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

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.

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Correspondence to Osnat Israeli.

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Israeli, O. A Shapley-based decomposition of the R-Square of a linear regression. J Econ Inequal 5, 199–212 (2007). https://doi.org/10.1007/s10888-006-9036-6

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Key words

  • inequality decomposition
  • R-Square
  • Shapley value

JEL Classification

  • C20
  • D63