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

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  • Osnat Israeli

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    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

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    File URL: http://hdl.handle.net/10.1007/s10888-006-9036-6
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    Bibliographic Info

    Article provided by Springer in its journal The Journal of Economic Inequality.

    Volume (Year): 5 (2007)
    Issue (Month): 2 (August)
    Pages: 199-212

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    Handle: RePEc:kap:jecinq:v:5:y:2007:i:2:p:199-212

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    Web page: http://springerlink.metapress.com/link.asp?id=111137

    Related research

    Keywords: inequality decomposition; R-Square; Shapley value; C20; D63;

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    References

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    1. 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.
    2. Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
    3. 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.
    4. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
    5. Fei, John C H & Rainis, Gustav & Kuo, Shirley W Y, 1978. "Growth and the Family Distribution of Income by Factor Components," The Quarterly Journal of Economics, MIT Press, vol. 92(1), pages 17-53, February.
    6. 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 107-15, February.
    7. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
    8. Pyatt, Graham & Chen, Chau-nan & Fei, John, 1980. "The Distribution of Income by Factor Components," The Quarterly Journal of Economics, MIT Press, vol. 95(3), pages 451-73, November.
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    Cited by:
    1. Slonimczyk, Fabian, 2011. "Earnings inequality and skill mismatch in the U.S.: 1973-2002," MPRA Paper 35449, University Library of Munich, Germany.
    2. Christian Dustmann & Anna Okatenko, 2013. "Out-migration, Wealth Constraints, and the Quality of Local Amenities," Norface Discussion Paper Series 2013017, Norface Research Programme on Migration, Department of Economics, University College London.
    3. Hüttner, Frank & Sunder, Marco, 2011. "Decomposing R2 with the Owen value," Working Papers 100, University of Leipzig, Faculty of Economics and Management Science.
    4. Sebastian Leitner & Robert Stehrer, 2009. "Determinants of Inequality in Selected SEE Countries: Results from Shapley Value Decompositions," wiiw Balkan Observatory Working Papers 84, The Vienna Institute for International Economic Studies, wiiw.
    5. Deutsch, Joseph & Dumas, Audrey & Silber, Jacques, 2013. "Estimating an educational production function for five countries of Latin America on the basis of the PISA data," Economics of Education Review, Elsevier, vol. 36(C), pages 245-262.
    6. Sebastian Leitner & Robert Stehrer, 2011. "Subgroup and Shapely Value Decompositions of Multidimensional Inequality: An Application to South East European Countries," wiiw Balkan Observatory Working Papers 96, The Vienna Institute for International Economic Studies, wiiw.
    7. Jean-Marie Grether & Nicole Mathys & Jaime de Melo, 2009. "Scale, Technique and Composition Effects in Manufacturing SO 2 Emissions," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 43(2), pages 257-274, June.

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