Friday, July 18, 2008

The Inheritance of Inequality: Big Insight, Small Error   posted by Herrick @ 7/18/2008 03:58:00 PM

Gintis and Bowles have done great work cleaning up a lot of the discussion about cooperation, evolution, and economic outcomes. A Google Scholaring of their names turns up 14 items with over 100 citations, most of which would be well worth reading for GNXP regulars.

But that said, in their 2002 Journal of Economic Perspectives piece "The Inheritance of Inequality," they appear to make a small error. It's an error that's all-too-easy for even good folks to make: They apparently squared the h-squared.

Their big insight and their small error are all part of answering a simple question: How much of the correlation of income between parent and child can be explained by the heritability of IQ? You might think it's straightforward: IQ is highly heritable, so if there's some channel linking IQ to income, then it's all over but the shouting.

But numbers matter. And Gintis/Bowles work out the numbers, finding that there's a weak link in that causal chain: The low correlation (0.27 according to Gintis and Bowles) between IQ and wages. The causal chain goes like this:

1. Parental earnings have a 0.27 correlation with parent's IQ.
2. Heritability of IQ between parent and child is a bit more than 1/2 of h-squared (why a bit more? assortive mating). They take an h-squared of 0.5 for IQ.
3. Child's earnings have a 0.27 correlation with child's IQ.

So the net result is 0.27*0.3*0.27 = 0.022 (page 10). A very small number, especially since the raw parent-child income correlation in U.S. data is about 0.4. So yes, knowing a parent's income helps you predict their adult (especially male) child's income. But only 5% (or 0.022/0.4) of the total correlation can be explained by IQ's impact on wages. Small potatoes.

(Oh, but where's the small error? It's where Gintis and Bowles report that the net result is 0.01 instead of 0.022--a difference that I can most easily attribute to a mistaken squaring of the h-squared.)

If I really wanted to get that net result up from a measly 5%--if I knew in my heart that IQ really was a driving force in intergenerational income inequality--then how would I do it? Well, I might use a higher heritability of IQ, I might assume more assortive mating, or I might assume a bigger correlation between wages and IQ.

Hard to do much to budge that IQ/wage link: Zax and Rees's paper only has a 0.3 correlation between teenage IQ and middle-aged wages, and when Cawley, Heckman et al. regress NLSY wages on the first 10 principal components of the AFQT, they get a similar result.

So you think maybe a higher heritability of IQ will save you? Well, let's just go all the way to perfect heritability of IQ and perfect assortive mating on IQ. In other words, let's see if "IQ clones" will be have enough similarity in wages to match the 0.4 intergenerational correlation of income.

Will the IQ clones have similar incomes? Not so much. (0.3^2)*1 still equals something small: 0.09. Less than 1/4 of the intergeneration correlation in income. Medium-sized potatoes, but we had to make a ton of ridiculous assumptions to get there.

It's that doggone low correlation between IQ and wages, a correlation that has to be squared because we're comparing parent to child. So a high heritability of IQ doesn't imply a high heritability of IQ-caused-income. Another reminder that lots of things impact your wages: Not just how smart you are.

Gintis and Bowles work through some finger exercises to argue for big environmental effects, and that's all well and good. But to my mind, the interesting fact is that income is still highly heritable!

G/B report that MZT (identical twin) earnings correlation is 0.56, and DZT (fraternal twin) earnings correlation is 0.36, so using the crudest of approximations, the heritability of earnings is still (0.56-0.36)*2=0.4. So income apparently has a modestly high heritability, but most of it can't be explained by the IQ-wage channel. Looks like the genetic heritability of income is being driven mostly by non-IQ channels.

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