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Bimodal t-ratios: the impact of thick tails on inference


  • Carlo V. Fiorio
  • Vassilis A. Hajivassiliou
  • Peter C. B. Phillips


This paper studies the distribution of the classical t-ratio with data generated from distributions with no finite moments and shows how classical testing is affected by bimodality. A key condition in generating bimodality is independence of the observations in the underlying data-generating process (DGP). The paper highlights the strikingly different implications of lack of correlation versus statistical independence in DGPs with infinite moments and shows how standard inference can be invalidated in such cases, thereby pointing to the need for adapting estimation and inference procedures to the special problems induced by thick-tailed (TT) distributions. The paper presents theoretical results for the Cauchy case and develops a new distribution termed the "double-Pareto", which allows the thickness of the tails and the existence of moments to be determined parametrically. It also investigates the relative importance of tail thickness in case of finite moments by using TT distributions truncated on a compact support, showing that bimodality can persist even in such cases. Simulation results highlight the dangers of relying on naive testing in the face of TT distributions. Novel density estimation kernel methods are employed, given that our theoretical results yield cases that exhibit density discontinuities. Copyright The Author(s). Journal compilation Royal Economic Society 2010.

Suggested Citation

  • Carlo V. Fiorio & Vassilis A. Hajivassiliou & Peter C. B. Phillips, 2010. "Bimodal t-ratios: the impact of thick tails on inference," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 271-289, July.
  • Handle: RePEc:ect:emjrnl:v:13:y:2010:i:2:p:271-289

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    References listed on IDEAS

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    7. Dhiman Das, 2004. "A Bayesian algorithm for a Markov Switching GARCH model," Computing in Economics and Finance 2004 30, Society for Computational Economics.
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    Cited by:

    1. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    2. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.
    3. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
    4. Klein, Torsten L., 2014. "Communicating quantitative information: tables vs graphs," MPRA Paper 60514, University Library of Munich, Germany.

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