative Bubbles," Journal of Finance, American Finance Association, vol. 61(3), pages 1073-1117, June.
    10. Allen F. & Morris S. & Postlewaite A., 1993. "Finite Bubbles with Short Sale Constraints and Asymmetric Information," Journal of Economic Theory, Elsevier, vol. 61(2), pages 206-229, December.
    11. Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
    12. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    13. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    14. Azariadis, Costas & Smith, Bruce, 1998. "Financial Intermediation and Regime Switching in Business Cycles," American Economic Review, American Economic Association, vol. 88(3), pages 516-536, June.
    15. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-154, March-Apr.
    16. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    17. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    18. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    19. Markus K. Brunnermeier & Stefan Nagel, 2004. "Hedge Funds and the Technology Bubble," Journal of Finance, American Finance Association, vol. 59(5), pages 2013-2040, October.
    20. 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.
    21. Roche, Maurice J., 2001. "The rise in house prices in Dublin: bubble, fad or just fundamentals," Economic Modelling, Elsevier, vol. 18(2), pages 281-295, April.
    22. Anderson, Robert C, 1974. "Paintings as an Investment," Economic Inquiry, Western Economic Association International, vol. 12(1), pages 13-26, March.
    23. Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-530, June.
    24. 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.
    25. John R. Conlon, 2004. "Simple Finite Horizon Bubbles Robust to Higher Order Knowledge," Econometrica, Econometric Society, vol. 72(3), pages 927-936, May.
    26. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    27. Franklin Allen & Gary Gorton, 1993. "Churning Bubbles," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 813-836.
    28. Bohl, Martin T., 2003. "Periodically collapsing bubbles in the US stock market?," International Review of Economics & Finance, Elsevier, vol. 12(3), pages 385-397.
    29. Piergiorgio Alessandri, 2006. "Bubbles and fads in the stock market: another look at the experience of the US," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 11(3), pages 195-203.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Bubbles; Asset prices; Steady state; Non-linear time series; TAR Models;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:bbk:bbkefp:1208. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.