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Heavy tails of OLS

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  • Mikosch, Thomas
  • de Vries, Casper G.

Abstract

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions.

Suggested Citation

  • Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:205-221
    DOI: 10.1016/j.jeconom.2012.08.015
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    Cited by:

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    2. Maarten R C van Oordt & Chen Zhou, 2019. "Estimating Systematic Risk under Extremely Adverse Market Conditions," Journal of Financial Econometrics, Oxford University Press, vol. 17(3), pages 432-461.
    3. Kanishka Misra & Paolo Surico, 2014. "Consumption, Income Changes, and Heterogeneity: Evidence from Two Fiscal Stimulus Programs," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(4), pages 84-106, October.
    4. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    5. Maarten van Oordt & Chen Zhou, 2015. "Systemic risk of European banks: Regulators and markets," DNB Working Papers 478, Netherlands Central Bank, Research Department.
    6. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.
    7. Chen, Wang & Zhang, Zhiwen & Hamori, Shigeyuki & Kinkyo, Takuji, 2021. "Not all bank systemic risks are alike: Deposit insurance and bank risk revisited," International Review of Financial Analysis, Elsevier, vol. 77(C).

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    More about this item

    Keywords

    Heavy tails; OLS estimator distribution; Small sample inference;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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