一种对不平等敏感的离散指数
Un índice discreto sensible a la desigualdad
AI总结：
本研究提出新型不平等测算指标IDRM，该指标满足多项理论性质，在跨国及墨西哥微观数据验证中，相比传统指数展现出更优的一致性、敏感性与精度，能更好反映收入分布差异。
摘要：
本文提出了最大值处相对不平等指数（IDRM），这是一种新颖且直观的测算指标，旨在捕捉群体内部的不平等现象，例如收入不平等。该指数基于这样的理念：个体因自身在分布中的位置不同，会感受到不同程度的不平等，尤其是相较于顶层群体的不平等。其核心假设是，对于处于较低位置的个体而言，以顶层位置为参照的不平等对其福祉的影响更大，且相对于最大值的不平等是最为关键的。\nIDRM满足多项理想的理论性质，研究人员借助这些性质对其进行评估，并将其与不平等研究领域广泛认可的测算指标进行对比。从这一角度来看，IDRM被证明与传统测算指标一样稳健，且表现优于基尼（Gini）指数和道尔顿（Dalton）指数——它满足九项关键性质中的八项，包括可按群体子群进行分解的性质。\n在一项使用58个国家的收入数据以及墨西哥微观数据的对比分析中，研究以基尼指数、泰尔（Theil）指数和阿特金森（Atkinson）指数为基准，结果显示IDRM具备更优的一致性、对不平等的敏感性，在分组数据中的偏差更小，精度也更高。该指数能够反映收入分布的不同形态，对不平等的程度表现出更高的敏感度。
英文摘要：
This paper introduces the Relative Inequality Index at the Maximum (IDRM), a novel and intuitive measure designed to capture inequality within a population, such as income inequality. The index is based on the idea that individuals experience varying levels of inequality depending on their position within the distribution, particularly with respect to those at the top. The key assumption is that for individuals in lower positions, inequalities referenced to the top positions have greater impact on their well-being and the inequality relative to maximum is the most critical. The IDRM fulfills desirable theoretical properties which were used for its evaluation and comparison against widely accepted measures in inequality literature. From this perspective, the IDRM is shown to be as robust as traditional measures and outperforms the Gini and Dalton indices by satisfying eight out of nine key properties, including decomposability across population subgroups. In a comparative analysis using income data from 58 countries and microdata from Mexico, with the Gini, Theil, and Atkinson indices as benchmarks, the IDRM demonstrates superior consistency, sensitivity to inequality, reduced bias in grouped data, and enhanced precision. This index reflects the varying forms of income distribution, showing heightened sensitivity to the magnitude of inequality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
