-glcurve-: a program for generalised Lorenz curves and related structures

The well-known Lorenz curve for a variable y plots L(p(y)) against p(y) where p(y) is the cumulative distribution function of y and L(p(y)) is the cumulative share of y up to p(y) (i.e. it is a plot of cumulative income shares against cumulative population share). The generalised Lorenz curve, is the Lorenz curve with y-ordinates multiplied by the mean of y. This tool is frequently used by economists to present and compare income distributions because of the relation existing between GL dominance and traditional second-order stochastic dominance and the close link between these concepts and social welfare comparisons.

This talk introduces glcurve, a program basically designed to draw generalised Lorenz curves for a given continuous variable. glcurve has two attractive features: on the one hand it is flexible in the sense that it can be used to draw related graphs such as Lorenz curves, concentration curves or “TIP” curves and, on the other hand, permits easy visual dominance checks by population subgroups. The interest of generalised Lorenz curves comparisons will be emphasised and the simple data transformations needed to obtain related structures will also be illustrated.

Reference:

Jenkins S.P. and P. Van Kerm. 1999.

sg107: Generalized Lorenz Curves and Related Graphs. Stata Technical Bulletin 48: 25—29.