Lies, damned lies, and income distributions.

It’s been a while since I fired up the old blog machine, but this morning I came across an article so spectacularly misleading that I felt compelled.

The link showed up in my Facebook feed with the preview line “America’s poorest are about as rich as India’s richest”, which the author repeats again in the middle of the article.

The author is commenting on a feature of a graph contained in the article, which is that the top 5% of the Indian population clock in at the world’s 68th percentile for income (after adjustment for local purchasing power), as do the bottom 5% of Americans.

What isn’t stated explicitly is that those groups are composed of 50 million and 15 million people, respectively, and that the average income in each group (which is what the points in the graph are based on) is a basically meaningless number.

The first reason for this is that comparing income in purchasing power parity across very different economies doesn’t necessarily yield useful information, since it means very different things to be unable to afford different goods in different places. If you can’t afford a car in Kuala Lumpur, that doesn’t really matter, since you have a great public transport system available to get you to work – if you can’t afford a car in rural Queensland, you’re in deep shit.

The second reason, and the one that renders the leading line of the article so staggeringly wrong, is statistical. The statement that America’s poorest are as rich as India’s richest should be obviously wrong to anybody who knows anything at all about poverty in the U.S. or wealth in India. The richest people in India own companies, mansions, and BMWs, just like the richest people everywhere. The poorest people in America are either bankrupt or have debts greater than their assets (regardless of their income). And, as an aside, for this reason it doesn’t even make sense to equate “income” and “poverty”, really – one person might have a small income but own their own home, or while someone else might have both a high income and huge debts, and be living paycheque to paycheque. “Poverty” isn’t the same as “low income”.

But on top of that, even if it did make sense – because of the way income is distributed, the top and bottom 5% of the income distributions of any country contain huge, huge discrepancies in income within them. The Americans at the very bottom of the income scale aren’t just a little bit worse off than the people at the 4.5% mark – they are catastrophically worse off. Likewise, the top 0.5% of Indian society (about 6 million people) aren’t making a little bit more money than the people at the 95.5% mark – they are making orders of magnitude more.

Because India and the US have pretty high wealth inequality and very large populations, and because of this quirk of income distributions at the extremes, talking about the mean incomes of the top and bottom 5% of the population in each country is both economically and statistically meaningless.

 

The graphs above show the kind of shape that each end of the income distributions would have in each country (based on my knowledge of income distributions, not actual values – the values on the y axis don’t represent anything real). These two graphs have the same mean value – but it would be absolutely absurd to say the people on the far left of the US graph are as well off as the people on the far right of the Indian graph – you can see very clearly that that isn’t true. Means are only informative when they’re used to describe data that sit on a bell curve. I hope anybody reading this, even if they’re not into statistics, is able to see that those graphs are not bell curves. The average income of each group doesn’t tell you anything.

To give another example, it might be the case that the shortest quarter of men have the same mean height as the tallest quarter of women, but it would be absolutely ludicrous for me to use that fact as the basis for a statement that “the shortest men are as tall as the tallest women”. That’s obviously not true, because the mean height I’m using doesn’t actually give us any information about people at either extreme. That’s not what means do – they tell you about the middle of a bell curve, not its ends.

There are only two broader interpretations of the statement “America’s poorest are about as rich as India’s richest” that I can see – either India is a place of such misery that even it’s richest citizens live like the worst-off characters in The Wire, or the American poor are so fantastically well off that they live as well Bollywood’s biggest stars, and they ought to think themselves lucky. Both are simultaneously laughable and offensive, and I’m genuinely disappointed that this one got through to the keeper at a progressive news website.

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