There is a new book called The Spirit Level, which claims to prove that most social problems are directly caused by income inequality. So if people in the U.S are more obese than Swedes, it is because middle class Americans they are stressed because they earn less than rich Americans, and eat more (not joking). The “proof” for this is cross country correlation between inequality and various measures.

As a social science student, I am taught to take causality seriously. If you want to argue that inequality causes obesity, you have to actually prove it. Correlations are not scientific proof.

From a theoretical perspective, social problems cause inequality, or are often both caused by deeper ills. In fact it is difficult to think about a social problem that does not cause inequality! Low level of human capital makes your more likely to not take care of your health and causes low income. Bad norms cause crime and low income. Drug use causes problems and low income. Family disruptions causes social problems and low income. And so on.

If The Spirit Level wants to make extraordinary claims (middle class people become more likely to die if the rich grow richer) they need extraordinary evidence. But they have no evidence at all, just correlations. That is why no one in scientific circles takes this book very seriously. However in Sweden it is making a huge impact.

Blogger Danne Nordling pointed out a strange fact about the book. Its measure of inequality, the most important factor in the book, is not gini, the standard inequality result. They seem to use 20/20 richest and poorest ratio. Why make this strange choice, when their source (UN Human Development Index) has gini? I smell data mining.

First for fun I did a simple regression of life expectancy on income inequality and per capita GDP for all countries the UN has data for. The correlation between inequality and health is not statistically significant.

Second I approximately redid the exercise in their book, I did a regression of inequality as measures by Gini and life expectancy for 28 OECD countries, again from the UN HDI. The result is not only that it again is not statistically significat, income inequality is positively correlated with life expectancy!

If I add per capita GDP to the regression, the p value is 0.29 for a positive relationship between health and inequality.

If a Social Democrat 5 minutes ago was convinced that “inequality kills” based on a cross country correlation, are they now convinced if I claim that I have “proven” than income inequality leads to longer life expectancy? How about my “proof” that income inequality makes you happy?

Swedish Social Democrats do not understand causality. They are excited about a book with a horrible methodological problem to start with (reverse causality), weak evidence (correlations) whose correlations are not even robust to using the standard measure of inequality.

PS. From a personal perspective, this book bothers me. It’s not at all the leftist message, but that they are giving cross country regressions a bad name. This kind of scientific abuse has caused economists to be very dismissive of any use of cross country regressions. Basically, as a rule of thumb, they completely dismiss cross country regressions altogether, because unserious people misuse it so much.

However I think that if you have solid theory and there are no serious endogeneity problems, you should be able to use countries as quasi-experiments, as long as you are careful. Have a solid story about causality, no reverse causality or third factor problems, and don’t push your results too hard, and go ahead and use cross country. For some problems, such as the effect of taxation on long run outcome, there is no other good measure of treatment.

Update:

Richard Wilkinson responds to me, and it is a amazingly week responce.

Wilkinson claims that the relationship between inequality and life expectancy remains if you use Gini. Look at his nice graph. Convincing, isn’t it?

It shouldn’t be. First of all he amazingly does not look at the straightforward measure “Life expectancy”. He uses some index. Here is the exact same graph if we look at the most intuitive measure of health, the standard, straightforward “life expectancy”, with the same countries Wilkinson used:

Not quite as nice, is it? Your eyes are not deceiving you, there is no statistically significant relationship between Gini and Life expectancy in the 21 countries Wilkinson looks at. The p value is 0.46.

That’s really it. End of story. He has written a book about the fact that inequality kills you, even though there is no statistically significant relationship, even a weakly statistically significant relationship (say p 0.1), between life expectancy and inequality.

Second, why are there 21 countries, when the OECD has more members? Out of the OECD countries, Wilkinson excludes 9 nations. I can understand excluding Mexico and Turkey, as they are third world nations. But He also excludes South Korea, Czech Republic, Hungary, Luxemburg, Poland, Slovak Republic and Iceland. I included the full list in my other post, let me put here here is well:

The relationship between Gini and Life expectancy is as you see essentially zero, and no where close to statistically significant, p value 0.78. (At least, unlike the U.N data, with the OECD data the relationship is not the opposite of what Wilkinson claims…)

Why would he include Portugal, but not Korea and Czech Republic (that are richer than Portugal), or Slovak Republic (that is as rich as Portugal)? One reason he excludes them is that Czech Republic and Slovak Republic have very even distribution of income, but low life expectancy. Portugal fits his story, it is unequal and does bad. Czech Republic and Slovak Republic don’t fit his story, since they are equal and do bad.

Now, if you ask me, I would say that the reason these two nations have low life expectancy is that they have low income. But once we control for income, we have to control for income for every country. In that case the relationship between gini and life expectancy becomes even weaker. As you remember I controlled for income using EVERY country in the U.N list, and the relationship between gini and life expectancy was no longer statistically significant!

This man has very weak evidence, and is data-mining like crazy. He does not use Gini, the standard measure, because it doesn’t tell him what he wants. He does not use life expectancy, the standard and intuitive measure, because there is no statistically significant relationship between life expectancy and inequality. He removed 7 out of 28 standard OECD countries, because some of them have low inequality and bad outcomes.

The lesson is: Don’t believe a word Wilkinson says before you have had a chance to verify it by looking at the source data yourself. He is not a objective scientists giving you realible data, he is selling you a story.

Of course the book is full of this type of graph. The central argument, the supposedly solid relationship between health and inequality, was a fraud, an optical trick created by data mining. How reliable do we expect the rest of the graphs in the book to be? The naive Swedish Social Democrats, perhaps desperate for new ideas, have been fooled by these guys. The Social Dems should ask for their money back.

I will give you the data, so you can run your own regressions.

If you see Wilkinson, ask him:

* How can he claim that inequality kills, when there is no statistically significant relationship between the standard measure of inequality (Gini) and the standard measure of health (Life expectancy)?

Remember: This is true regardless if he uses OECD data or UN data. In fact the OECD data is kinder to him than the UN HDI data, according to both sources there is no statistically significant relationship, not even close, and in the UN HDI the relationship between inequality and life expectancy is even mildly positive.

* Why did he use an odd measure of inequality and some index instead of the standard measures?

*When the standard measures refute his story, why does he not mention this to his audience, as a scientist would?

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