统计与信息论坛

使用上市公司高管薪酬数据和胡润富豪榜数据估计住户调查数据中收入信息覆盖不足的区间，将传统收入数据的合并拓展至多源收入数据的内生序贯合并。为评估合并效果，运用EM算法估计其有限元混合分布，并利用拟合面积误差比率分别对基于内生合并点与外生合并点生成的多源收入数据进行评估。此外，使用合并后的数据集测度不平等指标，以提高对高收入群体的统计调查进度和广度。研究结果显示，基于内生合并点将高收入和过高收入群体的数据信息补充到住户调查数据中，修正了影响住户调查数据准确描述收入分配尾部的小样本问题，使用基于内生合并点将住户调查数据与高收入数据进行序贯合并后的数据集误差比率的值，相对低于基于外生合并点将住户调查数据与胡润富豪榜收入数据进行合并，能够降低对收入差距的低估，更准确地反映居民收入分配状况，为共同富裕进程中规范收入分配秩序提供数据支撑。

This paper proposes a novel approach to measuring income inequality in China by constructing a multi-source income dataset that more effectively captures the full spectrum of income distribution, particularly the upper tail.A key methodological innovation lies in the sequential merging of contemporaneous income data from three distinct data sources—household surveys, executive compensation records, and billionaire wealth rankings—enabling the endogenous identification of merging thresholds between these data sources.This strategy addresses the long-standing underrepresentation of high-income individuals in household survey data and enhances the accuracy and comprehensiveness of income inequality measurement.The merging procedure identifies two internal thresholds using representative ratios and their cumulative counterparts.These thresholds determine the income levels at which the original household data are systematically reweighted to account for high-income individuals.Specifically, household income data are drawn from two major nationally representative surveys: the China Family Panel Studies(CFPS 2016—2020) and the Chinese General Social Survey(CGSS 2015—2021),which reliably capture income patterns of low-and middle-income groups.For the high-income group, income data of listed company executives is used.For the ultra-high-income group, income data from the Hurun Rich List is adopted.Empirical results show that in 2015,the first merging point—between survey data and executive compensation data—corresponded to the 81st income percentile(RMB 62 500),rising to RMB 111 200 in 2021.The second merging point—between executive compensation and billionaire income—corresponded to the 91st percentile(RMB 1.21 million) in 2015 and RMB 1.41 million in 2021.Lorenz curves are employed to visualize income distribution before and after data integration.After correction, the upper tail of the distribution shows a noticeable “bulge”,suggesting a higher and more accurate income concentration among top earners.This pattern holds across years, underscoring the systematic underestimation of inequality in raw household survey data.These indicate that high-income undercoverage in surveys persists and intensifies over time.To evaluate the effect of the merging procedure, the paper adopts an Expectation-Maximization(EM) algorithm to estimate a flexible mixture distribution that combines three components: normal—normal—Pareto.Among several candidate models, this combination yields the best fit, as it minimizes the distribution error ratio—a metric used to evaluate the goodness-of-fit between empirical and estimated income distributions.The endogenous merging approach outperforms the exogenous one in capturing the multi-source data's distributional properties, offering a stronger empirical foundation for future studies.Further, the merged dataset not only recovers a more realistic income distribution but also supports more accurate estimation of inequality metrics such as the K coefficient and top income shares.In summary, this paper offers a data-enhanced and methodologically rigorous approach to better understanding income inequality in China.By sequential merging diverse income data sources through a theoretically grounded and statistically validated process, the study provides a valuable tool for policymakers seeking to monitor and adjust excessively high incomes in pursuit of common prosperity.