Inequality: a question of measurement?

Elon Musk, the boss of Tesla and SpaceX, earns 500 dollars per second, which is what half the world earns in a month. Since the 1980s, economists have been paying close attention to the sharp rise in global inequality. How can it be measured? Should we take into consider income, assets, the average, the median, or the inter-decile range? A. Atkinson and T. Piketty have looked at the highest incomes, S. Jenkins at the dynamics of household incomes in the UK, and A. Krueger on the rise of inequality in the United States.

However, there is one measure of inequality that has been the object of consensus for many years: the Gini index. Developed by the Italian statistician Corrado Gini in the early 20^th century, this index takes the form of a value between 0 and 1, with zero representing perfect equality and 1 the greatest inequality. This measure is now widely used around the world to analyse inequalities between countries, and over time. According to the World Bank, in 2021 Sweden has a coefficient of 0.298, France 0.315 and Brazil 0.529. In China, it rose from 0.437 in 2010 to 0.371 in 2020, signalling a decline in inequality.

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Economists Frank A. Cowell and Emmanuel Flachaire show that the Gini index can behave in unexpected ways. By increasing the income of a person who is wealthier than the average for the group studied, a measurement with the Gini index reduces inequality, rather than increasing it. The researchers investigate this anomaly and study the performance of other inequality measures in their article "Inequality Measurement and the Rich: Why Inequality Increased More Than We Thought", published in 2024 in the journal The Review of Income and Wealth.

Properties of the indices

Using an axiomatic approach, the authors study the properties of the index and those of two other measures: the Theil index and the mean logarithmic deviation (MLD), both developed by Henri Theil, a Dutch professor of econometrics in the 1960s. They range from 0, which represents perfect equality, to infinity, which represents the greatest inequality.

The Gini, Theil and MLD indices measure the distance between the observed distribution of incomes and a situation of perfect equality where all individuals receive the same income. The distance is defined differently depending on the measure used. The Gini index is based on absolute differences, while the Theil and MLD indices use logarithmic differences. Furthermore, the Theil index is more sensitive to variations between high incomes than the other two indices.

All three indices are unaffected by scale, meaning that if the income of each person is multiplied by two, as happens in the case of inflation, for example, inequality remains unchanged. This principle of invariance to scale stipulates that comparisons of inequality should not be affected by proportional changes in income or wealth. It is respected by dividing incomes by their mean, which allows inequality to be compared independently of the absolute scale of the data.