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How measurement error affects inference in linear regression

Author

Listed:
  • Erik Meijer

    (University of Southern California)

  • Edward Oczkowski

    (Charles Sturt University)

  • Tom Wansbeek

    (University of Groningen)

Abstract

Measurement error biases OLS results. When the measurement error variance in absolute or relative (reliability) form is known, adjustment is simple. We link the (known) estimators for these cases to GMM theory and provide simple derivations of their standard errors. Our focus is on the test statistics. We show monotonic relations between the t-statistics and $$R^2$$ R 2 s of the (infeasible) estimator if there was no measurement error, the inconsistent OLS estimator, and the consistent estimator that corrects for measurement error and show the relation between the t-value and the magnitude of the assumed measurement error variance or reliability. We also discuss how standard errors can be computed when the measurement error variance or reliability is estimated, rather than known, and we indicate how the estimators generalize to the panel data context, where we have to deal with dependency among observations. By way of illustration, we estimate a hedonic wine price function for different values of the reliability of the proxy used for the wine quality variable.

Suggested Citation

  • Erik Meijer & Edward Oczkowski & Tom Wansbeek, 2021. "How measurement error affects inference in linear regression," Empirical Economics, Springer, vol. 60(1), pages 131-155, January.
    • Handle: RePEc:spr:empeco:v:60:y:2021:i:1:d:10.1007_s00181-020-01942-z
    DOI: 10.1007/s00181-020-01942-z
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    References listed on IDEAS

    as
    1. Jakob De Haan & Erik Leertouwer & Erik Meijer & Tom Wansbeek, 2003. "Measuring central bank independence: a latent variables approach," Scottish Journal of Political Economy, Scottish Economic Society, vol. 50(3), pages 326-340, August.
    2. Meijer, Erik & Wansbeek, Tom, 2000. "Measurement error in a single regressor," Economics Letters, Elsevier, vol. 69(3), pages 277-284, December.
    3. Lecocq, Sébastien & Visser, Michael, 2006. "What Determines Wine Prices: Objective vs. Sensory Characteristics," Journal of Wine Economics, Cambridge University Press, vol. 1(1), pages 42-56, April.
    4. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    5. Susanne M. Schennach, 2016. "Recent Advances in the Measurement Error Literature," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 341-377, October.
    6. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    7. Atsushi Inoue & Gary Solon, 2010. "Two-Sample Instrumental Variables Estimators," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 557-561, August.
    8. J. R. Lockwood & Daniel F. McCaffrey, 2020. "Recommendations about estimating errors-in-variables regression in Stata," Stata Journal, StataCorp LP, vol. 20(1), pages 116-130, March.
    9. Edward Oczkowski & Hristos Doucouliagos, 2015. "Wine Prices and Quality Ratings: A Meta-regression Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 97(1), pages 103-121.
    10. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    11. Klaas Sijtsma, 2009. "On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 107-120, March.
    12. Merckens, Arjen & Wansbeek, Tom, 1989. "Formula manipulation in statistics on the computer: Evaluating the expectation of higher-degree functions of normally distributed matrices," Computational Statistics & Data Analysis, Elsevier, vol. 8(2), pages 189-200, July.
    13. Edward Oczkowski, 2001. "Hedonic Wine Price Functions and Measurement Error," The Economic Record, The Economic Society of Australia, vol. 77(239), pages 374-382, December.
    14. Meijer, Erik & Spierdijk, Laura & Wansbeek, Tom, 2017. "Consistent estimation of linear panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 200(2), pages 169-180.
    15. Cardebat, Jean-Marie & Paroissien, Emmanuel, 2015. "Standardizing Expert Wine Scores: An Application for Bordeaux en primeur ," Journal of Wine Economics, Cambridge University Press, vol. 10(3), pages 329-348, December.
    16. Baltagi, Badi H., 2015. "The Oxford Handbook of Panel Data," OUP Catalogue, Oxford University Press, number 9780199940042.
    17. Erik Meijer & Tom Wansbeek, 2007. "The Sample Selection Model from a Method of Moments Perspective," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 25-51.
    18. repec:dgr:rugsom:00f14 is not listed on IDEAS
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    Cited by:

    1. Qi Li & Vasilis Sarafidis & Joakim Westerlund, 2021. "Essays in honor of Professor Badi H Baltagi," Empirical Economics, Springer, vol. 60(1), pages 1-11, January.
    2. Li, Qi & Sarafidis, Vasilis & Westerlund, Joakim, 2020. "Essays in Honor of Professor Badi H Baltagi: Editorial," MPRA Paper 104751, University Library of Munich, Germany.

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    More about this item

    Keywords

    Measurement error; Generalized method of moments; Expert rating; Hedonic regression; Wine quality; Structural equation model;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
    • Q11 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Aggregate Supply and Demand Analysis; Prices

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