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The effect of explanatory variables on income: A tool that allows a closer look at the differences in income

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  • Tutz, Gerhard
  • Berger, Moritz

Abstract

Investigation of the effect of covariates on income typically relies on regression models with a transformed income. An underlying assumption is that the exact income is available. However, in surveys reported income is often available in income brackets only. For such grouped data one can use ordered regression models, which in their simplest form with a linear predictor work in a similar way as regression models for exact income. They yield an overall measure of the effect of covariates but fail to detect the specific structure of the effects of single covariates. A model is proposed that allows a closer look at the effect of single covariates, showing in more detail how the income is determined by explanatory variables. The model exploits the potential of sequential regression models, which are extended to allow for varying coefficients. The model is not harder to use than classical regression models but is much more informative. The method is illustrated by using data from the German Socio-Economic Panel Study and the United States Census Bureau.

Suggested Citation

  • Tutz, Gerhard & Berger, Moritz, 2020. "The effect of explanatory variables on income: A tool that allows a closer look at the differences in income," Econometrics and Statistics, Elsevier, vol. 16(C), pages 28-41.
    • Handle: RePEc:eee:ecosta:v:16:y:2020:i:c:p:28-41
    DOI: 10.1016/j.ecosta.2018.12.001
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    References listed on IDEAS

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    1. Göran Kauermann & Gerhard Tutz & Josef Brüderl, 2005. "The survival of newly founded firms: a case‐study into varying‐coefficient models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 145-158, January.
    2. S. K. Singh & G. S. Maddala, 2008. "A Function for Size Distribution of Incomes," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 2, pages 27-35, Springer.
    3. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    4. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    5. Luigi Ermini & David F. Hendry, 2008. "Log Income vs. Linear Income: An Application of the Encompassing Principle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 807-827, December.
    6. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    7. S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
    8. Deaton, Angus & Arora, Raksha, 2009. "Life at the top: The benefits of height," Economics & Human Biology, Elsevier, vol. 7(2), pages 133-136, July.
    9. Nathan Berg & Donald Lien, 2002. "Measuring The Effect Of Sexual Orientation On Income: Evidence Of Discrimination?," Contemporary Economic Policy, Western Economic Association International, vol. 20(4), pages 394-414, October.
    10. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    11. J. Peyhardi & C. Trottier & Y. Guédon, 2015. "A new specification of generalized linear models for categorical responses," Biometrika, Biometrika Trust, vol. 102(4), pages 889-906.
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