Un índice discreto sensible a la desigualdad

Abstract: 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.