6.2.2. The Gini Coefficient in the Case of the Pareto Distribution

The corresponding Gini coefficient, labeled G, is the concentration ratio applied to income distribution and is defined as:

(6.3)

Re-arranging and simplifying the terms yields a coefficient depending only on the parameter δ:

(6.4)

Clearly, the α coefficients will be used again to compute the Gini coefficients as δ = 1 – 1/α. As there are as many α coefficients as income brackets, we are able to average a value of α for each state in each year.

We now turn to the application to the United States from 1965 to 2003.