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A bias test for heteroscedastic linear least squares regression

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  • Blankmeyer, Eric

Abstract

A correlation between regressors and disturbances presents challenging problems in linear regression. Issues like omitted variables, measurement error and simultaneity render ordinary least squares (OLS) biased and inconsistent. In the context of heteroscedastic linear regression, this note proposes a bias test that is simple to apply. It does not reveal the size or sign of OLS bias but instead provides a statistic to assess the probable presence or absence of bias. The test is examined in simulation and in real data sets.

Suggested Citation

  • Blankmeyer, Eric, 2022. "A bias test for heteroscedastic linear least squares regression," MPRA Paper 116605, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:116605
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    File URL: https://mpra.ub.uni-muenchen.de/116605/1/MPRA_paper_116605.pdf
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    References listed on IDEAS

    as
    1. Deepankar Basu, 2020. "Bias of OLS Estimators due to Exclusion of Relevant Variables and Inclusion of Irrelevant Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(1), pages 209-234, February.
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    3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    4. George Milunovich & Minxian Yang, 2018. "Simultaneous Equation Systems With Heteroscedasticity: Identification, Estimation, and Stock Price Elasticities," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 288-308, April.
    5. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    6. Portnoy, Stephen & Welsh, A. H., 1992. "Exactly what is being modelled by the systematic component in a heteroscedastic linear regression," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 253-258, March.
    7. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    8. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
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    More about this item

    Keywords

    Linear regression; least squares bias; heteroscedasticity; Fisher transformation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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