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Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index


  • Matti Langel


  • Yves Tillé


Zenga’s new inequality curve and index are two recent tools for measuring inequality. Proposed in 2007, they should thus not be mistaken for anterior measures suggested by the same author. This paper focuses on the new measures only, which are hereafter referred to simply as the Zenga curve and Zenga index. The Zenga curve Z(α) involves the ratio of the mean income of the 100α % poorest to that of the 100(1−α)% richest. The Zenga index can also be expressed by means of the Lorenz Curve and some of its properties make it an interesting alternative to the Gini index. Like most other inequality measures, inference on the Zenga index is not straightforward. Some research on its properties and on estimation has already been conducted but inference in the sampling framework is still needed. In this paper, we propose an estimator and variance estimator for the Zenga index when estimated from a complex sampling design. The proposed variance estimator is based on linearization techniques and more specifically on the direct approach presented by Demnati and Rao. The quality of the resulting estimators are evaluated in Monte Carlo simulation studies on real sets of income data. Finally, the advantages of the Zenga index relative to the Gini index are discussed. Copyright Springer-Verlag 2012

Suggested Citation

  • Matti Langel & Yves Tillé, 2012. "Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1093-1110, November.
  • Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1093-1110
    DOI: 10.1007/s00184-011-0369-1

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    References listed on IDEAS

    1. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
    2. Paolo Radaelli, 2010. "On the Decomposition by Subgroups of the Gini Index and Zenga's Uniformity and Inequality Indexes," International Statistical Review, International Statistical Institute, vol. 78(1), pages 81-101, April.
    3. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    4. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    5. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 1996. "Poverty measurement with contaminated data: A robust approach," European Economic Review, Elsevier, vol. 40(9), pages 1761-1771, December.
    6. Greselin, Francesca & Pasquazzi, Leo & Zitikis, Ricardas, 2009. "Zenga’s new index of economic inequality, its estimation, and an analysis of incomes in Italy," MPRA Paper 17147, University Library of Munich, Germany.
    7. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(3), pages 191-219, December.
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    Cited by:

    1. Lucio Barabesi & Giancarlo Diana & Pier Perri, 2015. "Gini index estimation in randomized response surveys," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 45-62, January.
    2. Greselin Francesca, 2014. "More Equal and Poorer, or Richer but More Unequal?," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 99-117, December.
    3. Francesca Greselin & Simone Pellegrino & Achille Vernizzi, 2017. "Lorenz versus Zenga Inequality Curves: a New Approach to Measuring Tax Redistribution and Progressivity," Working papers 046, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    4. repec:aen:journl:ej38-4-mussini is not listed on IDEAS
    5. Michele Zenga, 2016. "On the decomposition by subpopulations of the point and synthetic Zenga (2007) inequality indexes," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 375-405, December.


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