Stata codes for Gini and Theil decomposition

ineqdeco does a good job in the decomposition of Theil index, which corresponds to "GE(1)" in ineqdeco's parlance. The by() option defines the subgroups for analysis.

descogini decomposes the Gini coefficient by income source and allows the calculation of the impact that a marginal change in a particular income source will have on inequality. descogini can be used with bootstrap to obtain standard errors and confidence intervals.

Lerman and Yitzhaki (1985) show that the Gini coefficient for total income inequality, G, can be represented as G = sigma(Sk*Gk*Rk), where Sk represents the share of source k in total income, Gk is the source Gini corresponding to the distribution of income from source k, and Rk is the Gini correlation of income from source k with the distribution of total income. The influence of any income component upon total income inequality depends on:

• how important the income source is with respect to total income (Sk);
• how equally or unequally distributed the income source is (Gk); and
• how the income source and the distribution of total income are correlated (Rk).

The product of Gk and Rk is the pseudo Gini for each income source.