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The Asymptotic Distribution of the Generalized Gini Indices of Inequality

Author

Listed:
  • Garry F. Barrett
  • Krishna Pendakur

Abstract

This paper presents the asymptotic distributions of the S-Gini and E-Gini relative and absolute indices of inequality. The generalized Gini indices are defined in terms of Lorenz ordinates and results on the asymptotic covariance matrix of Lorenz ordinates are used to derive the large sample properties of the indices. The methods are illustrated by examining changes in the distribution of nondurable consumption in Canada over the 1980s. The authors find that inequality was lower in 1972 and 1990 than in 1984. Over the entire data period, relative inequality was either static or increased slightly, while absolute inequality declined.

Suggested Citation

  • Garry F. Barrett & Krishna Pendakur, 1995. "The Asymptotic Distribution of the Generalized Gini Indices of Inequality," Canadian Journal of Economics, Canadian Economics Association, vol. 28(4b), pages 1042-1055, November.
  • Handle: RePEc:cje:issued:v:28:y:1995:i:4b:p:1042-55
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    Citations

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    Cited by:

    1. Thomas Demuynck, 2012. "An (almost) unbiased estimator for the S-Gini index," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 109-126, March.
    2. Garry F. Barrett & Thomas F. Crossley & Christopher Worswick, 2000. "Consumption and Income Inequality in Australia," The Economic Record, The Economic Society of Australia, vol. 76(233), pages 116-138, June.
    3. Shahateet, Mohammed & Al-Tayyeb, Saud, 2007. "Regional consumption inequalities in Jordan: Empirical study," MPRA Paper 57400, University Library of Munich, Germany.
    4. Yang Wei & Zhouping Li & Yunqiu Dai, 2022. "Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices," Statistical Papers, Springer, vol. 63(5), pages 1415-1475, October.
    5. Cosme Vodounou, 2004. "Pauvreté, croissance et ciblage : propriétés asymptotiques des estimateurs des élasticités avec application au Bénin," Revue d’économie du développement, De Boeck Université, vol. 12(2), pages 65-84.
    6. Peter Warr & Sitthiroth Rasphone & Jayant Menon, 2015. "Two Decades of Declining Poverty Despite Rising Inequality in Laos," Departmental Working Papers 2015-13, The Australian National University, Arndt-Corden Department of Economics.
    7. Jean-Yves Duclos, 2000. "Gini Indices and the Redistribution of Income," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 7(2), pages 141-162, March.
    8. Peter Warr & Sitthiroth Rasphone & Jayant Menon, 2018. "Two Decades of Declining Poverty but Rising Inequality in Laos," Asian Economic Journal, East Asian Economic Association, vol. 32(2), pages 165-185, June.
    9. Duclos, Jean-Yves & Tabi, Martin, 1999. "Inégalité et redistribution du revenu, avec une application au Canada," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(1), pages 95-122, mars-juin.
    10. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2015. "Entropy maximization under the constraints on the generalized Gini index and its application in modeling income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 657-666.
    11. Peter Warr & Lwin Lwin Aung, 2018. "Poverty and inequality impact of natural disasters: Myanmar, 2005 to 2010," Departmental Working Papers 2018-15, The Australian National University, Arndt-Corden Department of Economics.
    12. St鰨ane Mussard & Patrick Richard, 2012. "Linking Yitzhaki's and Dagum's Gini decompositions," Applied Economics, Taylor & Francis Journals, vol. 44(23), pages 2997-3010, August.
    13. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics, Canadian Economics Association, vol. 43(4), pages 1122-1148, November.
    14. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2017. "Maximum Tsallis entropy with generalized Gini and Gini mean difference indices constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 554-560.
    15. Giovanni Maria Giorgi & Paola Palmitesta & Corrado Provasi, 2006. "Asymptotic and bootstrap inference for the generalized Gini indices," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 107-124.
    16. Urvashi Dhawan-Biswal, 2002. "Consumption and Income Inequality: The Case of Atlantic Canada from 1969­1996," Canadian Public Policy, University of Toronto Press, vol. 28(4), pages 513-537, December.
    17. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, Jafar, 2018. "New functional forms of Lorenz curves by maximizing Tsallis entropy of income share function under the constraint on generalized Gini index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 280-288.
    18. Warr, Peter & Aung, Lwin Lwin, 2019. "Poverty and inequality impact of a natural disaster: Myanmar’s 2008 cyclone Nargis," World Development, Elsevier, vol. 122(C), pages 446-461.
    19. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    20. Lwin Lwin Aung & Peter Warr, 2021. "Decomposing changes in inequality: Evidence from Myanmar," Review of Development Economics, Wiley Blackwell, vol. 25(3), pages 1172-1196, August.

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