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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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    Cited by:

    1. 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.
    2. Kristoffer Pons Bertelsen, 2019. "Comparing Tests for Identification of Bubbles," CREATES Research Papers 2019-16, Department of Economics and Business Economics, Aarhus University.
    3. Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    4. Wei-Fong Pan, 2019. "Detecting bubbles in China’s regional housing markets," Empirical Economics, Springer, vol. 56(4), pages 1413-1432, April.
    5. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    6. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    7. Xie, Zixiong & Chen, Shyh-Wei & Wu, An-Chi, 2019. "Asymmetric adjustment, non-linearity and housing price bubbles: New international evidence," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    8. Kivedal, Bjørnar Karlsen, 2013. "Testing for rational bubbles in the US housing market," Journal of Macroeconomics, Elsevier, vol. 38(PB), pages 369-381.
    9. Dooruj Rambaccussing, 2015. "Modelling Housing Prices using a Present Value State Space Model," Dundee Discussion Papers in Economics 285, Economic Studies, University of Dundee.
    10. 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.
    11. Wei Long & Dingding Li & Qi Li, 2016. "Testing explosive behavior in the gold market," Empirical Economics, Springer, vol. 51(3), pages 1151-1164, November.
    12. 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.
    13. 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).
    14. Pedersen, Thomas Quistgaard & Schütte, Erik Christian Montes, 2020. "Testing for explosive bubbles in the presence of autocorrelated innovations," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 207-225.
    15. Evren Ceritoglu & Seyit Mumin Cilasun & Ufuk Demiroglu & Aytul Ganioglu, 2019. "An analysis to detect exuberance and implosion in regional house prices in Turkey," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 19(2), pages 67-82.
    16. Alain Hecq & Elisa Voisin, 2019. "Predicting bubble bursts in oil prices during the COVID-19 pandemic with mixed causal-noncausal models," Papers 1911.10916, arXiv.org, revised Mar 2021.
    17. Tom Engsted, 2016. "Fama On Bubbles," Journal of Economic Surveys, Wiley Blackwell, vol. 30(2), pages 370-376, April.
    18. 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).
    19. Juan Huang & Geoffrey Qiping Shen, 2017. "Residential housing bubbles in Hong Kong: identification and explanation based on GSADF test and dynamic probit model," Journal of Property Research, Taylor & Francis Journals, vol. 34(2), pages 108-128, April.

    More about this item

    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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