信息不完全下收入或财富基尼系数的估算

Estimation of the Gini Coefficient with Incomplete Income or Wealth Information

研究目标:在收入或财富信息不完全时对基尼系数进行估算,并对估算的误差进行分析。研究方法:在基尼系数子群分解的基础上,推导得到极高收入群体、极低收入群体以及两者同时信息不完全时收入基尼系数的三个估算公式。研究发现:当极高收入群体人口比重p_(H)极小,极低收入群体收入比重s_(L)极小时,推导得到的近似公式G非常接近真实的基尼系数,同时在理论上严格证明了误差ΔG的上界为s_(L)+p_(H),并得到真实基尼系数的估计区间为[G-(S_(L)+p_(H)),G]。研究创新:将基尼系数的这种近似估算,从极高收入群体信息不完全的情况,推广到极低收入群体信息不完全的情况,最后又推广到收入分布两端同时信息不完全这种更加一般化的情况,还对近似估算的误差进行了理论分析,并给出了相应的估计区间。研究价值:本文研究有助于正确解读不完全的收入或财富信息背后的实际含义,利用本文所提出的方法,基于相关的辅助信息,可以对基尼系数进行合理修正,从而得到更接近真实基尼系数的估算结果。

Research Objectives:This paper is to estimate the Gini coefficient when income or wealth information is incomplete,and to analyze the estimation error.Research Methods:Based on the subgroup decomposition of Gini coefficient,three estimation formulas of income Gini coefficient are derived with incomplete information for extremely high-income group,extremely low-income group and both groups above.Research Findings:The approximate formula(G)is very close to the real Gini coefficient when the population proportion of extremely high-income group(p_(H))is very small and the income share of extremely low-income group(s_(L))is very small.It is strictly proved that the upper bound of the error(ΔG)is s_(L)+p_(H).So the estimation interval of real Gini coefficient is[G-(s_(L)+p_(H)),G].Research Innovations:This approximate estimation of Gini coefficient is extended from incomplete information for extremely high-income group to incomplete information for extremely low-income group,and finally to incomplete information for both groups above.The error of approximate estimation is also analyzed theoretically,and the corresponding estimation interval is given.Research Value:The research in this paper is helpful for us to understand the actual meaning behind the incomplete income or wealth information.Based on the method proposed in this paper and the relevant auxiliary information,we can get the estimation results closer to the real Gini coefficient.