## Income and IQ

As I noted in my recent post on Malcolm Gladwell’s Outliers, Gladwell ignored the possibility that traits with a genetic component, other than IQ, might play a role in determining success. His approach reminded me of a useful paper by Samuel Bowles and Herbert Gintis from 2002 on the inheritance of inequality. Bowles and Gintis sought to explain the observed correlation between parental and child income (a correlation of around 0.4) by examining IQ, other genetic factors, environment, race and schooling.

As an example of the consequences of the transmission of income. Bowles and Gintis cited a paper by Hertz which showed that a son born to someone in the top decile of income had a 22.9 per cent chance of attaining that decile himself, compared to a 1.3 per cent chance for someone born to parents in the bottom decile. Conversely, a child born to parents in the top decile had only a 2.4 per cent chance of finishing in the lowest decile compared to over 31.2 per cent for those born to bottom decile parents.

As Gladwell did, Bowles and Gintis started their examination with IQ. To calculate the inheritance of income through genetically inherited IQ, Bowles and Gintis considered the correlation between parent IQ and income, the heritability of IQ from parent to child and the correlation between IQ and income for the child. Breaking this down, Bowles and Gintis used the following steps and estimates:

1. The correlation between parental income and IQ is 0.266.

2.If the parents’ genotypes are uncorrelated, the genetic correlation between the genotype of the parents and of the child is 0.5. This can be increased with assortive mating (people pairing with people more like themselves) to a maximum of one (clones mating). Bowles and Gintis use 0.6.

3.The heritability of IQ is 0.5.

4. The correlation between child income and IQ is 0.266.

Multiplying these four numbers together gives the intergenerational correlation of income due to genetically based transmission of IQ. I think there is a mistake in the calculations used by Bowles and Gintis, as they find an intergenerational correlation of 0.01, where I calculated 0.02. This leads to genetically inherited IQ variation explaining 5.3 per cent of the observed intergenerational correlation in income. Regardless of the error, this is a low proportion of the income heritability. (After I wrote this post I did a google search to find if someone had spotted this error before – and they had – on a earlier Gene Expression post on this same paper.)

I would have used some slightly higher numbers, but pushing the numbers to the edges of feasible estimates, such as increasing the correlation between income and IQ to 0.4, the genetically based correlation between parent and child IQ to 0.8 and the degree of assortive mating so that parent-child genotype correlation is 0.8 only yields an intergenerational correlation of 0.10. Genetically inherited IQ would account for approximately 26 per cent of the observed intergenerational correlation.

Unlike Gladwell, Bowles and Gintis then asked what role other genetic factors may play. By using twin studies, which provide an estimate of the degree of heritability of income (using the difference in correlation between fraternal and identical twins) and the degree of common environments of each type of twin, Bowles and Gintis estimated that genetic factors explain almost a third (0.12) of the 0.4 correlation between parent and child income. Loosening their assumptions on the degree of shared environments by identical twins compared to fraternal twins (i.e. assuming near identical environments for both identical and fraternal twins) can generate a higher estimate of the genetic basis of almost three-quarters of the variability in income.

From this, it seems that genetic inheritance plays an important role income transmission between generations. The obvious question is what these factors might be. I expect that patience or ability to delay gratification must play a role, although I would expect that there would be a broad suite of relevant personality traits. I would also expect that appearance and physical features would be relevant. Bowles and Gintis do not take their analysis to this point.

The authors finished their analysis with some consideration of other factors, and conclude that race, wealth and schooling are more important than IQ as a transmission mechanism of income across generations (although as the authors noted, they may have overestimated the importance of race by not including a measure of cognitive performance in the regression). That conclusion may be fair, but as they had already noted, there is a substantial unexplained genetic component.

This highlights the paper’s limitation, as once the specific idea that heritability of IQ is a substantial cause of intergenerational income inequality has been dented, the identification of other (but unknown) genetic factors leaves open a raft of questions about income heritability. Using Bowles and Gintis’s conservative estimates, we still have 25 per cent of income heritability being put down to genetic factors without any understanding of what these traits are and the extent of the role they play.

In their conclusion, Bowles and Gintis touch on whether policy interventions might be based on these results. They are somewhat vague in their recommendations, but suggest that rather than seeking zero intergenerational correlation, interventions should target correlations that are considered unfair. They suggest, as examples, that there are large majorities supporting compensation for inherited disabilities while intervention for good looks is not appropriate.

One thing I find interesting in an analysis of heritability such as this is that over a long enough time horizon, to the extent that someone with a trait has a fitness advantage (or disadvantage), the gene(s) behind the trait will move to fixation (or be eliminated) as long as heritability is not zero. The degree of heritability is relevant only to the rate at which this occurs and only in a short-term context. The obvious question then becomes (which is besides the point of this post) whether IQ currently yields a fitness advantage. Over a long enough time period, variation will tend to eliminate itself and Bowles and Gintis would be unable to find any evidence of IQ heritability affecting income across generations.

**This a cross-post from my blog Evolving Economics, which is my usual blogging home.

Bowles, S., & Gintis, H. (2002). The Inheritance of Inequality Journal of Economic Perspectives, 16 (3), 3-30 DOI: 10.1257/089533002760278686

1. Correct me if I’m wrong, but isn’t it an error to make claims about the intergenerational transmission based on heritability quotients?

After all, a trait may be highly heritable but not pass on from one generation to the next. This is because the relevant genes and environments may differ from one generation to the next.

So I understand how we can make claims about genes and income within a generation, but by what logic can you extend this to intergenerational transmission?

2. @ben g, to call it an error is to overstate the case. Obviously, heritability of a trait can change significantly from generation to generation, which would make any intergenerational calculations an error. But heritability can also remain relatively consistent (making certain assumptions about the environment and selection pressures) and can be useful in examining intergenerational change, as is often done in quantitative genetics.

Bowles and Gintis’s implicit assumption of a constant environment and heritability is fair given the purpose of their paper (and I tend to think it is also a broadly accurate assumption). Over the time covered by the generations of interest, there has been a relatively consistent correlation between income and IQ and parent and child IQ, and consistently high heritability of IQ in the populations of interest. As the paper shows, the specific heritability calculations are not the most significant factor in obtaining the result – it is the magnitude of the income-IQ correlation (or income-other genetic factors correlation) that tends to limit the degree to which IQ and genetic factors can be used to explain the strong correlation between parent and child income.

3. Wouldn’t health be a very likely place to look for highly heritable income-affecting things? Chronic physical or mental health problems can have a huge impact on how much money you make.

I wonder how big an impact that might have.

4. Jason,

Even if heritability stayed the same from one generation, that wouldn’t necessarily indicate intergenerational genetic transmission. That’s because equally heritable but different causes may underly the trait for each generation.

I would guess that there are some traits like g, work ethic, etc. which are valuable and transmitted from one generation to the next. But with a changing economy/society I would also guess that the genes/environments which matter also change.

5. By the way, thanks for making this post. GNXP is the only intelligent blog for discussing behavior genetics and all its
implications. Lately it hasn’t had much on that particular subject so thanks for helping keep things rolling!

6. What is the justification for multiplying correlations? I mean, if A correlates with B which correlates with C, that does not necessarily imply that A correlates with C. Simply: correlation is not transitive. Why do you or the authors assume, that the result of such 3 transitional (?) steps will lead to any meaningful results? Besides, what is the purpose of using an estimate for genetic correlation in step 2 if in step 3 the parent-child IQ correlation due to genetic inheritance is used? Step 2 seems unnecessary. Or maybe step 3 should have been IQ and underlying genotype correlation, but then one would need a similar step between parent IQ and parent genotype [step 2.5].

7. @Nador, thanks for your comment. I agree that correlation is not transitive, but I consider that the assumption of transitivity is reasonable for the ballpark purpose of the exercise.

On your second point, the estimate in step 3 needs to be adjusted by step 2 as there are two parents. Step 2 is whole genotype correlation.

8. Brad Delong quotes Bob Herbert saying that in Northern Ireland, Catholics had IQs about 15 points lower than Protestants. Is that accurate?

9. Surely the main determinant of my children’s INCOME is my WEALTH. This has been especially true over the last 50 years because nominal interest rates have been unprecedentedly high.

10. The evidence would suggest that IQ is more important than socio-economic status. From Herrnstein and Murray’s The Bell Curve:

The second broad implication is that parental SES is important but not decisive. In terms of this figure, a student with very well-placed parents, in the top 2 percent of the socioeconomic scale, had only a 40 percent chance of getting a college degree if he had only average intelligence. A student with parents of only average SES – lower middle class, probably without college degrees themselves – who is himself in the top 2 percent of 1Q had more than a 75 percent chance of getting a degree.

Once again, the common stereotype of the talented-but-disadvantaged- youth-denied-educational-opportunity does not seem to exist in significant numbers any longer. Only seven-tenths of 1 percent of whites in the NLSY were both “prime college material” (IQs of 1 15 or above) and markedly disadvantaged in their socioeconomic background (in the bottom quartile on the SES index). Among this tiny group, it is true that fewer than half (46 percent) got college degrees. Those who did not, despite having high IQs, may be seen as youths who suffered from having a disadvantaged background. But recall that this group consists of only four-tenths of 1 percent of all white youths. A category of worthy white young persons denied a college education because of circumstances surely exists to some degree, but of such small size that it does not constitute a public policy problem.

What about another stereotype, the untalented child of rich parents who gets shepherded through to a degree? Almost 5 percent of white youths had below-average 1Qs (under 100) and parents in the top quartile of socioeconomic status. Of those, only 12 percent had gotten college degrees, representing just six-tenths of 1 percent of white youths. Judging from these data, the common assertion that privileged white parents can make sure their children do well in school, no matter what, may be exaggerated.

Or this:

For example, imagine a white person born in 1961 who came from an unusually deprived socioeconomic background: parents who worked at the most menial of jobs, often unemployed, neither of whom had a high school education (a description of what it means to have a socioeconomic status index score in the 2d centile on socioeconomic class). If that person has an IQ of 100 – nothing special, just the national average – the chance of falling below a poverty-level income in 1989 was 11 percent. It is not zero, and it is not as small as the risk of poverty for someone from a less punishing environment, but in many ways this is an astonishing statement of progress. Conversely, suppose that the person comes from the 2d centile in IQ but his parents were average in socioeconomic status which means that his parents worked at skilled jobs, had at least finished high school, and had an average income. Despite coming from that solid background, his odds of being in poverty are 26 percent, more than twice as great as the odds facing the person from a deprived home but with average intelligence.

In sum: Low intelligence means a comparatively high risk of poverty. If a white child of the next generation could be given a choice between being disadvantaged in socioeconomic status or disadvantaged in intelligence, there is no question about the right choice.

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