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A Shapley-based decomposition of the R-Square of a linear regression

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  • Osnat Israeli

Abstract

This note suggests a new way of determining the exact contributions of the explanatory variables to the R-Square of a linear regression. The proposed methodology combines the so-called Shapley approach (Chantreuil and Trannoy, Inequality decomposition values: the trade-off between marginality and consistency. THEMA Discussion Paper, Université de Cergy-Pontoise, France 1999; Shorrocks, Decomposition Procedures for Distributional Analysis: A Unified Framework Based on the Shapley Value (mimeo), University of Essex, 1999) with the Fields (Res. Labor Econ., 22:1–38, 2003) decomposition. Copyright Springer Science+Business Media, Inc. 2007

Suggested Citation

  • Osnat Israeli, 2007. "A Shapley-based decomposition of the R-Square of a linear regression," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 199-212, August.
    • Handle: RePEc:kap:jecinq:v:5:y:2007:i:2:p:199-212
    DOI: 10.1007/s10888-006-9036-6
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    References listed on IDEAS

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    1. F. Chantreuil & A. Trannoy, 1999. "Inequality decomposition values : the trade-off between marginality and consistency," THEMA Working Papers 99-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Mercedes Sastre & Alain Trannoy, 2002. "Shapley inequality decomposition by factor components: Some methodological issues," Journal of Economics, Springer, vol. 9(1), pages 51-89, December.
    3. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    4. Graham Pyatt & Chau-nan Chen & John Fei, 1980. "The Distribution of Income by Factor Components," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 451-473.
    5. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    6. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    7. John C. H. Fei & Gustav Ranis & Shirley W. Y. Kuo, 1978. "Growth and the Family Distribution of Income by Factor Components," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(1), pages 17-53.
    8. C. Seidl & Patrick Moyes & A. F. Shorrocks, 2002. "Inequalities: Theory, experiments and applications," Post-Print hal-00157353, HAL.
    9. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
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    More about this item

    Keywords

    inequality decomposition; R-Square; Shapley value; C20; D63;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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