A simple method for measuring inequality

The Gini index, while widely used to measure socioeconomic inequality, particularly in income distribution, has limitations. It is less sensitive to changes at the extremes of the income distribution, and its use can lead to ambiguous rankings when Lorenz curves intersect. Other indices, like the Atkinson index, address these issues by incorporating social welfare functions but introduce subjectivity through the choice of inequality aversion parameters. Generalized entropy indices provide an alternative but still don't fully capture the nuances of income inequality. The paper aims to present a novel approach that overcomes these limitations by combining the strengths of the Gini index with a focus on the income shares of the top and bottom 10% of the population, offering a more comprehensive measure of income inequality. The Gini index, calculated from the Lorenz curve, summarizes inequality in a single, easily interpretable statistic (0-1), making cross-country comparisons feasible. However, its reliance on a single metric overlooks crucial information about disparities at the distribution's extremes. The Atkinson index, while offering a complete ranking of income distributions by integrating a social welfare function, suffers from the dependence of rankings on the subjective selection of social welfare functions. This leads to varying conclusions depending on the specific function and parameter choices. To avoid welfare-based judgments, the generalized entropy indices serve as a viable alternative; however, even these indices have not fully overcome the limitations of the Gini coefficient. This paper suggests a composite index to better address the shortcomings of existing measures.

The paper reviews existing measures of income inequality, starting with the Gini index and its widespread use across various scientific disciplines. It highlights the limitations of the Gini index, particularly its insensitivity to inequality at the tails of the distribution. The Atkinson index and Generalized Entropy indices are discussed as alternatives which attempt to provide a complete ranking and avoid reliance on social welfare judgments. However, the authors highlight the challenges associated with choosing the appropriate inequality aversion parameter for the Atkinson index and the limitations of using GE indices when Lorenz curves intersect. The lack of a universally accepted measure of inequality that comprehensively captures the various aspects of inequality, particularly those at both ends of the distribution, is presented as the motivation for this study.

The proposed inequality index combines three indicators: the Gini index, the income share of the top 10% (T₁₀), and the income share of the bottom 10% (B₁₀). The authors introduce a ratio (T₁₀/B₁₀) to capture the income gap between the wealthiest and poorest segments of the population. An intermediate variable, Hᵢ, is calculated using the formula: Hᵢ = 1 - (T₁₀/B₁₀)^(1/4). This introduces a weighting parameter (α) to balance the weight of the Hᵢ with that of the Gini index. Initially, the authors estimate this parameter empirically, but then propose using α = 0.25 (¼) for simplicity and ease of calculation. Using this, the inequality index (Iᵢ) for any given country is calculated as: Iᵢ = (Giniᵢ + Hᵢ²) / √2. The values of Iᵢ range from 0 to 1, facilitating straightforward interpretation and cross-country comparison. The authors use annual data from 2005 to 2015 from the World Bank and OECD databases to demonstrate their method. Data for 2015 is primarily used due to its greater coverage of countries. Descriptive statistics of the ratio, Gini index, and Hᵢ, alongside correlation coefficients, are calculated and reported. The authors verify the index's functionality using countries with identical Gini indices but different T₁₀/B₁₀ ratios and vice versa. The paper further tests its ability to capture situations where the Gini index is stable while the T₁₀/B₁₀ ratio shows an increase, thus indicating increasing income inequality despite a static Gini index. Finally, the authors propose an extension to incorporate more inter-percentile ratios (e.g., P80/P20, P70/P30) to create an even more comprehensive inequality index, adapting the formula for multiple H terms.

The study's key findings demonstrate the effectiveness of the proposed inequality index. The index successfully distinguishes income inequality between countries sharing the same Gini index but differing in their T₁₀/B₁₀ ratios. Table 1, using 2015 World Bank data for 75 countries, illustrates this by comparing Greece and Thailand, which have the same Gini index (0.360) but different T₁₀/B₁₀ ratios (13.8 and 8.9 respectively). The index assigns higher inequality to Greece (Iᵢ = 0.425) than to Thailand (Iᵢ = 0.391). Similarly, the index differentiates countries with the same T₁₀/B₁₀ ratios but varying Gini indices. Malta and the Slovak Republic, both exhibiting a T₁₀/B₁₀ ratio of 6.74 in 2015 (Table 1), are shown to differ in their income inequality based on the Gini index (0.294 and 0.265) and, consequently, the new index (0.339 and 0.327). Importantly, the index captures the dynamic where the Gini index remains stable but the T₁₀/B₁₀ ratio increases, signaling rising inequality despite the seemingly stable Gini index (Mexico's case in the paper). Table 1 provides the ranking based on the Gini index and the newly proposed index. The changes in rankings when comparing the two indexes demonstrates the ability to capture income inequality that was not obvious with the Gini index alone. There are 62 out of 75 countries in 2015 where the ranking changes, while 13 countries remain in the same ranking when compared against the ranking using the Gini Index. Table 2 presents similar findings using the OECD IDD for 35 countries, providing additional validation of the index's performance. Similar findings were shown for countries using data from OECD IDD in 2015. The paper shows examples of United Kingdom and Israel with the same Gini coefficient but differ in the T10/B10 ratio, and Ireland and Switzerland showing similar T10/B10 ratio but have different Gini coefficient. The figures also shows the evolution of Gini coefficient, T10/B10 ratio, and inequality index across time for several countries.

The proposed inequality index addresses the limitations of the Gini index and inter-decile ratios by providing a more comprehensive measure of income inequality. By incorporating both the overall inequality (Gini index) and the income gap between the top and bottom 10%, the index captures aspects of inequality that are overlooked by individual measures. The results demonstrate that the index can differentiate income inequality in cases where the Gini index alone is insufficient. The inclusion of the T₁₀/B₁₀ ratio provides additional information about inequality at the tails of the distribution, particularly regarding the gap between the richest and poorest. The simplicity of the calculation and readily available data make it practical for wide use. This index improves upon existing methods by offering a simple yet robust composite index for income inequality without the need for microdata. The robustness is indicated by the various examples given in the paper which demonstrates the effectiveness of the index in distinguishing inequality in situations where traditional indexes are insufficient. This has implications for policy-making, as it enables a more nuanced understanding of income distribution for more informed decision-making.

The study successfully presents a simple yet effective inequality index combining the Gini index with the ratio of income shares between the top and bottom 10%. The index overcomes limitations of previous approaches by offering a more comprehensive measure sensitive to inequality at both ends of the income distribution. This index is simple to calculate, uses easily accessible data, and provides valuable insights into income inequality. Future research could explore the incorporation of additional inter-percentile ratios to further enhance the index's sensitivity and accuracy, thus obtaining more comprehensive measure of inequality that takes into consideration the overall income distribution. This could lead to more informed policy interventions focused on reducing income inequality.

While the proposed index offers several advantages, it's important to note that two countries could potentially share the same index value but exhibit different Lorenz curves. This highlights that the index might not fully capture all aspects of inequality and therefore may not always provide a complete picture of income distribution. The choice of using only the top and bottom 10% might overlook important variations within other segments of the population. The study's reliance on readily available aggregated data might miss finer details that could be revealed by using microdata. However, the authors acknowledge this limitation and propose incorporating more inter-percentile ratios to create an even more robust index to overcome this limitation. Further research may be needed to investigate how these additional ratios would be incorporated.