Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index
Résumé |
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. |
Mots-clés |
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 | Article de périodique (Anglais) |
Date de publication | 17-9-2012 |
Nom du périodique | Metrika |
Volume | 75 |
Numéro | 8 |
Pages | 1093-1110 |
URL | http://link.springer.com/article/10.1007%2Fs00184-011-0369-1 |
Liée au projet | Convention Université de Neuchâtel/Office fédéral de la s... |