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

Author

Listed:
  • 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)

Abstract

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
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    File URL: https://eprints.bbk.ac.uk/id/eprint/5951
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    References listed on IDEAS

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    Keywords

    Bubbles; Asset prices; Steady state; Non-linear time series; TAR Models;
    All these keywords.

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