Identifying the Real Income Disparity in Prefecture-Level Cities in China: Measurement of Subnational Purchasing Power Parity Based on the Stochastic Approach

Common prosperity has become the consensus of the times on development. This study aims to establish a generalized framework of the multilateral index number system under the stochastic approach and further derive the Geary–Khamis (GK) system and the Rao system under the stochastic approach to measure subnational Purchasing Power Parities (PPPs) for quantifying the real income disparity, excluding the effect of prices in prefecture-level cities in China, accurately. The results reveal that: (1) The GK system and the Rao system under the stochastic approach have advantages in addressing information loss and reliability measures, and further improve the spatial price index theory; (2) The distribution of price levels in China is in line with the trend of decreasing economic levels from east to west, which may be related to the Penn effect; (3) Compared with nominal income, real income increased significantly, and the ratio of the highest to the lowest real income in China decreased from 2.62 to 2.02. Real income, excluding the effect of prices, shows a new characteristic of moving toward the north for the high-income agglomeration areas and toward the southwest for the low-income agglomeration areas. These findings are conducive to the adoption of regionally differentiated measures to promote the realization of common prosperity, which has significant practical relevance.