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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

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, Oxford University Press, 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, Oxford University Press, vol. 92(1), pages 17-53.
    8. 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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    3. Eric Wong & Andrew Tsang & Steven Kong, 2016. "How Does Loan-To-Value Policy Strengthen Resilience of Banks to Property Price Shocks ¡V Evidence from Hong Kong," International Real Estate Review, Asian Real Estate Society, vol. 19(1), pages 120-149.
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    5. Vakulenko, Elena & Leukhin, Roman, 2015. "Investigation of demand for the foreign workforce in Russian regions using applications for quotas," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 37(1), pages 67-86.
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    7. Vargas, Andrés & Lo, Alex Y. & Rohde, Nicholas & Howes, Michael, 2016. "Background inequality and differential participation in deliberative valuation: Lessons from small-group discussions on forest conservation in Colombia," Ecological Economics, Elsevier, vol. 129(C), pages 104-111.
    8. 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.
    9. Shabana Mitra, 2016. "Synergies Among Monetary, Multidimensional and Subjective Poverty: Evidence from Nepal," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 125(1), pages 103-125, January.
    10. Kerry B. Hudson & Joaquin L. Vespignani, 2014. "Understanding the Deviations of the Taylor Rule: A New Methodology with an Application to Australia," CAMA Working Papers 2014-78, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    11. Nikolova, Milena, 2016. "Minding the happiness gap: Political institutions and perceived quality of life in transition," European Journal of Political Economy, Elsevier, vol. 45(S), pages 129-148.
    12. Jean-Marie Grether & Nicole Mathys & Jaime de Melo, 2009. "Scale, Technique and Composition Effects in Manufacturing SO 2 Emissions," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 43(2), pages 257-274, June.
    13. Juliane Begenau & Berardino Palazzo, 2017. "Firm Selection and Corporate Cash Holdings," NBER Working Papers 23249, National Bureau of Economic Research, Inc.
    14. Beatriz Muriel Hernández, 2016. "An Analysis of Firm Characteristics as Earnings Determinants: The Urban Bolivia Case," Development Research Working Paper Series 04/2016, Institute for Advanced Development Studies.
    15. Rafael P. Ribas, 2014. "Liquidity Constraints, Informal Financing, and Entrepreneurship: Direct and Indirect Effects of a Cash Transfer Programme," Working Papers 131, International Policy Centre for Inclusive Growth.
    16. Fabián Slonimczyk, 2013. "Earnings inequality and skill mismatch in the U.S.: 1973–2002," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(2), pages 163-194, June.
    17. 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.
    18. Hüttner, Frank & Sunder, Marco, 2011. "Decomposing R2 with the Owen value," Working Papers 100, University of Leipzig, Faculty of Economics and Management Science.

    More about this item

    Keywords

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

    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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