Multidimensional Economic Dispersion Index and Application
提出一个基于洛伦兹超曲面的多维经济分散指数（MEDI），作为基尼系数的自然扩展，用于评估多个社会资源的不平等水平，并在中国省会城市数据中展示了其比经典基尼系数捕捉更多信息的能力。
The Gini index is widely used in economics as a measure of inequality with respect to income or wealth. However, it is not applicable when we consider evaluating the inequality level using more than one social resources. To comprehensively evaluate the social inequality level, we propose a multidimensional economic dispersion index (MEDI) based on the Lorenz hyper-surface determined by the distributions of multiple social resources. The MEDI is a natural extension of the Gini index and is equivalent to the Gini index in the presence of only one resource. We propose an estimator for the MEDI with good statistical properties and develop an algorithm to calculate the estimate. We further apply the MEDI for an empirical analysis to evaluate the social inequality level of Chinese provincial capitals. The results reveal some interesting phenomena of Chinese social inequalities and also demonstrate how the MEDI captures more information in complex economic situations than the classical Gini index.