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Bias of OLS Estimators due to Exclusion of Relevant Variables and Inclusion of Irrelevant Variables

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  • Deepankar Basu

Abstract

In this paper, I discuss three issues related to bias of OLS estimators in a general multivariate setting. First, I discuss the bias that arises from omitting relevant variables. I offer a geometric interpretation of such bias and derive sufficient conditions in terms of sign restrictions that allows us to determine the direction of bias. Second, I show that inclusion of some omitted variables will not necessarily reduce the magnitude of bias as long as some others remain omitted. Third, I show that inclusion of irrelevant variables in a model with omitted variables can also have an impact on the bias of OLS estimators. I use a running example of a simple wage regression to illustrate my arguments.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:obuest:v:82:y:2020:i:1:p:209-234
    DOI: 10.1111/obes.12322
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    Cited by:

    1. Ahmed, Walid M.A., 2021. "How do Islamic equity markets respond to good and bad volatility of cryptocurrencies? The case of Bitcoin," Pacific-Basin Finance Journal, Elsevier, vol. 70(C).
    2. François Bourguignon & A. Hector Moreno M., 2020. "On synthetic income panels," Working Papers halshs-01988068, HAL.
    3. Deepankar Basu, 2023. "Formal Covariate Benchmarking to Bound Omitted Variable Bias," Papers 2306.10562, arXiv.org.
    4. Blankmeyer, Eric, 2022. "A bias test for heteroscedastic linear least squares regression," MPRA Paper 116605, University Library of Munich, Germany.
    5. Roy, Jayjit, 2021. "The effect of employment protection legislation on international trade," Economic Modelling, Elsevier, vol. 94(C), pages 221-234.
    6. Justin Callais & Andrew T. Young, 2022. "Does rigidity matter? Constitutional entrenchment and growth," European Journal of Law and Economics, Springer, vol. 53(1), pages 27-62, February.
    7. Deepankar Basu, 2022. "Bounds for Bias-Adjusted Treatment Effect in Linear Econometric Models," Papers 2203.12431, arXiv.org.
    8. Bruno Merlevede & Angelos Theodorakopoulos, 2021. "Productivity effects of internationalisation through the domestic supply chain," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 808-832, September.

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