IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/0154.html
   My bibliography  Save this paper

Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation

Author

Listed:
  • David A. Belsley

Abstract

This paper suggests and examines a straightforward diagnostic test procedure that 1) provides numerical indexes whose magnitudes signify the presence of one or more near dependencies among columns of a data matrix X, and 2) provides a means for determining, within the linear regression model, the extent to which each such near dependency is degrading the least- squares estimation of each regression coefficient. In most instances this latter information also enables the investigator to determine specifically which columns of the data matrix are involved in each near dependency. The diagnostic test is based on an interrelation between two analytic devices, the singular-value decomposition (closely related to eigensystems) and a matching regression-variance decomposition. Both these devices are developed in full. The test is successfully given empirical content through a set of experiments that examine its behavior when applied to several different series of data matrices having one or more known near dependencies that are weak to begin with and are made to became systematically more nearly perfectly collinear. The general diagnostic properties of the test that result from these experiments and the steps required to carry out the test are summarized, and then exemplified by application to real economic data.

Suggested Citation

  • David A. Belsley, 1976. "Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation," NBER Working Papers 0154, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0154
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w0154.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David A. Belsley, 1974. "Estimation of Systems of Simultaneous Equations, and Computational Specifications of GREMLIN," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 551-614, National Bureau of Economic Research, Inc.
    2. Kumar, T Krishna, 1975. "Multicollinearity in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 365-366, August.
    3. David A. Belsley & Virginia Klema, 1974. "Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition," NBER Working Papers 0066, National Bureau of Economic Research, Inc.
    4. Douglas M. Hawkins, 1973. "On the Investigation of Alternative Regressions by Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 275-286, November.
    5. Haitovsky, Yoel, 1969. "Multicollinearity in Regression Analysis: Comment," The Review of Economics and Statistics, MIT Press, vol. 51(4), pages 486-489, November.
    6. O'Hagan, John W & McCabe, Brendan, 1975. "Tests for the Severity of Multicollinearity in Regression Analysis: A Comment," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 368-370, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roy E. Welsch & Edwin Kuh, 1977. "Linear Regression Diagnostics," NBER Working Papers 0173, National Bureau of Economic Research, Inc.
    2. H J P Timmermans, 1981. "Multiattribute Shopping Models and Ridge Regression Analysis," Environment and Planning A, , vol. 13(1), pages 43-56, January.
    3. G. Acosta & M. Graña & J. P. Pinasco, 2006. "Condition numbers and scale free graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 381-385, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emilian Dobrescu, 2018. "Functional trinity of public finance in an emerging economy," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 7(1), pages 1-27, December.
    2. Jørgen Lauridsen & Jesùs Mur, 2006. "Multicollinearity in cross-sectional regressions," Journal of Geographical Systems, Springer, vol. 8(4), pages 317-333, October.
    3. Claudia García-García & Catalina B. García-García & Román Salmerón, 2021. "Confronting collinearity in environmental regression models: evidence from world data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 895-926, September.
    4. Michis Antonis A, 2009. "Regression Analysis of Marketing Time Series: A Wavelet Approach with Some Frequency Domain Insights," Review of Marketing Science, De Gruyter, vol. 7(1), pages 1-43, July.
    5. Jiaqiang Sun & Anita Binti Rosli & Adrian Daud, 2025. "Efficiency analysis of listed pharmaceutical companies in China: A method combining three-stage DEA with undesirable output, PCA, and tobit regression," PLOS ONE, Public Library of Science, vol. 20(8), pages 1-33, August.
    6. David A. Belsley & Virginia Klema, 1974. "Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition," NBER Working Papers 0066, National Bureau of Economic Research, Inc.
    7. William P. O’Hare, 2016. "A State Level Assessment of the Well-Being of Black Children in the United States," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 9(1), pages 277-297, March.
    8. Cho, Woohyun & Windle, Robert J. & Dresner, Martin E., 2017. "The impact of operational exposure and value-of-time on customer choice: Evidence from the airline industry," Transportation Research Part A: Policy and Practice, Elsevier, vol. 103(C), pages 455-471.
    9. Jong-Hyun Paik & Moon-Koo Kim & Jong-Hyun Park, 2017. "The antecedents and consequences of technology standardizations in Korean IT small and medium-sized enterprises," Information Technology and Management, Springer, vol. 18(4), pages 293-304, December.
    10. Phuong Bui & Phuc Nguyen, 2025. "Unveiling the Dynamics: Corporate Governance’s Impact on Firm Performance in Vietnam’s Thriving Market Landscape," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 16(2), pages 9095-9122, June.
    11. Izani Ibrahim & Craig MacPhee, 2003. "Export externalities and economic growth," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 12(3), pages 257-283.
    12. Sürücü, Lütfi & YIKILMAZ, İbrahim & MASLAKÇI, Ahmet, 2022. "Exploratory Factor Analysis (EFA) in Quantitative Researches and Practical Considerations," OSF Preprints fgd4e, Center for Open Science.
    13. Jiaqiang Sun & Anita Binti Rosli & Adrian Daud & Xia Yan, 2025. "Evaluation of Operational Efficiency in China’s Pharmaceutical Industry and Analysis of Environmental Impacts," Economies, MDPI, vol. 13(4), pages 1-35, March.
    14. Richard C. Rockwell, 1975. "Assessment of Multicollinearity," Sociological Methods & Research, , vol. 3(3), pages 308-320, February.
    15. Avimanyu Datta, 2016. "Evaluating The Antecedents Of Foundational Innovations: A Longitudinal Look At Patents From Information Technology Industry," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-29, January.
    16. Gene Golub & Virginia Klema & G. W. Stewart, 1977. "Rosetak Document 4: Rank Degeneracies and Least Square Problems," NBER Working Papers 0165, National Bureau of Economic Research, Inc.
    17. Ana Carneiro & Hélder Fernando Pedrosa e Sousa & Maria Alzira Pimenta Dinis & Ângela Leite, 2021. "Human Values and Religion: Evidence from the European Social Survey," Social Sciences, MDPI, vol. 10(2), pages 1-18, February.
    18. Baah Kusi & Elikplimi Agbloyor & Agyapomaa Gyeke‐Dako & Simplice Asongu, 2022. "Financial sector transparency, financial crises and market power: A cross‐country evidence," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4431-4450, October.
    19. Enache, Daniel & Weihs, Claus, 2004. "Importance Assessment of Correlated Predictors in Business Cycles Classification," Technical Reports 2004,66, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Jong-Hyun Paik & Moon-Koo Kim & Jong-Hyun Park, 0. "The antecedents and consequences of technology standardizations in Korean IT small and medium-sized enterprises," Information Technology and Management, Springer, vol. 0, pages 1-12.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:0154. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.