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Beyond the Gini index: Measuring inequality with the Balance of Inequality index

Author

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  • Giorgio Di Maio

    (Politecnico di Milano)

  • Paolo Landoni

    (Politecnico di Milano)

Abstract

In the first part of this paper, we present the Balance of Inequality (BOI) index, a new approach to the measurement of inequality in which each individual is given a weight equal to her income, and the barycenter of the income distribution is used to measure its inequality. The BOI index features an intuitive physical interpretation and a simple graphical representation that shows the income distribution and the inequality measure together. The index’s lower and upper bounds are always 0 and 1, which indicates that it is an accurate measure of inequality even when applied to small populations and small samples – cases in which the Gini index is downward biased. We also show that the BOI index is related to the Gini index. In the second part of the paper, we decompose inequality by population subgroups for both the BOI, and Gini indices with a new approach that considers the distribution of the individual members of each subgroup in the population. This decomposition is accomplished by introducing the barycenter of the subgroups for cases of perfect equality and perfect inequality, the asymmetry effect and the irregularity effect. After demonstrating that the BOI index is decomposable by population subgroups, we show that i) the lower and upper bounds of the BOI index and of the Gini index are computable when grouped data or mean incomes are available but the inequalities within subgroups are unknown (without any assumptions regarding the distribution function), ii) the BOI index and the Gini index can be computed with frequency distributions, and iii) the average within-subgroup inequality implied in the Gini indices of the population inequality given with grouped data can be computed. We also show that the Lambert-Aronson (1993) residual i) can be non-null when the subsets do not overlap and ii) is not the effect of the overlapping between subgroups but of the approach used. Finally, we outline the BOI index decomposition by income sources and propose a new formulation of the population principle.

Suggested Citation

  • Giorgio Di Maio & Paolo Landoni, 2015. "Beyond the Gini index: Measuring inequality with the Balance of Inequality index," a/ Working Papers Series 1506, Italian Association for the Study of Economic Asymmetries, Rome (Italy).
    • Handle: RePEc:ais:wpaper:1506
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    References listed on IDEAS

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    Cited by:

    1. Alessio Guandalini, 2022. "Things you should know about the Gini index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 76(4), pages 4-12, October-D.
    2. Rob Clark & Kara Snawder, 2020. "A Cross-National Analysis of Lifespan Inequality, 1950–2015: Examining the Distribution of Mortality Within Countries," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 148(3), pages 705-732, April.
    3. Giorgio Di Maio, 2022. "The barycenter of the distribution and its application to the measurement of inequality: The Balance of Inequality, the Gini index, and the Lorenz curve," Working Papers 493, University of Milano-Bicocca, Department of Economics, revised Mar 2022.

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    More about this item

    Keywords

    Inequality measurement; Gini index; Inequality decomposition by population subgroups; Inequality decomposition by income sources; Balance of Inequality; BOI index; Asymmetry Effect; Irregularity Effect; R concentration ratio.;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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