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A Test for Endogeneity in Regressions

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  • Thomas B. Marvell

Abstract

Textbook theory predicts that t-ratios decline towards zero in regressions when there is increasing collinearity between two independent variables. This article shows that this rarely happens if the two variables are endogenous, and coefficients increase greatly with more collinearity. The purposes of this article are 1) to illustrate this bias and explain why it occurs, and 2) to use the phenomenon to develop a test for endogeneity. For the test, one creates a variable that is highly collinear with the independent variable of interest, and endogeneity is indicated if t-ratios do not decline with increasing collinearity. False negatives are possible, but not likely. The test is confirmed with algebraic examples and simulations. I give many empirical examples of the bias and the test, including testing exogeneity assumptions behind instrumental variables and Granger causality.

Suggested Citation

  • Thomas B. Marvell, 2025. "A Test for Endogeneity in Regressions," EERI Research Paper Series EERI RP 2025/05, Economics and Econometrics Research Institute (EERI), Brussels.
    • Handle: RePEc:eei:rpaper:eeri_rp_2025_05
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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2025_05.pdf
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    References listed on IDEAS

    as
    1. Chatelain, Jean-Bernard & Ralf, Kirsten, 2014. "Spurious regressions and near-multicollinearity, with an application to aid, policies and growth," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 39(A), pages 85-96.
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    4. Arturs Kalnins, 2018. "Multicollinearity: How common factors cause Type 1 errors in multivariate regression," Strategic Management Journal, Wiley Blackwell, vol. 39(8), pages 2362-2385, August.
    5. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    6. Spanos, Aris & McGuirk, Anya, 2002. "The problem of near-multicollinearity revisited: erratic vs systematic volatility," Journal of Econometrics, Elsevier, vol. 108(2), pages 365-393, June.
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    8. Julda Kielyte, 2008. "Estimating Panel Data Models in the Presence of Endogeneity and Selection," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 51(2), pages 1-19.
    9. John Komlos, 2020. "Multicollinearity in the Presence of Errors-in-Variables Can Increase the Probability of Type-I Error," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 63(1), pages 1-17.
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    More about this item

    Keywords

    Endogeneity; collinearity; simultaneity; omitted variable bias; instrumental variables.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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