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Testing for rational bubbles in a co-explosive vector autoregression

Author

Listed:
  • Tom Engsted

    (CREATES, School of Economics and Management, Aarhus University, DK-8000 Aarhus C)

  • Bent Nielsen

    (Nuffield College, Oxford OX1 1NF, U.K.)

Abstract

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The analysis for the no-bubble case is done within the traditional Johansen model for I(1) variables, while the bubble model is analysed using a co-explosive framework. The methodology is illustrated using US stock prices and dividends for the period 1872-2000.

Suggested Citation

  • Tom Engsted & Bent Nielsen, 2010. "Testing for rational bubbles in a co-explosive vector autoregression," Economics Papers 2010-W06, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1006
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    Keywords

    Rational bubbles; Explosiveness and co-explosiveness; Cointegration; Vector autoregression; Likelihood ratio tests.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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