Scott Alexander on Garett Jones’ book:
Hive Mind‘s “central paradox” is why IQ has very little predictive power among individuals, but very high predictive power among nations. Jones’ answer is [long complicated theory of social cooperation]. Why not just “signal-to-noise ratio gets higher as sample size increases”?
Me:
Can we rule out statistical artifact? Put it this way. Suppose we chose 1000 people at random. Then we create 50 groups of them. Group 1 has the 20 lowest IQ scores. Group 2 had the next 20 lowest IQ scores, etc. Then we run a regression of group average income on group average IQ for this sample of 50 groups. My prediction is that the correlation would be much higher than you would get if you just took the original sample of 1000 and did a correlation of IQ and income. I think that this is because grouped data will filter out noise well. Perhaps the stronger correlation among national averages is just a result of using (crudely) grouped data.
I think it’s not about R-squared (i.e. correlation), it’s about effect sizes.
Take a random infant born in Guatamala. Which will raise his expected income more: adding 10 points to his IQ, or moving him to the USA?
I though the same thing when I read Alexander’s review. I immediately thought of your earlier post making the same point.
Graphics of the raw data are worth a hundred thousand words. Alexander has an essential one in his post. I once tried to read Adam Smith’s Wealth of Nations – perhaps a kind of ancestor of Jones’ work – and found that entire laborious sections could have been better replaced with a simple chart or diagram. But that wasn’t fashionable or feasible nearly a quarter of a millennium ago.
The right presentation of the data is showing the evolution of the skewed and high-dispersion distribution fans of income from low to high IQ, or maybe a decliles-to-deciles bar chart. Things like that would help people see everything that is going on in one picture.
It looks like Jones had a lot of room for maneuver in how to present the statistical information through distilled coefficients, and he may have cherry-picked the way that seemed to give his thesis the strongest support. “People with high IQ’s have incomes that are all over the place. Yeah, on average, income rises quickly with IQ. But for any particular individual at whatever IQ level, they are going to earn a lot more money in a rich country than in a poor country. And now that most of the world is over the Communism hangover, rich countries tend to have a higher fraction of high-IQ people than poor countries.”
All that being said, our intellectual and political scene desperately needs something it does not have – a respectable way to talk about the impacts of immigration and costs and benefits of various policies – such as being selective on the basis of cognitive talent or cultural compatibility – without immediately collapsing into hysterical accusations of racist fascism.
The tight relationship between IQ and life outcomes in the domestic context has become a taboo third rail in the American intellectual scene, so it would be … um … convenient … to have some mainstream and respectable book to point to support the right conclusions without kicking the hornets nest, even if it gets there by some questionable route that is the only remaining available pathway when the direct route through ‘unspeakably ugly truth’ territory is blocked off.
Hive Mind‘s “central paradox” is why IQ has very little predictive power among individuals, but very high predictive power among nations.
Haven’t read the book but here’s my half-baked theory: the answer to the paradox is that IQ is important, but it does not correlate perfectly with traits like ambition, conscientiousness, and willingness to take risks, and you need a measure of all three in order to be highly successful. You need to consider how many smart but lazy people there are out there (like me, for example). Remember the Heinlein quote: “Throughout history, poverty is the normal condition of man. Advances which permit this norm to be exceeded — here and there, now and then — are the work of an extremely small minority, frequently despised, often condemned, and almost always opposed by all right-thinking people.”
To expand on that: living in a rich country is not just about what percentage of people have an IQ of 120 or higher, but how many Henry Fords there are among that group of people. A small subset of individuals are able to create way more value/utility for society than they are able to capture, financially. In other words, they invent or make products where the consumer surplus is extremely high. These people are few in number but their effect on society is enormous. Hence the high correlation between national IQ and wealth is stronger than at the individual level.
I would add that the real benefit of living in a developed country is that it provides the institutional detail to leverage the talents of those people, which might account for the lion’s share of the IQ effect at the national level.
How impactful would Henry Ford have been if he was born in Haiti?
I find it a little confusing when people implicitly talk about models without explicitly defining them. For instance, in the IQ – Income approach, it’s like they’re implicitly talking about comparing two models. The first is
Y_{i} = A + X_{i}B + e_{i}
Where Y is log income, X is the IQ, A is the intercept, B is the slope, and e is the error.
The alternative model is something like
Y_{i} = A_{j[i]} + e_{i}
A_{j} ~ N(a + X_{j} * b, sigma_{A})
The notation j[i] means that given individual i, you choose group j. In this case, the groups are based on IQ.
So then the question is, does this model explain the data better than the original. I don’t know, but I also haven’t seen anybody talk about it in this way.
I would think a lot of the difference between the two could be explained by the O-ring effect.
The richer the country the more opportunity there is for O-rings to form, which add a huge multiplier to the benefits of IQ/risk taking/conscientiousness, etc.
But the formation of O-rings probably has a lot of randomness and path dependence built into it, hence the shaky correlation between IQ and income at the individual level.
See Gelman on “The garden of forking paths” and the possibility of group level regressions showing significance purely by chance. Not to say the conjecture is wrong but adjustments must be made to eliminate the luck factor. Or use hierarchical Bayesian models for a robust solution.
It’s certainly possible that correlations among groups do not necessarily reflect correlations among individuals (thinking so would be the ecological fallacy). In your experiment, however, we know the correlation among individuals and the question is do we get a higher correlation when averaging into groups. I think the answer to this is no. In fact, rather than reducing noise averaging the data adds noise, relative to the true relationship, since you are throwing away some of your data.
Correlations can be tricky. Thus, I usually think about regression coefficients and in that case averaging and then running the regression will on average get you similar coefficients.