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Parametric modelling of inequality aversion to reduce the computing time of distributional fuzzy poverty measures with application to EU countries

Author

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  • Gianni Betti

    (University of Siena)

  • Federico Crescenzi

    (Universitas Mercatorum)

  • Lorenzo Mori

    (University of Bologna)

Abstract

This paper introduces a parametric approach for computing the fuzzy monetary (FM) index. We establish the relationship between this fuzzy index, which is frequently used to estimate inequality, and the Generalized Gini index through a parameter, $$\alpha$$ α , that reflects the degree of aversion to inequality. While, for the Generalized Gini index $$\alpha$$ α is chosen by the researcher for the FM index it is derived from data. To efficiently estimate FM, we first prove some technical results and then introduce a parametric method that accelerates the computation of $$\alpha$$ α , incorporating the closed-form expression of the Generalized Gini index for selected distributions. To assess the variability of the index, we propose a parametric bootstrap method. The results are validated through simulations, where we compare the original FM index with its parametric counterpart. Finally, we apply our approach to estimate inequality aversion in European countries.

Suggested Citation

  • Gianni Betti & Federico Crescenzi & Lorenzo Mori, 2025. "Parametric modelling of inequality aversion to reduce the computing time of distributional fuzzy poverty measures with application to EU countries," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(4), pages 687-705, September.
    • Handle: RePEc:spr:stmapp:v:34:y:2025:i:4:d:10.1007_s10260-025-00793-1
    DOI: 10.1007/s10260-025-00793-1
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    References listed on IDEAS

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    1. Daron Acemoglu, 2003. "Cross-Country Inequality Trends," Economic Journal, Royal Economic Society, vol. 113(485), pages 121-149, February.
    2. Alkire, Sabina & Foster, James & Seth, Suman & Santos, Maria Emma & Roche, Jose Manuel & Ballon, Paola, 2015. "Multidimensional Poverty Measurement and Analysis," OUP Catalogue, Oxford University Press, number 9780199689491.
    3. Gianni Betti & Francesca Gagliardi & Vijay Verma, 2018. "Simplified Jackknife Variance Estimates for Fuzzy Measures of Multidimensional Poverty," International Statistical Review, International Statistical Institute, vol. 86(1), pages 68-86, April.
    4. Walter Bossert & Satya R. Chakravarty & Conchita D’Ambrosio, 2019. "Multidimensional Poverty and Material Deprivation with Discrete Data," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 191-209, Springer.
    5. Arnstein Aassve & Gianni Betti & Stefano Mazzuco & Letizia Mencarini, 2007. "Marital disruption and economic well‐being: a comparative analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(3), pages 781-799, July.
    6. Simona Iammarino & Andrés Rodriguez-Pose & Michael Storper, 2019. "Regional inequality in Europe: evidence, theory and policy implications," Journal of Economic Geography, Oxford University Press, vol. 19(2), pages 273-298.
    7. Jacques Silber (ed.), 2023. "Research Handbook on Measuring Poverty and Deprivation," Books, Edward Elgar Publishing, number 20574, June.
    8. Sabina Alkire, James E. Foster, Suman Seth, Maria Emma Santos, Jose M. Roche and Paola Ballon, 2015. "Multidimensional Poverty Measurement and Analysis: Chapter 9 - Distribution and Dynamics," OPHI Working Papers ophiwp090_ch9.pdf, Queen Elizabeth House, University of Oxford.
    9. Sabina Alkire, James E. Foster, Suman Seth, Maria Emma Santos, José M. Roche and Paola Ballon, 2015. "Multidimensional Poverty Measurement and Analysis: Chapter 7 - Data and Analysis," OPHI Working Papers ophiwp088_ch7.pdf, Queen Elizabeth House, University of Oxford.
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    11. Francesca Bettio & Elisa Ticci & Gianni Betti, 2020. "A Fuzzy Index and Severity Scale to Measure Violence Against Women," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 148(1), pages 225-249, February.
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    15. Gianni Betti & Federico Crescenzi & Vasco Molini & Lorenzo Mori, 2024. "Estimation of Multidimensional Poverty in Morocco: A Small Area Estimation Approach Using Meteorological and Socio-economic Covariates," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 175(2), pages 545-575, November.
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    21. Gianni Betti & Rossella Soldi & Ilija Talev, 2016. "Fuzzy Multidimensional Indicators of Quality of Life: The Empirical Case of Macedonia," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 127(1), pages 39-53, May.
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