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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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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Heavy tails; OLS estimator distribution; Small sample inference;

    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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