Measuring Income Inequality: Gini, Theil, Hoover & Atkinson Indices

In modern society, discussions of fairness and unfairness arise frequently in education, income, and resource allocation, prompting the need for quantitative measures. This article examines four widely used inequality measurement indices.

Gini Index

The Gini Index measures income or wealth inequality using the Lorenz curve. Its value ranges from 0 (perfect equality) to 1 (perfect inequality). If everyone earns the same amount, the index is 0; if one person holds all income, the index is 1.

Theil Index

The Theil Index is an entropy‑based measure of distribution inequality. It captures both the magnitude of income gaps and the entropy of the income distribution.

Hoover Index

The Hoover (Robin Hood) Index quantifies the proportion of total income that would need to be redistributed to achieve perfect equality. Its value also lies between 0 and 1.

Atkinson Index

The Atkinson Index measures the welfare loss caused by inequality, using a sensitivity parameter that reflects how much weight is given to low‑income individuals; larger values indicate higher sensitivity to low incomes.

Using a hypothetical village with four households earning 5,000, 10,000, 20,000, and 100,000 yuan, the calculated indices are:

Gini Index: 0.1371

Theil Index: 0.0320

Hoover Index: 0.1129

Atkinson Index: 0.0164

These values indicate a modest level of income inequality. A comparative table of G20 countries shows how these indices vary across nations.

Overall, the four indices provide a comprehensive toolkit for evaluating income distribution and its impact on social welfare.