IDEAS home Printed from https://ideas.repec.org/a/sae/somere/v44y2015i3p508-533.html
   My bibliography  Save this article

Decomposing the Gini Inequality Index

Author

Listed:
  • Beatriz Larraz

Abstract

The aim of this article is to propose a new breakdown of the Gini inequality ratio into three components ( within-group inequality, between-group inequality, and intensity of transvariation between groups to the total inequality index). The between-group inequality concept computes all the differences in salaries between men and women. The main contribution is to show this relationship when dealing with noninteger frequency data appearing on survey data. This article also proves the relationship between the very intuitive Gini concentration ratio and the very commonly used Gini index in the case of discrete distributions with a finite number of observations. The former refers to the relationship between the cumulative proportion of population and income, while the latter is the absolute mean difference divided by twice the arithmetic mean. This article complements the inequality decomposition literature that has stemmed from Gini’s work. The research is applied to analyze gender income inequality in a Spanish region using Spanish Structure of Earnings Survey data from 2010.

Suggested Citation

  • Beatriz Larraz, 2015. "Decomposing the Gini Inequality Index," Sociological Methods & Research, , vol. 44(3), pages 508-533, August.
    • Handle: RePEc:sae:somere:v:44:y:2015:i:3:p:508-533
    DOI: 10.1177/0049124114546046
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0049124114546046
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0049124114546046?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
    ---><---

    References listed on IDEAS

    as
    1. Zagier, Don, 1983. "Inequalities for the Gini coefficient of composite populations," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 103-118, October.
    2. Frick, Joachim R. & Grabka, Markus M. & Groh-Samberg, Olaf, 2012. "Dealing With Incomplete Household Panel Data in Inequality Research," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 41(1), pages 89-123.
    3. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
    4. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
    5. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    6. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    7. Stephane Mussard, 2004. "The bidimensional decomposition of the Gini ratio. A case study: Italy," Applied Economics Letters, Taylor & Francis Journals, vol. 11(8), pages 503-505.
    8. Giovanni Maria Giorgi, 2005. "Gini's scientific work: an evergreen," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-315.
    9. Rasner, Anika & Frick, Joachim R. & Grabka, Markus M., 2013. "Statistical Matching of Administrative and Survey Data: An Application to Wealth Inequality Analysis," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 42(2), pages 192-224.
    10. 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.
    11. Anika Rasner & Joachim R. Frick & Markus M. Grabka, 2013. "Statistical Matching of Administrative and Survey Data," Sociological Methods & Research, , vol. 42(2), pages 192-224, May.
    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. Larraz, Beatriz & Herrera, Marcos, 2016. "Factores condicionantes y dependencia espacial en el grado de concentración salarial en España/Determinants of Wage Inequality in Spain: A Spatial Approach," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 34, pages 597-618, Agosto.

    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 & 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.
    2. Dagum, Camilo, 2001. "Desigualdad del rédito y bienestar social, descomposición, distancia direccional y distancia métrica entre distribuciones," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 17, pages 5-52, Abril.
    3. Michele Costa, 2016. "Overlapping component and inequality decomposition: a simulation study for the Gini index," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 193-205, August.
    4. 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.
    5. repec:csb:stintr:v:12:y:2010:i:3:p:597-614 is not listed on IDEAS
    6. 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.
    7. 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.
    8. Mauro Mussini, 2010. "On the Link between Silber and Dagum Decomposition of the Gini Index," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 11(3), pages 597-614, December.
    9. 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.
    10. Achille VERNIZZI & Maria Giovanna MONTI & Marek KOSNY, 2006. "An overall inequality reducing and horizontally equitable tax system with application to Polish data," Departmental Working Papers 2006-15, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. 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.
    12. 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.
    13. Francesca Battisti & Francesco Porro, 2023. "A multi-decomposition of Zenga-84 inequality index: an application to the disparity in CO $$_2$$ 2 emissions in European countries," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 957-981, September.
    14. Chiang, Yen-Sheng, 2015. "Inequality measures perform differently in global and local assessments: An exploratory computational experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 1-11.
    15. 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.
    16. Benito Frosini, 2012. "Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures," Empirical Economics, Springer, vol. 43(1), pages 175-197, August.
    17. repec:ebl:ecbull:v:4:y:2003:i:7:p:1-6 is not listed on IDEAS
    18. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    19. Jacques Silber, 2020. "Foreword," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 97-98, August.
    20. Rafael Salas & John A. Bishop & Lester A. Zeager, 2018. "Second‐Order Discrimination and Generalized Lorenz Dominance," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(3), pages 563-575, September.
    21. 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.
    22. 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.

    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:sae:somere:v:44:y:2015:i:3:p:508-533. 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: SAGE Publications (email available below). General contact details of provider: .

    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.