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A Note on Sen's Representation of the Gini Coefficient: Revision and Repercussions

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  • Stark, Oded

    (University of Bonn)

Abstract

Sen (1973 and 1997) presents the Gini coefficient of income inequality in a population as follows. "In any pair-wise comparison the man with the lower income can be thought to be suffering from some depression on finding his income to be lower. Let this depression be proportional to the difference in income. The sum total of all such depressions in all possible pair-wise comparisons takes us to the Gini coefficient." (This citation is from Sen 1973, p. 8.) Sen's verbal account is accompanied by a formula (Sen 1997, p. 31, eq. 2.8.1), which is replicated in the text of this note as equation (1). The formula yields a coefficient bounded from above by a number smaller than 1. This creates a difficulty, because the "mission" of a measure of inequality defined on the unit interval is to accord 0 to perfect equality (maximal equality) and 1 to perfect inequality (maximal inequality). In this note we show that when the Gini coefficient is elicited from a neat measure of the aggregate income-related depression of the population that consists of the people who experience income-related depression, then the obtained Gini coefficient is "well behaved" in the sense that it is bounded from above by 1. We conjecture a reason for a drawback of Sen's definition, and we present repercussions of the usage of the "well-behaved" Gini coefficient.

Suggested Citation

  • Stark, Oded, 2024. "A Note on Sen's Representation of the Gini Coefficient: Revision and Repercussions," IZA Discussion Papers 16856, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp16856
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    References listed on IDEAS

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    1. Lidia Ceriani & Paolo Verme, 2012. "The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(3), pages 421-443, September.
    2. Amartya Sen, 1976. "Real National Income," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 19-39.
    3. Oded Stark & Wiktor Budzinski, 2021. "A social‐psychological reconstruction of Amartya Sen’s measures of inequality and social welfare," Kyklos, Wiley Blackwell, vol. 74(4), pages 552-566, November.
    4. Stark, Oded, 2023. "On a tendency in health economics to dwell on income inequality and underestimate social stress," Economics & Human Biology, Elsevier, vol. 49(C).
    5. Oded Stark, 2020. "An Economics-Based Rationale for the Rawlsian Social Welfare Program," Research on Economic Inequality, in: Inequality, Redistribution and Mobility, volume 28, pages 179-186, Emerald Group Publishing Limited.
    6. George Deltas, 2003. "The Small-Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 226-234, February.
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    More about this item

    Keywords

    Sen's definition of the Gini coefficient of income inequality; aggregate income-related depression of a population; a well-behaved Gini coefficient;
    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
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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