A correspondent emails me a link to http://gregmankiw.blogspot.com/2009/08/least-surprising-correlation-of-all.html...

Greg Mankiw looks at:

And says:

The Least Surprising Correlation of All Time: [S]o what? This fact tells us nothing about the causal impact of income on test scores.... Suppose we were to graph average SAT scores by the number of bathrooms a student has in his or her family home. That curve would also likely slope upward.... But it would be a mistake to conclude that installing an extra toilet raises yours kids' SAT scores. It would be interesting to see the above graph reproduced for adopted children only. I bet that the curve would be a lot flatter.

And he drops it there.

But merely saying that correlation is not always causation and dropping the issue is, I think, profoundly unhelpful--and shows a... lack of work ethic as well.

Off the top of my head...

IIRC, the age-adjusted correlation between log income and IQ is 0.4: take someone with a log income higher by one standard deviation than average--these days someone with a middle-age-adjusted family income of $100,000-$120,000 rather than $60,000-$80,000--and their IQ is likely to be 0.4 standard deviations (6 points) above average. The individual heritability of IQ is about 0.5: take an individual with a IQ 6 points above average and their children will be expected to have an IQ 3 points above average. SAT scores have a mean of 500, a standard deviation of 100, and a high but not a perfect (0.7) correlation with IQ.

So if we compare people whose parents have an income of $100,000-$120,000 to those with an income of $60,000-$80,000 we would expect to see 1 x 0.4 x 0.5 x 0.7 x 100 = 14 points. The actual jump in the graph Mankiw refers to is twice as large.

The rule of thumb, I think, is that half of the income-test score correlation is due to the correlation of your test scores with your parents' IQ; and half of the income-test score correlation is coing purely from the advantages provided by that component of wealth uncorrelated with your parents' (genetic and environmental!) IQ.

The curve is less steep, but there is definitely a "what" here to be thought about.

The masters at explaining this, of course, are (Googles) Samuel Bowles and Herbert Gintis, "The Inheritance of Inequality" http://www.umass.edu/preferen/gintis/intergen.pdf...

**UPDATE:** Conor Clarke reminds me of Christiane Capron and Michael Duyme (1989), "Assessment of Effects of Socio-Economic Status on IQ: A Full Cross-Fostering Study," *Nature* http://www.nature.com/nature/journal/v340/n6234/pdf/340552a0.pdf: "changes in IQ resulting from changes in postnatal environment are of similar magnitude and exhibit the same general trend independently of the SES of the adopted children's biological paretnts."