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Decomposing the Gini Inequality Index

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  • 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
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    References listed on IDEAS

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    1. Zagier, Don, 1983. "Inequalities for the Gini coefficient of composite populations," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 103-118, October.
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    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
    10. 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.
    11. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
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    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.

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