Income distribution is often presented in "Lorenz curves". The following is an attempt to defy conventional wisdom:

This chart fails my self-sufficiency test...

A few elements of this graph are confusing. The same set of shading is used to classify two different variables. The annotation of "Top" and "Bottom" appears arbitrary. The rightmost column, representing top 0.1% of taxpayers, has the same width as the leftmost column, representing the bottom 20%.

Why not stick with a *Lorenz curve*? This presentation is versatile. The diagonal is a line of "equality": for example, the (20%,20%) point on this line indicates that the top 20% of the population (ranked by decreasing income) took exactly 20% of the income growth in 2003.

A lot of information can be read off this chart: the top 0.1% earners took about 25% of all income increase; the top 1% took 40%; the top 20% took almost 80%. In general, a curve that bends away from the diagonal (like this one) depicts severe inequality.

However, in many practical situations as is here, comparison with the diagonal is meaningless. The "ideal" society would probably not be one in which annual income growth is equally distributed among all taxpayers. (I'll leave the rationalization to economists and sociologists.)

More helpful is a graph that shows relative changes in inequality. If I add a second curve (orange) showing the distribution of income (as opposed to income *growth*), then we see a trend of increasing inequality! The large bend from the diagonal indicates that income distribution is far from "equal"; what's more, the distribution of incremental income is even more skewed.

*For more analysis*: The Richest 0.1% II

Reference: "At the Very Top, a Surge in Income in '03", New York Times, Oct 5 2005.

I've long wondered why government agencies--like the military--who profess concern for their junior members, always give raises based on a percentage of income. It would seem that an occasional "flat raise"--$50/month for everyone--would bring the two curves back in synch. Hmm, sounds like a good homework problem for my students...

Posted by: Mike Anderson | Oct 07, 2005 at 07:37 AM