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On the Ambiguous Consequences of Omitting Variables


  • Giuseppe De Luca

    (University of Palermo, Italy)

  • Jan Magnus

    (VU University Amsterdam, the Netherlands)

  • Franco Peracchi

    (University of Tor Vergata, Rome, Italy)


This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.

Suggested Citation

  • Giuseppe De Luca & Jan Magnus & Franco Peracchi, 2015. "On the Ambiguous Consequences of Omitting Variables," Tinbergen Institute Discussion Papers 15-061/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20150061

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    References listed on IDEAS

    1. Frost, Peter A, 1979. "Proxy Variables and Specification Bias," The Review of Economics and Statistics, MIT Press, vol. 61(2), pages 323-325, May.
    2. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(01), pages 60-68, February.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    4. Kinal, Terrence & Lahiri, Kajal, 1983. "Specification Error Analysis with Stochastic Regressors," Econometrica, Econometric Society, vol. 51(4), pages 1209-1219, July.
    5. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, March.
    6. Jan R. Magnus & Andrey L. Vasnev, 2007. "Local sensitivity and diagnostic tests," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 166-192, March.
    7. McCallum, B T, 1972. "Relative Asymptotic Bias from Errors of Omission and Measurement," Econometrica, Econometric Society, vol. 40(4), pages 757-758, July.
    8. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    9. Jan R. Magnus & Giuseppe De Luca, 2016. "Weighted-Average Least Squares (Wals): A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 30(1), pages 117-148, February.
    10. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-759, May.
    11. Garber, Steven & Klepper, Steven, 1980. "Extending the Classical Normal Errors-in-Variables Model," Econometrica, Econometric Society, vol. 48(6), pages 1541-1546, September.
    12. Kevin A. Clarke, 2005. "The Phantom Menace: Omitted Variable Bias in Econometric Research," Conflict Management and Peace Science, Peace Science Society (International), vol. 22(4), pages 341-352, September.
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    More about this item


    Omitted variables; Misspecification; Least-squares estimators; Bias; Mean squared error;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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