Income Inequality IV

William Easterly presents maps of the world, the United States, and the vicinity of New York University to illustrate that “income inequality behaves like a fractal”. There’s a reason for the infinite symmetry that he points out: it’s an artifact. Although he claims that a

tastefully chosen color scheme that is consistent across all maps (rich is red or brown-red, poor is pale yellow, in between is orange)

since there’s no consistency in the colors between maps there’s enormously less to this than meets the eye. In the map of the world the United States (rich) is colored in a deep reddish brown; Burundi (poor) on the other hand is drawn in a pale yellowish tan. In the map of the vicinity of NYU the West Village (rich) is colored the deep reddish brown; the Lower East Side pale yellowish tan.

The per capita GDP (the figure being used to decide on the colors) in the United States is about $46,000. The per capita GDP in Burundi is $300, a 15,000-fold diffence.

However, the per capita GDP of the West Village is $101, 346 while the per capita GDP in Lowest East Side is $14,916, a less than eight-fold difference. If the same color scheme had been used in both maps the entirety of the NYU map would have been deep reddish brown. The color scheme decision is apparently arbitrary. It proves very little more than that it is possible to color a map with different colors to suit yourself. If it demonstrates anything about income inequality it is to refute the idea that there’s a great deal of income inequality within the United States rather than to support it.

Felix Salmon adds:

The trend, then, I think, is for inequality to increasingly ignore national borders. You can get rich clusters across borders, as in say the area between Porto Alegre, Montevideo, and Buenos Aires, or any number of megaregions in Europe. At the same time, the gaps between the richest and the poorest areas of most countries are only growing larger.

Easterly’s map of the world, where every country is a uniform color, conceals more than it reveals. Once upon a time, national borders were useful boundaries to use when measuring per-capita income across the planet. And given that statistical agencies are still national, that’s not going to change any time soon. But those numbers are going to be less and less informative as pockets of wealth spring up in poor countries, and pockets of poverty persist in middle-income nations.

2 comments… add one
  • A fractal implies deterministic non-linear system of equations that look stochastic. Most searches for “chaos” in economic data have been less than fruitful and if you think you can break new ground in this area…good luck. You can see that Easterly is out of his depth with the cotton price comment. When I worked at the BLS the research division I was in had several people who worked on this kind of thing and had access to unbelievably large and detailed data sets on prices and the conclusion was: nice theory, but really no substance here.

    Maybe we’ll find it in income inequality, but here is something else to consider…notice that he mostly lighter colored portions of the map are also areas that have lower population densities. So would we see the same level of detail if we picked Montana and started zooming in? I doubt it. I bet if we picked Montana then started zooming in on various regions we find quite a few that simply went to zero–i.e. the level of jaggedness would disappear to a nice smooth uniform color.

    So…nice theory, but not much substance here.

  • steve Link

    Agreed. Not sure what he was trying to prove. Hard enough to study inequality within a nation.

    Interesting Vienneau has an interesting bit on inequality and its effects on recessions. Very mathematical.

    http://robertvienneau.blogspot.com/2010/08/why-income-equality-leads-to.html

    Steve

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