Methods to Calculate the Upper Bound of Gini Coefficient Based on Grouped Data and the Result for China

TL;DR

This paper presents an efficient algorithm to accurately determine the maximum possible Gini coefficient from grouped data without income brackets, with applications to China's urban and rural income inequality from 2003 to 2008.

Contribution

It introduces a novel algorithm with provable guarantees for calculating the exact upper bound of the Gini coefficient from grouped data.

Findings

Computed upper bounds for China's urban and rural Gini coefficients (2003-2008)

Algorithm guarantees exactness and efficiency in upper bound calculations

Provides insights into income inequality measurement limitations

Abstract

Determining an upper bound, particularly the optimal upper bound of the Gini coefficient when dealing with grouped data without specified income brackets, remains an important and open question. In this paper, we introduce an efficient algorithm to calculate the exact optimal upper bound of the Gini coefficient with provable guarantees. To exemplify these methods, we also offer computed results for the Gini coefficients of urban and rural China spanning the years 2003 to 2008.