IDEAS home Printed from https://ideas.repec.org/a/kap/jecinq/v5y2007i2p199-212.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10888-006-9036-6
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10888-006-9036-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stéphane Mussard & Michel Terraza, 2009. "Décompositions des mesures d'inégalité : le cas des coefficients de Gini et d'entropie," Recherches économiques de Louvain, De Boeck Université, vol. 75(2), pages 151-181.
    2. Arthur Charpentier & Stéphane Mussard, 2011. "Income inequality games," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 529-554, December.
    3. Stéphane Mussard, 2006. "Une réconciliation entre la décomposition en sous-groupes et la décomposition en sources de revenu de l'indice de Gini. La multi-décomposition de l'indicateur de Gini," Annals of Economics and Statistics, GENES, issue 81, pages 169-193.
    4. Carlo V. Fiorio, 2006. "Understanding Inequality Trends:Microsimulation Decomposition for Italy," STICERD - Distributional Analysis Research Programme Papers 78, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Teixidó Figueras, Jordi & Duro Moreno, Juan Antonio, 2012. "Ecological Footprint Inequality: A methodological review and some results," Working Papers 2072/203168, Universitat Rovira i Virgili, Department of Economics.
    6. Chantreuil, Frédéric & Fourrey, Kévin & Lebon, Isabelle & Rebière, Thérèse, 2021. "Magnitude and evolution of gender and race contributions to earnings inequality across US regions," Research in Economics, Elsevier, vol. 75(1), pages 45-59.
    7. C. Chameni Nembua, 2008. "The 'natural' bidimensional decomposition of inequality indices: evaluating factor contributions to households welfare inequality in Cameroon, 1996-2001," Applied Economics Letters, Taylor & Francis Journals, vol. 15(12), pages 963-970.
    8. Frank Cowell & Carlo Fiorio, 2011. "Inequality decompositions—a reconciliation," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 509-528, December.
    9. Stéphane Mussard, 2006. "La décomposition des mesures d’inégalité en sources de revenu : l’indice de Gini et les généralisations," Cahiers de recherche 06-05, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    10. Chantreuil, Frédéric & Fourrey, Kévin & Lebon, Isabelle & Rebiere, Therese, 2020. "Decomposing US Income Inequality à La Shapley: Race Matters, but Gender Too," IZA Discussion Papers 12950, Institute of Labor Economics (IZA).
    11. Giuseppe Pignataro, 2010. "Measuring equality of opportunity by Shapley value," Economics Bulletin, AccessEcon, vol. 30(1), pages 786-798.
    12. Jurkatis, Simon & Strehl, Wolfgang, 2014. "Gini decompositions and Gini elasticities: On measuring the importance of income sources and population subgroups for income inequality," Discussion Papers 2014/22, Free University Berlin, School of Business & Economics.
    13. Simon Jurkatis, "undated". "Dos and Don'ts of Gini Decompositions," BDPEMS Working Papers 2013003, Berlin School of Economics.
    14. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    15. Frank Cowell & Carlo V. Fiorio, 2010. "GINI DP 4: Inequality Decompositions," GINI Discussion Papers 4, AIAS, Amsterdam Institute for Advanced Labour Studies.
    16. Jordi Teixidó-Figueras & Juan Duro, 2015. "International Ecological Footprint Inequality: A Methodological Review and Some Results," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(4), pages 607-631, April.
    17. Michele Giammatteo, 2007. "The bidimensional decomposition of inequality: A nested Theil approach," LIS Working papers 466, LIS Cross-National Data Center in Luxembourg.
    18. Cecilia García-Peñalosa & Elsa Orgiazzi, 2013. "Factor Components of Inequality: A Cross-Country Study," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 59(4), pages 689-727, December.
    19. Martin FOURNIER, 2001. "Inequality decomposition by factor component : a “rank-correlation” approach illustrated on the Taiwanese case," Discussion Papers (REL - Recherches Economiques de Louvain) 2001042, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    20. Mussard, Stéphane & Pi Alperin, Maria Noel, 2011. "Poverty growth in Scandinavian countries: A Sen multi-decomposition," Economic Modelling, Elsevier, vol. 28(6), pages 2842-2853.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jecinq:v:5:y:2007:i:2:p:199-212. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.