The Gini and Atkinson Indexes are both measures of inequality. The Gini measure however is a positive measure, whilst the Atkinson is a normative measure. A positive measure is purely statistical whereas a normative measure is “based on an explicit formulation of social welfare and the loss incurred from unequal distribution.”[1]
The Gini coefficient measures inequality using values of a frequency distribution. It is derived from the Lorenz curve framework. If the Lorenz curve is equal to zero, then it will be equal to the line of equality and everyone will have the same income. The more the curve deviates from the line of equality, the higher the inequality. Gini coefficients can be used to compare income distribution over time, making it possible to see how inequality changes over a period independent of absolute incomes.[2]
The main weakness of the index as a measure of income distribution is that it cannot differentiate between different kinds of inequalities. Theoretically, two Lorenz curves could intersect one another (showing different patterns of income inequality) but still result in a similar Gini coefficient. The Gini coefficient measures relative and not absolute wealth. Therefore, when a Gini coefficient of a developing country rises, this could be misleading. Changing income inequality by Gini coefficients may be down to things such as structural changes or immigration. A rising Gini coefficient suggests increasing inequality but it could be the case the number of people in the absolute poverty bracket actually decreases. Economies with similar incomes but different income distributions can actually have the same Gini index. For example, one economy has 50% of people with no income and the other 50% having equal income, giving a Gini index of 0.5. Another economy has 75% of the lowest income earning people with 25% of income while the other 25% of people have 75% of income which also gives a Gini index of 0.5. [3] Clearly the Gini coefficient will not always necessarily capture the whole picture about inequality within an economy.
Because of these limitations of the Gini coefficient, other methods can be used in combination or separately. For example, entropy measures such as the Atkinson index can be utilised.
The Atkinson measure allows for different parts of the income distribution to have certain levels of sensitivity to inequality. It incorporates a sensitivity parameter which allows the researcher to attach a weight to inequality at different points. Atkinson when creating the model was especially concerned with how the Gini measure could not place different weights on certain income brackets.[4]
In his paper ‘On the Measurement of Inequality’ Anthony B. Atkinson compared inequality in seven advanced and five developing countries. He compared three conventional measures (one of which was the Gini coefficient) against three differently weighted Atkinson indexes; the weight was increasing on poorer end of the scale. This data only highlighted the differences in the measures. With a weight of ε = 2 attached to the lower income scale, the Atkinson measure disagreed with the Gini coefficient in 17 cases. With ε = 1, a smaller inequality aversion, the Atkinson measure still disagreed in 5 cases. The results show that conclusions reached about income inequality is dependent on the level of inequality aversion. The reason for this is to do with the distribution of income. In developing countries, incomes are more equal at the lower end of the scale and less equal at the top than in developing countries. As we increase inequality aversion, more weight is placed upon the lower end of the scale causing distortions.[5]
The main difference between the two measures is therefore this sensitivity parameter. This parameter makes the Atkinson subjective whereas the Gini measure is objective.[6] While perhaps yielding a similar result when a low level of inequality aversion in the Atkinson measure is used, clearly by manipulating the Atkinson measure, results can differ greatly between the two. It is subjective because the user can choose what subgroups to weight more heavily than others. The Atkinson index is also subgroup consistent, this means if in a subgroup, inequality declines ceteris paribus, then overall inequality declines. It is also decomposable, which means the total inequality can be broken down to a weighted average of the inequality which exists within the subgroups. These two qualities are something which the Gini coefficient does not hold. The Gini coefficient gives an equal weight to the entire distribution but the Atkinson index gives more weight to the lower end of the distribution, this means it accounts more wholly for things such as income poverty and illiteracy.[7]
[5] A.B.Atkinson ‘On the Measurement of Inequality’, 1969, pg258-260
A World of Economics 