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

John Knight, Stephen Satchell and Nandini Srivastava
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Stephen Satchell: Department of Economics, Mathematics & Statistics, Birkbeck
Nandini Srivastava: Christ's College, University of Cambridge

No 1208, Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics

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.

Keywords: Bubbles; Asset prices; Steady state; Non-linear time series; TAR Models (search for similar items in EconPapers)
Date: 2012-04
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https://eprints.bbk.ac.uk/id/eprint/5951 First version, 2012 (application/pdf)

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