A Shapley-based decomposition of the R-Square of a linear regression
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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Volume (Year): 5 (2007)
Issue (Month): 2 (August)
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- Shorrocks, A F, 1982. "Inequality Decomposition by Factor Components," Econometrica, Econometric Society, vol. 50(1), pages 193-211, January.
- 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.
- Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
- 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.
- 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.
- Chantreuil, F. & Trannoy, A., 1999.
"Inequality Decomposition Values: the Trade-Off Between Marginality and Consistency,"
99-24, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- 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.
- Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
- 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.
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