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

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.