A new index to measure the income inequality for the poor and the rich with application

Posted: 6 Nov 2018

See all articles by Raymond Honfu Chan

Raymond Honfu Chan

City University of Hong Kong

Teng Chen

State University of New York (SUNY) - Department of Applied Mathematics and Statistics

Pui-lam Leung

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Wing-Keung Wong

Asia University, Department of Finance

Date Written: October 15, 2018

Abstract

Studying the characteristics of different income distributions, and compare the differences among different income distributions with respect to geographic regions, and changes over time periods is a very important area in economics. In order to compare the differences among different income distributions, different measures, including the Gini and Zenga indices have been developed. However, one of the limitations of the existing indices is that they only provide an overall measurement for the distribution, cannot provide the measure for any part of the distribution. However, comparing any different parts of the distribution or different distributions is very important. For example, we can compare the rich and the poor. Another limitation some existing measures including the Gini and Zenga indices is that they provide the same value for different distributions.

To circumvent the above limitations, this paper proposes a new index which can make comparison between any groups with different income level, for example, the richest group and the poorest group. The new index provides different values for different distributions and different parts of any distributions. The new index satisfies the axioms of inequality measures. The statistical inferential results of the new index are derived and their performance is tested by a simulation study. We illustrate the applicability of our proposed index to analyze the income data of Hong Kong and compare different groups in the distribution.

Keywords: Income distributions, Gini index, Zenga index, Poor-Rich Difference Index

Suggested Citation

Chan, Raymond Honfu and Chen, Teng and Leung, Pui-lam and Wong, Wing-Keung, A new index to measure the income inequality for the poor and the rich with application (October 15, 2018). Available at SSRN: https://ssrn.com/abstract=3266360

Raymond Honfu Chan

City University of Hong Kong ( email )

Tat Chee Avenue
Hong Kong
Hong Kong

Teng Chen

State University of New York (SUNY) - Department of Applied Mathematics and Statistics

Stony Brook, NY 11794
United States

Pui-lam Leung

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

Wing-Keung Wong (Contact Author)

Asia University, Department of Finance ( email )

Taiwan
Taiwan

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