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CHAPTER 7Measuring Income Inequality with the Gini, Palm, and Atkinson Indices

Increased income inequality is known to be correlated with increased crime (see siteresources.worldbank.org/DEC/Resources/Crime%26Inequality.pdf) and increased poverty (see www.odi.org/sites/odi.org.uk/files/odi-assets/publications-opinion-files/3876.pdf). Part of human nature is the desire to boil down a complex concept like inequality to a single number. In this chapter, we will discuss three widely measures of income inequality—the Gini index, the Palm index, and the Atkinson index—that facilitate easy comparison between the degree of inequality between countries.

The Gini Index

In 1912, Italian statistician Corrado Gini developed the Gini index for use in measuring the degree of inequality in a country's income distribution. To explain the calculation of the Gini index, we will assume all countries consist of 20 people. As a benchmark, we consider a country (named Equal) with complete income equality in which each resident has an annual income of 5 units. As shown in the worksheet named Typical in the workbook GiniTheory.xlsx (see Figure 7.1), consider another country (named Unequal) in which the income of individual n is proportional to n and we normalize the incomes to add up to 100. For example, Individual 1 has an income of .48, Individual 2 an income of .95, … Individual 20 has an income of 9.52. As shown in our example, computation of the Gini index requires the individual incomes to ...