Occasional reflections on Life, the World, and Mathematics

Why people hate statisticians


Andrew Dilnot, former head of the UK Statistics Authority and current warden (no really!) of Nuffield College, gave a talk here last week, at our annual event honouring Florence Nightingale qua statistician. The ostensible title was “Numbers and Public policy: Why statistics really matter”, but the title should have been “Why people hate statisticians”. This was one of the most extreme versions I’ve ever seen of a speaker shopping trite (mostly right-wing) political talking points by dressing them up in statistics to make the dubious assertions seem irrefutable, and to make the trivially obvious look ingenious.

I don’t have the slides from the talk, but video of a similar talk is available here. He spent quite a bit of his talk trying to debunk the Occupy Movement’s slogan that inequality has been increasing. The 90:10 ratio bounced along near 3 for a while, then rose to 4 during the 1980s (the Thatcher years… who knew?!), and hasn’t moved much since. Case closed. Oh, but wait, what about other measures of inequality, you may ask. And since you might ask, he had to set up some straw men to knock down. He showed the same pattern for five other measures of inequality. Case really closed.

Except that these five were all measuring the same thing, more or less. The argument people like Piketty have been making is not that the 90th percentile has been doing so much better than the 10th percentile, but that increases in wealth have been concentrated in ever smaller fractions of the population. None of the measures he looked was designed capture that process. The Gini coefficient, which looks like it measures the whole distribution, because it is a population average is actually extremely insensitive to extreme concentration at the high end. Suppose the top 1% has 20% of the income. Changes of distribution within the top 1% cannot shift the Gini coefficient by more than about 3% of its current value. He also showed the 95:5 ratio, and low-and-behold, that kept rising through the 90s, then stopped. All consistent with the main critique of rising income inequality.

Since he’s obviously not stupid, and obviously understands economics much better than I do, it’s hard to avoid thinking that this was all smoke and mirrors, intended to lull people to sleep about rising inequality, under the cover of technocratic expertise. It’s a well-known trick: Ignore the strongest criticism of your point of view, and give lots of details about weak arguments. Mathematical details are best. “Just do the math” is a nice slogan. Sometimes simple (or complex) calculations can really shed light on a problem that looks to be inextricably bound up with political interests and ideologies. But sometimes not. And sometimes you just have to accept that a political economic argument needs to be melded with statistical reasoning, and you have to be open about the entirety of the argument.

It got even weirder wehn he tried to knock down the obvious criticism, that wealth inequality is even greater than income inequality, and tends even more to entrench ethnic and class distinctions across the generations. Fair-minded people could come up with many reasonable ways to measure wealth. What they would not do is to do what Dilnot did, which is to show plots of the change over time in the fraction of the population that receives, at some point in their lives, “an inheritance”. As though the person who inherits one third of the parents’ wedding china is to be counted the same as the Sainsbury heirs. Meanwhile the wealthy have been pushing down the inheritance tax to increase the value of their unit of inheritance. Not to mention that most people these days are approaching retirement when their parents die, so the meaningful family support that will help people during their education and working lives is going to come from excess wealth that parents can share with them while they are still alive.

It’s not impossible to do this honestly, and to let yourself be informed by the data, to lead you to a more truthful conclusion than you would have come up with just spouting off on the basis of preconceptions. But that won’t happen if you’re trying to pretend that you’re just doing sums.

One amusing thing was how he started the talk with the old chestnut of asking the audience to estimate some statistical quantity that you feel like everyone ought to have some sense for. In this case, he asked for an estimate of the ratio of the 90th percentile to the 10th percentile of income in the UK, options being 4, 6, 8, 10, 12. I figured, I know that there are a lot of poor people in the country, particularly when you reckon that he north of England, where I’ve never been, is supposed to be a lot poorer than the south, so I must be well up into the 90s myself. Dividing my income by something like what I recall being the official poverty line gave me something between 4 and 6. Allowing for the fact that I was probably well over 90%, I said 4. The vast majority said 10 or 12. Asking around, it was clear that British people were mostly at the upper end. It did support his point that people who have lived here their whole lives think of themselves as average, even if the gaping inequality is obvious to foreigners who move here.

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