Polly Toynbee recently wrote on the relationship between income inequality and the prevalence of obesity (more inequality leads to more obesity, she claims). Naturally this has provoked the usual ignorant rebuttals from various corners of the web. Matthew Turner lists a few of these and points out that, whatever the merits or otherwise of Toynbee's piece -- frankly I have better things to do than read it, or the rebuttals, in any detail -- if you plot the prevalence of obesity against the Gini coefficient of income inequality for a bunch of OECD countries, you do indeed get a (weak) positive correlation.
Now, there are two important things to say about this. One is that the various countries of the OECD have substantially different cultures, and this is the sort of thing which is likely to influence the prevalence of obesity. Another is that different countries have widely differing populations, wheras the only sensible causal argument that could be made here is that people who live in unequal societies are (for some reason) more likely to be obese than those who live in more equal ones. On that basis, we should be looking at the data weighted by the populations of the various countries; but if you do this the results are dominated by the appearance of the US (very unequal, very obese, and very populous) and Japan (not very unequal, not very obese, quite populous).
One way around this is to look at obesity within the United States instead. It's true that there is cultural variation within the United States, but presumably it's less important than among the OECD countries; and a wide distribution of populations between the different states (which are the unit over which population, obesity and income data are most conveniently available), but it's not so skewed as the distribution of population in the OECD. Anyway, we can get somewhere with this:
The best-fit line has a slope of 11.45±11.33 (that's a standard error, not a confidence interval). So this provides very weak evidence for positive correlation (that is, the result is compatible with the two variables being uncorrelated and their being weakly correlated, but not with their being negatively correlated or strongly positively correlated). Any relationship in these data is far-from-striking.
Can we conclude anything useful from this? Not a lot, frankly, beyond that you shouldn't assume that somebody else's statistics are right just because they disagree with Polly Toynbee. I'm suspicious of this sort of thing anyway, because there's no explanation of how income inequality is supposed to make people obese. Toynbee seems to think it's (roughly) something to do with self-esteem, but doesn't really offer any evidence for this. I doubt that anyone's likely to get to the bottom of this one just using summary statistics.
(As an aside, you might be wondering what the Gini coefficient is or why it's a useful measure of income inequality. Wikipedia will tell you that it's defined as the area between the Lorenz curve of a distribution and the Lorenz curve of a uniform distribution, which sounds easy to calculate but not obviously meaningful; and MathWorld will tell you that it's the normalised mean of the absolute difference between each pair of incomes in the distribution, which sounds much more sensible but a pain to compute. These two definitions appear to be completely different, but surprisingly enough they turn out to be the same. Isn't that nice?)
Comments
Posted by Phil Rodgers, Tuesday, 1 June 2004 17:34 (link):
Hooray, a graph! But having read some Tufte over the weekend I'm compelled to remark that the areas of your circles aren't proportional to the populations they represent.
Posted by Chris Lightfoot, Tuesday, 1 June 2004 17:54 (link):
Quite right, and now fixed! Oops.
Posted by The Shamrockshire Eagle, editor and sole proprietor of, Tuesday, 1 June 2004 17:46 (link):
> how income inequality is supposed to make people obese.
Well, if you presume that Dr. Atkins was correct, then there is a link between consumption of carbohydrates and obesity. And then there is a further link between poverty and carbohydrate consumption: the poorer people are (yes, I know you said "income inequality", but I'm going to presume that in countries with high income inequality, that equates to more poor people), the higher the percentage of carbohydrate in their food, simply because it's cheaper than protein; and therefore the higher the incidence of obesity. It's more complicated than that really, because according to Atkins & Co., the different morphological types tend to have different weight-gain patterns: Dr. Mackarness, who wrote a little book with the self-explanatory title Eat Fat and Grow Slim, talks about a "Mr. Constant Weight" thin type and a contrasting "Mr. Fatten Easily" fat type, for instance. As well as that, Orwell long ago pointed out the fatuity of advising the poor to "eat better", because a feast of tasty processed rubbish is one of the few pleasures afforded them by income and (perhaps more importantly) upbringing. Which in turns leads to thoughts about the "culture of eating": how in some advanced industrial societies, notably Britain and America, the masses in general have no idea of what constitutes good food, and so eat rubbish even though they can actually afford better.
I can't back any of that up with figures, mind, so I should probably have kept my mouth shut!
Posted by Chris Lightfoot, Tuesday, 1 June 2004 17:57 (link):
OK. I agree entirely with the thesis that it's worth looking for a correlation between poverty -- or, properly, inability to afford good food -- and obesity. And it's true that income inequality and the number of poverty in the tail of the distribution where they can't afford food are likely to be well correlated.
Posted by Backword Dave, Tuesday, 1 June 2004 22:21 (link):
Sort of an explanation in The Way We Eat Now:
This doesn't explain why there's a negative correlation between income and obesity, but it offers some ideas.Posted by Peter Clay, Wednesday, 2 June 2004 10:12 (link):
Two thoughts on this:
Why does Virginia have a much lower Gini coefficient? Does it have some magic fiscal policy for reducing income inequality, and could this be replicated painlessly?
Secondly, given the discussion in the comments and the other outliers (Mississippi fattest, Colorado thinnest), could we have a graph of education level versus obesity?
Posted by Chris Lightfoot, Wednesday, 2 June 2004 12:52 (link):
My guess is that it's a data error. The data come from Luxembourg income Study Working Paper No. 292; in wave III of the study, the Gini coefficient was quoted as 0.307, whereas in wave IV it was quoted as 0.239. Now, all the computed Gini coefficients in the study changed between the two `waves', but that for Virginia changed by much more: plot of LIS wave III/IV Gini coefficient changes.
Removing Virginia from the fitted line changes the gradient to 13.58±15.05. This doesn't substantially change the conclusion.
(By the way, my instant reaction was `poverty', followed by `is poverty a fiscal policy?'. This is not accurate: plot of Gini coefficient against median household income. I think this probably tells you something about my prejudices about rural life in the United States.)
See plot of levels of school and university education. (I'm now kicking myself for not allowing <img...> in comments... hmm.)
This is a bit more convincing, actually. The population-weighted best fit lines have gradients with standard errors of ±24% for the high-school education variable, and ±16% for the university education variable (both population-weighted).
(Education data from the National Center for Education Statistics.)
Posted by Samantha Ayres, Monday, 21 February 2005 15:31 (link):
What exactly is this Gini coefficient in leymens terms? Who was surveyed for this data? (adults, children, entire population)
Posted by Chris Lightfoot, Monday, 21 February 2005 15:44 (link):
The Gini coefficient is `the average difference in wealth between every pair of people in the population, divided by the average wealth of people in the population'. So in a population where everyone has the same wealth, it is zero; in a population where half the population has no wealth and half the population has the same large wealth (imagine, say, slaves and slaveowners or similar), it is one. Between the two extremes larger values indicate larger inequality.
The surveys I quote results from here looked at household incomes, so presumably they surveyed a random sample of households intended to be representative of the whole population. The Gini coefficients are as quoted in the Luxembourg Income Study Working Paper No. 292, but that's a compilation of data compiled by national statistical agencies. I can't find a discussion of the exact US source and methodology in that paper but it's presumably buried in there somewhere.
Posted by Thomas Barnet-Lamb, Tuesday, 22 February 2005 23:41 (link):
I think a society in which half the society has nothing and half has all the wealth, split equally between them, has a Gini coeficcient of 1/2. A society with a Gini coefficient of 1 is a society in which one person holds all the wealth, I thought.
Posted by Chris Lightfoot, Wednesday, 23 February 2005 00:17 (link):
Quite right -- I've missed a factor of two.
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