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Testing for rational bubbles in a co-explosive vector autoregression

Author

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  • Tom Engsted

    () (Aarhus University and CREATES)

  • Bent Nielsen

    () (Nuffield College, Oxford UK)

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," CREATES Research Papers 2010-25, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-25
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    Cited by:

    1. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," SIRE Discussion Papers 2015-80, Scottish Institute for Research in Economics (SIRE).
    2. Philip Inyeob Ji & Glenn Otto, 2015. "Explosive Behaviour in Australian Housing Markets: Rational Bubbles or Not?," Discussion Papers 2015-27, School of Economics, The University of New South Wales.
    3. Dooruj Rambaccussing, 2015. "Modelling Housing Prices using a Present Value State Space Model," Dundee Discussion Papers in Economics 285, Economic Studies, University of Dundee.
    4. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," SIRE Discussion Papers 2015-32, Scottish Institute for Research in Economics (SIRE).
    5. Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    6. Engsted, Tom & Hviid, Simon J. & Pedersen, Thomas Q., 2016. "Explosive bubbles in house prices? Evidence from the OECD countries," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 40(C), pages 14-25.
    7. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-32, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Tom Engsted, 2016. "Fama On Bubbles," Journal of Economic Surveys, Wiley Blackwell, vol. 30(2), pages 370-376, April.
    9. Wei Long & Dingding Li & Qi Li, 2016. "Testing explosive behavior in the gold market," Empirical Economics, Springer, vol. 51(3), pages 1151-1164, November.
    10. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-80, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Daan Steenkamp, 2017. "How bubbly is the New Zealand dollar?," Reserve Bank of New Zealand Discussion Paper Series DP2017/03, Reserve Bank of New Zealand.
    12. Kivedal, Bjørnar Karlsen, 2013. "Testing for rational bubbles in the US housing market," Journal of Macroeconomics, Elsevier, vol. 38(PB), pages 369-381.

    More about this item

    Keywords

    Rational bubbles; Explosiveness and co-explosiveness; Cointegration; Vector autoregression; Likelihood ratio tests;

    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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