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The Zenga Index Reveals More Than the Gini and the Bonferroni Indexes. An Analysis of Distributional Changes and Social Welfare Levels

Author

Listed:
  • Monti Maria Giovanna

    (University of Milan, Italy;)

  • Pellegrino Simone

    (Department of Economics, Social Studies, Applied Mathematics and Statistics, University of Turin, Italy;)

  • Vernizzi Achille

    (Department of Economics, Management and Quantitative Methods, University of Milan, Italy;)

Abstract

In this paper we discuss the characteristics of the Zenga index and describe how it interprets both income inequality and social welfare. The Zenga index is quite different from those commonly used today. The difference is mainly due to the role played by income weights: they depend not only on income ranks but also on income distribution. To achieve our goals, we compare the Zenga index behaviour with that of other two indexes: the Gini and the Bonferroni index. The first issue we address concerns the effect of distributional changes in terms of inequality indexes. This analysis highlights how the Zenga index interprets income inequality differently with respect to the other two indexes. The second issue we consider is to determine the social welfare function associated to the Zenga index. We derive it by employing the method proposed by Dagum in 1990. By employing the Zenga social welfare function, we show that one can go beyond Dagum's remarks: when the income increase takes place in the top part of the income distribution, the social welfare can decrease when mean income increases. We can thus conclude that the Zenga inequality index reveals more than the Gini and Bonferroni indexes; in particular, it is more sensitive for evaluating income changes taking place in different parts of the income distribution.

Suggested Citation

  • Monti Maria Giovanna & Pellegrino Simone & Vernizzi Achille, 2024. "The Zenga Index Reveals More Than the Gini and the Bonferroni Indexes. An Analysis of Distributional Changes and Social Welfare Levels," Working papers 084, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    • Handle: RePEc:tur:wpapnw:084
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    References listed on IDEAS

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      • Simone Pellegrino, 2024. "The Gini Coefficient: Its Origins," Working papers 086, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
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    More about this item

    Keywords

    Peronal Income Tax; Gini Index; Bonferroni Index; Zenga Index; Social Welfare;
    All these keywords.

    JEL classification:

    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies
    • H24 - Public Economics - - Taxation, Subsidies, and Revenue - - - Personal Income and Other Nonbusiness Taxes and Subsidies

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