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New Perspectives on the Gini and Bonferroni Indices of Inequality

Author

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  • Satya R. Chakravarty

    (Indian Statistical Institute)

  • Palash Sarkar

    (Indian Statistical Institute)

Abstract

This paper rigorously demonstrates that for any unequal income distribution, the well-known Gini index of inequality is bounded above by the recently revived Bonferroni inequality index. The bound is exactly attained if and only if out of n incomes in the society, $(n -1)$ poor incomes are identical. The boundedness theorem is shown to possess a duality-type inequality implication. Reinterpreting a property of the absolute Gini index, noted by Weymark (1981), we propose a new postulate, `additive monotonicity', for inequality indices and analyse its sensitivity to the absolute and relative Bonferroni, and the relative Gini indices. Finally, we look at the pattern of the income distribution when a society wishes to guarantee a minimum income for the worst off person and fixes the inequality levels, as measured by the Gini and the Bonferroni indices, at some specific values.

Suggested Citation

  • Satya R. Chakravarty & Palash Sarkar, 2020. "New Perspectives on the Gini and Bonferroni Indices of Inequality," Working Papers 538, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2020-538
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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2020-538.pdf
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    References listed on IDEAS

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    Cited by:

    1. Satya Chakravarty & Palash Sarkar, 2020. "A Paradox for Inequality Indices," Working Papers 559, ECINEQ, Society for the Study of Economic Inequality.

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    More about this item

    Keywords

    Gini and Bonferroni indices; boundedness; additive monotonicity; maximin rule and lexicographic extension.;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

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