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Debunking the So-called Human Development Index of U.S. States

Alex Hoffman pointed me to this widely-circulated map comparing the fifty states in something called the Human Development Index:

As Alex points out, the coding of the map is kind of goofy: the states with the three lowest values are Louisiana at .801, West Virginia at .800, and Mississippi at .799, but their color scheme makes Mississippi stand out as the only yellow state in a sea of green.

But I’m concerned about more than that. Is Alaska really so developed as all that? And whassup with D.C., which, according to the table, is #4, behind only Connecticut, Massachusetts, and New Jersey? I know about gentrification and all that, but can D.C. really be #4 on any Human Development Index worth its name?

Time to look behind the numbers.

The report gives the following information:

The HDI combines three basic dimensions:

* Life expectancy at birth, as an index of population health and longevity

* Knowledge and education, as measured by the adult literacy rate (with two-thirds weighting) and the combined primary, secondary, and tertiary gross enrollment ratio (with one-third weighting).

* Standard of living, as measured by the natural logarithm of gross domestic product (GDP) per capita at purchasing power parity (PPP) in United States dollars.

OK, I think I see what’s going on. The 50 states don’t vary much by life expectancy, literacy, and school enrollment. Sure, Hawaiians live a few years longer than Mississippians, and there are some differences in who stays in school, but by far the biggest differences between states, from these measures, are in GDP. The average income in Connecticut is twice that of Mississippi.

To check out the relation between HDI and income, I loaded in the tabulated HDI numbers and plotted them vs. some state income numbers (excluding D.C., unfortunately) that I happened to already have on my computer:

Interesting. The pattern in strong but nonlinear. Let’s try plotting the ranks:

The pattern seems pretty clear, with most of the states falling right on the 45-degree line. The correlation between the two rankings is 86%. I’m actually surprised the correlation isn’t higher–and I’m surprised the first scatterplot above is so nonlinear–but, then again, I’m using state income rather than GDP, so maybe there’s something going on there.

(In response to some mathematically-inclined readers: No, the log transformation is not what’s doing this, at least not if you’re logging income as is stated in the report. Logging stretches out the lower end of the scale a bit but does not change the overall pattern of the plot. The income values don’t have enough dynamic range for the log transformation to have much effect.)

Or maybe more is going on with those other components than I realize. If anyone’s interested in following up on this, I suggest looking into South Carolina and Kentucky, which are so close in average income and so far apart on the HDI (see the top scatterplot above).

Searching around, I found the aforementioned numbers that range from 0.799 to 0.962, and another set that range from 3.58 to 6.37. The rankings of these two sets are identical; unfortunately I couldn’t find the exact formula for either of these. But I did find this report which gives some formulas and also, in its Appendix B, the actual numbers used for the 50 states in preliminary calculations. These rankings do not exactly agree with the ones shown in the map–in the preliminary data, Massachusetts, not Connecticut, is #1, D.C. is in the lower half, and Alaska is second-to-last.

So I’m not completely sure what’s happening here. But if you go by the maps that everybody’s linking to (having appeared in Catherine Rampell’s New York Times blog), you’re pretty much just mapping state income and giving it a fancy transformation and a fancy new name.

P.S. To clarify a point made by several people in the discussion: I’m not commenting one way or another on the Human Development Index as used for international comparisons. What I’m criticizing is the application to the U.S. and the implication that the widely-distributed map is doing much more than ranking state incomes with a wacky color scheme.

P.P.S. More here, here, here, and here. (That last link explains, among other things, that “percent” means “divided by 100.”)

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