Login
Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index
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 (alpha) involves the ratio of the mean income of the 100 alpha% poorest to that of the 100(1-alpha)% 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.
   
Keywords Gini, inequality, influence function, sampling, variance estimation
   
Citation Langel, M., & Tillé, Y. (2012). Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index. Metrika, 75(8), 1093-1110.
   
Type Journal article (English)
Date of appearance 17-9-2012
Journal Metrika
Volume 75
Issue 8
Pages 1093-1110
URL http://link.springer.com/article/10.1007%2Fs00184-011-0369-1
Related project Convention Université de Neuchâtel/Office fédéral de la s...