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Spurious relationships arising from aggregate variables in linear regression

Author

Listed:
  • David J. Armor

    (George Mason University)

  • Chenna Reddy Cotla

    (George Mason University)

  • Thomas Stratmann

    (George Mason University)

Abstract

Linear regressions that use aggregated values from a group variable such as a school or a neighborhood are commonplace in the social sciences. This paper uses Monte Carlo methods to demonstrate that aggregated variables produce spurious relationships with other dependent and independent variables in a model even when there are no underlying relationships among those variables. The size of the spurious relationships (or postulated effects) increases as the number of observations per group decreases. Although this problem is remedied by including the individual-level variable in the regression, the problem has not been discussed in the methodological literature. Accordingly, studies using aggregate variables must be interpreted with caution if the individual-level measurements are not available.

Suggested Citation

  • David J. Armor & Chenna Reddy Cotla & Thomas Stratmann, 2017. "Spurious relationships arising from aggregate variables in linear regression," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(3), pages 1359-1379, May.
    • Handle: RePEc:spr:qualqt:v:51:y:2017:i:3:d:10.1007_s11135-016-0335-0
    DOI: 10.1007/s11135-016-0335-0
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    References listed on IDEAS

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    1. Eric A. Hanushek & John F. Kain & Steven G. Rivkin, 2009. "New Evidence about Brown v. Board of Education: The Complex Effects of School Racial Composition on Achievement," Journal of Labor Economics, University of Chicago Press, vol. 27(3), pages 349-383, July.
    2. Jeffrey M. Wooldridge, 2003. "Cluster-Sample Methods in Applied Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 133-138, May.
    3. Moulton, Brent R, 1990. "An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Unit," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 334-338, May.
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    Cited by:

    1. Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.

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