Inference for the Zenga Inequality Index

• Activity Number: 664
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Matti Langel*+ and Yves Tillé
• Companies: University of Neuchâtel and University of Neuchâtel
• Keywords: inequality ; sampling ; linearization ; variance estimation ; Gini index ; influence function

Abstract

The Zenga Index is a recent inequality measure associated with a new inequality curve, the Zenga curve. The Zenga curve $Z(\alpha)$ is 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 and robustness issues are briefly discussed.