Computing the Gini coefficient using Lorenz curve definition

[Andrea Ciaccio]

Hi everyone,
I am using Time Use data from ISTAT (data are not longitudinal). Since I would like to carry out both a within and between group inequality analysis, I would like to know if there is any command computing the Gini Index as described here: "The Gini coefficient is the ratio of the area between the line of perfect equality and the Lorenz curve, over the area of the triangle below the line of perfect equality" (Altintas, Casarico and Sommacal- working paper). Furthermore, is there a way to test differences in Gini Coefficient between groups (e.g. testing if the gini Coefficient of higher educated mother is equal to that one of lower educated ones)?
Thank you in advance

[FernandoRios]

Just type "help gini" and it will provide you with a large set of commands that have been built to calculate the Gini coefficient. While not all of them estimate the Gini based on the "area definition" of the lorenz curve, they are equivalent.
For tests across ginis, (ratios or diferences), i think a solution would be to use bootstrap to obtain the empirical distribution of such difference.
HTH
Fernando

[Andrea Ciaccio]

Thank you a lot for your answer.
Do you know if it is possible to save the Gini coefficient and then use it in a Loess regression (Altintas, Casarico and Sommacal in their working paper do this way)?
Thank you again
Andrea

[Stephen Jenkins]

In addition to Fernando Rios's wise remarks, observe that svylorenz on SSC (search svylorenz) will provide you estimates ot the Gini coefficient and its SE (derived using linearization methods rather than bootstrap). Note also its subpop() option which may help with the subgroup comparisons. ineqdeco and ineqdec0, both on SSC, provide inequality estimates with decompositions by population subgroup (e.g individuals classified by mother's education status). For SE estimates using these programs, you would need to bootstrap.

[Andrea Ciaccio]

Thank you a lot for your answer Prof. Jenkins