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

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  • Matti Langel

    ()

  • Yves Tillé

Abstract

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

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File URL: http://hdl.handle.net/10.1007/s00184-011-0369-1
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Bibliographic Info

Article provided by Springer in its journal Metrika.

Volume (Year): 75 (2012)
Issue (Month): 8 (November)
Pages: 1093-1110

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Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1093-1110

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Related research

Keywords: Inequality; Sampling; Influence function; Gini; Variance estimation;

References

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  1. 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, 04.
  2. repec:hal:cesptp:halshs-00176029 is not listed on IDEAS
  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 306-16, August.
  4. 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.
  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. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," Journal of Economic Inequality, Springer, vol. 1(3), pages 191-219, December.
  7. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-31.
  8. 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.
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