Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index
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
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 75 (2012)
Issue (Month): 8 (November)
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/statistics/journal/184/PS2|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
- 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.
- 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.
- 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.
- Frank A. Cowell & Emmanuel Flachaire, 2004. "Income distribution and inequality measurement : the problem of extreme values," Cahiers de la Maison des Sciences Economiques v04101, Université Panthéon-Sorbonne (Paris 1).
- Frank A. Cowell & Emmanuel Flachaire, 2007. "Income distribution and inequality measurement: The problem of extreme values," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00176029, HAL.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1093-1110. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.