理解不等性测度的经典分解性：一种图形分析
Understanding Classical Decomposability of Inequality Measures: A Graphical Analysis
AI总结：
本文提出一个几何诊断框架，通过二维收入份额单纯形分析三人口收入分布，揭示分解性在不同测度中的表现，发现分解性并非二元属性，且组间残差是主要失败来源。
摘要：
本文提出一个几何诊断框架，通过二维收入份额单纯形分析三人口收入分布，揭示分解性在不同测度中的表现，发现分解性并非二元属性，且组间残差是主要失败来源。
英文摘要：
This paper develops a geometric diagnostic framework for classical inequality decomposability. Representing the simplest nontrivial setting of three-person income distributions as points on the two-dimensional income-share simplex, we translate population-share-weighted and income-share-weighted decomposability into concrete geometric restrictions on within- and between-group residuals, making it possible to localise and characterise violations across measures. Applied to the Mean Log Deviation, the Gini coefficient, the coefficient of variation, and the Theil index, the analysis shows that decomposability is not a binary property as measures fail in qualitatively distinct ways, and the between-group residual is consistently the primary locus of failure. Negative between-group residuals render the decomposition uninterpretable and arise for the coefficient of variation and the Theil index under population-share weighting, and for the Mean Log Deviation under income-share weighting. Stylised numerical examples quantify the resulting misinterpretation scenarios for applied researchers.
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