IDEAS home Printed from https://ideas.repec.org/p/shr/wpaper/06-11.html
   My bibliography  Save this paper

La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature

Author

Listed:
  • Stéphane Mussard

    (GREDI, Université de Sherbrooke and GEREM, Université de Perpignan)

  • Françoise Seyte

    (CREA, University of Luxembourg, Faculty of Law Economics and Finance)

  • Michel Terraza

    (LAMETA, Université de Montpellier I)

Abstract

Gini and entropy are the most use measures to gauge income inequalities. We show that each measure yields different subgroup decomposition techniques into within-group inequalities and between-group inequalities. Then, we show that the Gini index has been decomposed into many ways to bring out a third measure of income inequalities.scales.

Suggested Citation

  • Stéphane Mussard & Françoise Seyte & Michel Terraza, 2006. "La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature," Cahiers de recherche 06-11, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    • Handle: RePEc:shr:wpaper:06-11
    as

    Download full text from publisher

    File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-0611.pdf
    File Function: First version, 2006
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cowell, Frank A. & Kuga, Kiyoshi, 1981. "Additivity and the entropy concept: An axiomatic approach to inequality measurement," Journal of Economic Theory, Elsevier, vol. 25(1), pages 131-143, August.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    3. Das, T & Parikh, A, 1982. "Decomposition of Inequality Measures and a Comparative Analysis," Empirical Economics, Springer, vol. 7(1-2), pages 23-48.
    4. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    5. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    6. Deutsch, Joseph & Silber, Jacques, 1997. "Gini's "Transvariazione" and the Measurement of Distance between Distributions," Empirical Economics, Springer, vol. 22(4), pages 547-554.
    7. Mahar K. Mangahas, 1974. "Income Inequality in the Philippines: A Decomposition Analysis," UP School of Economics Discussion Papers 197415, University of the Philippines School of Economics.
    8. Branko Milanovic & Shlomo Yitzhak, 2006. "Decomposing World Income Distribution: Does The World Have A Middle Class?," IBT Journal of Business Studies (JBS), Ilma University, Faculty of Management Science, vol. 2(2), pages 88-110.
    9. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    10. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    11. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
    12. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
    13. Irma Adelman & Amnon Levy, 1984. "Decomposing Theil'S Income Of Income Inequality Into Between And Within Components: A Note," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 30(1), pages 119-121, March.
    14. Adelman, Irma & Levy, Amnon, 1986. "Decomposing Theil's Index of Income Inequality: A Reply," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 32(1), pages 107-108, March.
    15. de MESNARD, Louis, 1997. "A propos des problèmes causés par les indices de mesure d’inégalité de Gini et de Kakwani," LATEC - Document de travail - Economie (1991-2003) 1997-13, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
    16. 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.
    17. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166, Elsevier.
    18. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    19. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    20. Rafael Salas, 2002. "Multilevel interterritorial convergence and additive multidimensional inequality decomposition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 207-218.
    21. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    22. Mookherjee, Dilip & Shorrocks, Anthony F, 1982. "A Decomposition Analysis of the Trend in UK Income Inequality," Economic Journal, Royal Economic Society, vol. 92(368), pages 886-902, December.
    23. Wagstaff, Adam, 2002. "Inequality aversion, health inequalities and health achievement," Journal of Health Economics, Elsevier, vol. 21(4), pages 627-641, July.
    24. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
    25. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
    26. Stéphane Mussard & Michel Terraza & Françoise Seyte, 2003. "Decomposition of Gini and the generalized entropy inequality measures," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-6.
    27. Irma Adelman & Amnon Levy, 1986. "Decomposing Theil'S Index Of Income Inequality: A Reply," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 32(1), pages 107-108, March.
    28. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October.
    29. 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.
    30. Chakravarty, Satya Ranjan & Dutta, Bhaskar, 1987. "A note on measures of distance between imcome distributions," Journal of Economic Theory, Elsevier, vol. 41(1), pages 185-188, February.
    31. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
    32. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    33. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    34. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    35. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    36. repec:ebl:ecbull:v:4:y:2003:i:3:p:1-5 is not listed on IDEAS
    37. Silber, Jacques, 1993. "Inequality Decomposition by Income," The Review of Economics and Statistics, MIT Press, vol. 75(3), pages 545-547, August.
    38. Cowell, Frank A, 1988. "Inequality Decomposition: Three Bad Measures," Bulletin of Economic Research, Wiley Blackwell, vol. 40(4), pages 309-312, October.
    39. repec:ebl:ecbull:v:4:y:2003:i:7:p:1-6 is not listed on IDEAS
    40. repec:rus:hseeco:15683 is not listed on IDEAS
    41. 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.
    42. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    43. repec:ilo:ilowps:158323 is not listed on IDEAS
    44. Adelman, Irma & Levy, Amnon, 1984. "Decomposing Theil's Income of Income Inequality into Between and Within Components: A Note," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 30(1), pages 119-121, March.
    45. Dagum, Camilo, 1987. "Measuring the Economic Affluence between Populations of Income Receivers," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 5-12, January.
    46. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    47. Milanovic, Branko & Yitzhaki, Shlomo, 2002. "Decomposing World Income Distribution: Does the World Have a Middle Class?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 48(2), pages 155-178, June.
    48. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    49. Shlomo Yitzhaki & Robert I. Lerman, 1991. "Income Stratification And Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
    50. Ebert, Udo, 1984. "Measures of distance between income distributions," Journal of Economic Theory, Elsevier, vol. 32(2), pages 266-274, April.
    51. R. Robert Russell, 1985. "A Note on Decomposable Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 347-352.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giovanni M. Giorgi & Alessio Guandalini, 2018. "Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality," Econometrics, MDPI, vol. 6(2), pages 1-16, April.

    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. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Statistics Norway, Research Department.
    3. Mornet, Pauline & Zoli, Claudio & Mussard, Stéphane & Sadefo-Kamdem, Jules & Seyte, Françoise & Terraza, Michel, 2013. "The (α, β)-multi-level α-Gini decomposition with an illustration to income inequality in France in 2005," Economic Modelling, Elsevier, vol. 35(C), pages 944-963.
    4. 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.
    5. Frank A Cowell, 2003. "Theil, Inequality and the Structure of Income Distribution," STICERD - Distributional Analysis Research Programme Papers 67, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. St鰨ane Mussard & Patrick Richard, 2012. "Linking Yitzhaki's and Dagum's Gini decompositions," Applied Economics, Taylor & Francis Journals, vol. 44(23), pages 2997-3010, August.
    7. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    8. Stéphane Mussard & Pi Alperin María Noel & Françoise Seyte & Michel Terraza, 2005. "Extensions Of Dagum’S Gini Decomposition," Cahiers de recherche 05-07, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    9. Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    10. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    11. Luc Savard & Stéphane Mussard, 2005. "Horizontal and Vertical Redistribution and Micro-simulation," Cahiers de recherche 05-03, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    12. Geoffrey Warner, 2001. "A lorenz curve based index of income stratification," The Review of Black Political Economy, Springer;National Economic Association, vol. 28(3), pages 41-57, December.
    13. St鰨ane Mussard & Luc Savard, 2012. "The Gini multi-decomposition and the role of Gini's transvariation: application to partial trade liberalization in the Philippines," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1235-1249, April.
    14. 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.
    15. Michele Giammatteo, 2007. "The bidimensional decomposition of inequality: A nested Theil approach," LIS Working papers 466, LIS Cross-National Data Center in Luxembourg.
    16. Simon Jurkatis, "undated". "Dos and Don'ts of Gini Decompositions," BDPEMS Working Papers 2013003, Berlin School of Economics.
    17. Paul Allanson, 2018. "On the Measurement of the Overall Degree of Income Stratification between Groups," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(2), pages 388-405, June.
    18. Alina Jędrzejczak, 2014. "Income Inequality and Income Stratification in Poland," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(2), pages 269-282, March.
    19. Frank Cowell, 2005. "Theil, Inequality Indices and Decomposition," Working Papers 01, ECINEQ, Society for the Study of Economic Inequality.
    20. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.

    More about this item

    Keywords

    Decomposition; Entropy; Gini;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

    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:shr:wpaper:06-11. 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: Jean-François Rouillard (email available below). General contact details of provider: https://edirc.repec.org/data/deushca.html .

    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.