Comments on the Possible Swindle
By Arnold Kling
Several interesting comments on this post. The puzzle is this: let X be the correlation between parental IQ and children’s IQ. Let Y be the correlation between the child’s IQ and the child’s future earnings. Let Z be the correlation between parental earnings and the child’s future earnings. Why is Z much higher than X times Y?
Steve Sailer writes,
Correlation isn’t the same as effect size. In a complex system with many factors, a single factor can have a low correlation but still have a sizable effect
I think of effect size as the numerator in correlation. If you have a big effect size and a low correlation, then you must have a big denominator–in this case, a high variance of income. But that would tend to lower Z along with Y, so I think that the puzzle still stands.
John Thacker writes,
Correlation coefficients only measure the linear relationship, not any nonlinear relationship. It’s quite possible that there is a nonlinear relationship. Ordinarily linear relationships dominate with two normally distributed r.v., so it’s okay. However, if there’s covariance between IQ and environment then the mathematical assumptions and simplifications fail, the chain of reasoning falls apart, and the conclusion does not hold.
But again it seems to me that nonlinearity ought to hurt Z as well as hurt Y. I have a hard time coming up with a story in which the relationship between IQ and income is nonlinear but the relationship between parental income and child’s income is linear.
Bruce Charlton recommends a paper by Daniel Nettle. That paper says,
The data show clearly that general ability, an IQ-like score, is indeed a predictor of class mobility. Those reaching the professional class had a GA score about one and a half standard deviations higher than those reaching the unskilled class, regardless of their class of origin.
…The relationship of parental social class to attained social class was weak (6% of the variation). Most of this was mediated through General Ability. Partialling out GA differences left only 3% of the variation to be explained by direct effects of paternal class on occupational opportunities…
The vast majority of variation in both attained class and class mobility is not accounted for by IQ. …Nonetheless, intelligence is the strongest single factor causing class mobility in contemporary societies that has been identified.
This is an interesting study, but it loses considerable precision by aggregating people into broad income classes. As I interpret the study, doing so brings Z down from something like .5 to something like .06
Personally, I think that the Bowles-Gintis-DeLong swindle comes from lowballing both X and Y. If you say that X is .2 and Y is .2, then X times Y is .04, which is close to zero as a correlation. If you say that X is .6 and Y is .6, then X times Y is .36, which is fairly big in terms of correlation.
I think that the correlation of parents’ IQ with childrens’ IQ is much higher than what you would get with random mating. I also think that this correlation has been getting higher in recent years, as more men choose women for their intelligence rather than for their obedience or domesticity. So I would expect X to be higher than the .2 that Bowles and Gintis appear to work with.
I also think that for measuring the impact of IQ on income, you have to be careful not to control for things that IQ can affect. Bowles and Gintis allow IQ to affect schooling. But it also may affect health, ability to defer gratification, marital stability, and other factors that affect income. By the time you are finished, you may wind up with a value for Y of .5 or higher.
Anyway, the overall point is that there is a large margin of error in estimating X times Y. If you were to report a 90 percent confidence interval for the product, rather than a specific number, my guess is that it would include values close to 0, but also values close to Z.