15 July 2012

Reversion to the mean and social mobility

In her FT Money investment advice column on 7 July, Merryn Somerset Webb returned to a favourite subject. She had been looking at a report by Mark Urquhart from Baillie Gifford:
According to him, the four most dangerous words in investment are not, as most of us think: “this time, it’s different.” They are: “reversion to the mean”.  
… we are living in a period of exceptionally rapid change – change that can have a “profound effects on equities”. Take the way Urquhart satisfied himself with the definition of reversion to the mean. He looked it up on Wikipedia [my link], a website now accessed by 15 per cent of internet users every day, and viewed by pretty much everyone as the starting point for researching anything. Just 12 years ago, Wikipedia didn’t exist.  
… Set too much store by reversion to the mean and you will be “routinely tempted to sell out of long term winners and into clunkers . . . this is not an obvious winning investment strategy”.
And on this basis, and probably wisely, she advised against buying shares in banks just because they appear historically cheap. The same statistical phenomenon (under its alternative name of regression to the mean) had come up in another journalist’s article a month earlier but in a different context. In the Daily Telegraph on 9 June Damian Thompson, impressed by Charles Murray’s book Coming Apart: The State of White America, 1960-2010, reported:
A hundred years ago, says Murray, most Americans in the top five per cent of cognitive ability had ordinary occupations. They were very clever shopkeepers, farmers, housewives and factory workers. But they didn’t somersault over their peers. One reason is that they couldn’t marry very smart people. High intelligence was scattered evenly across America, so a gifted farm worker might have to travel 100 miles before he met a woman as bright as he was. Instead, he married an ordinary local girl, and their children, regressing to the mean, were only slightly cleverer than their schoolfriends. The explosion of college education changed that. Universities plucked bright kids out of their home towns like a tornado and suddenly they found that they weren’t in Kansas any more. Young people hooked up with equally intelligent partners and passed on two sets of smart genes.
Read carelessly this might leave the impression that the “gifted” farm worker’s intelligence when diluted by that of the “ordinary” local girl had been nulled to the average whereas “bright kids” nowadays find “equally intelligent” partners” and so can “pass on “two sets of smart genes”, undiluted as it were. Thompson is no doubt well aware that we all get not two, but only the one set of genes which combine the traits we inherit from our parents. But more interesting is what Murray actually said in trying to explain the emergence of a new upper class in white America. This is a class based on high educational attainment providing access to the most elite and well-rewarded forms of employment as “mind workers” or “symbolic analysts”. He defines it as:
… the most successful 5 percent of adults ages 25 or over who are working in managerial positions, in the professions (medicine, the law, engineering and architecture, the sciences and university faculty) and in content-production jobs in the media. (page 20)
His first proposition is that high cognitive ability is a prerequisite for such employment although success depends on other factors such as motivation and interpersonal skills. But don’t be misled by the fact that:
… the correlation of IQ scores with performance among those people who are attorneys, screenwriters and biochemists is modest. [But] to be a top attorney, screenwriter or biochemist, you have to be very smart in the ways that IQ tests measure. (page 47)
Murray calls the point that Thompson picked up, about parents now being more likely to be equally intelligent, “the increase in cognitive homogamy”. However, this does not eliminate regression to the mean and he argues that:
… the expected value of the IQ of a grown-up offspring is 40 percent toward the population mean from the parents’ midpoint IQ (page 65)
He takes the IQ levels associated with levels of educational attainment:

and then casts the expected IQ of the child in terms of the parents education:

followed by a very significant passage:
These represent important differences in the resources that members of the next generation take to the preservation of their legacy. Consider first a college graduate who marries a high school graduate, each with the average cognitive ability for their educational level (113 and 99, respectively). Their expected midpoint IQ is 106. Suppose they have built a small business, been highly successful, and leave $5 million to their son. If their son has the expected IQ of a little less than 105, he will have only about a 50 percent chance of completing college even assuming that he tries to go to college. Maybe he inherited extraordinary energy and determination from his parents, which would help, but those qualities regress to the mean as well. Shirtsleeves to shirtsleeves in three generations is a likely scenario for the progeny of that successful example. Compare that situation with the one facing th  e son of two parents who both graduated from elite schools. If he has exactly the expected IQ of l2l, he has more than an 80 percent chance of getting a degree if he goes to college. These percentages are not a matter of statistical theory. They are based on the empirical experience of both the 1979 and 1997 cohorts of the National Longitudinal Survey of Youth [NLSY] - if you had an IQ of 105 or one of 121 and entered college, those are the probabilities that you ever got a degree.  
In addition to those differing chances of graduation are qualitative differences between young people with IQs of 105 and 121. First, the reasons that someone with an IQ of 105 doesn't finish college probably include serious academic difficulties with the work, whereas the reasons a person with an IQ of 121 doesn't finish college almost certainly involve motivation or self-discipline-no one with an IQ of 121 has to drop out of college because he can't pass the courses. Second, there is a qualitative difference in the range of occupations open to those two young persons. The one with an accurately measured IQ of 105 cannot expect to be successful in any of the prestigious professions that are screened for IQ by their educational requirements (e.g., medicine, law, engineering, academia). It is unlikely that he can even complete those educational requirements. Someone with an accurately measured IQ of 121 can succeed in any of them if his mathematical and verbal talents are both strong, or succeed in the ones geared to his talents if there is an imbalance between mathematical and verbal ability.  
Now think in terms of an entire cohort of children. Where will the next generation of children with exceptional cognitive ability come from? For purposes of illustration, let's say that "exceptionally high cognitive ability" means the top five centiles of the next generation of white children. More than a quarter of their parents may be expected to have a midpoint IQ of more than 125. Another quarter may be expected to have midpoint parental IQ of I17 - 125. The third quarter may be expected to have midpoint parental IQ of 108 - 117. That leaves one quarter who will be the children of parents with midpoint parental IQ of less than 108. Only about 14 percent of that top five centiles of children are expected to come from the entire bottom half of the distribution of white parents.   
Therein lies the explanation for that startling statistic I reported earlier about SAT scores: In 2010, 87 percent of the students with 700-plus scores in Critical Reading or Mathematics had a parent with a college degree, and 57 percent had a parent with a graduate degree. Those percentages could have been predicted pretty closely just by knowing the facts about the IQs associated with different educational levels and the correlation between parental and child IQ. They could have been predicted without making any theoretical assumptions about the roles of nature and nurture in transmitting cognitive ability and without knowing anything about the family incomes of those SAT test-takers, how many test preparation courses their children took, whether they went to private schools, or how ingenious the educational toys in the household were when they were toddlers.  
In an age when the majority of parents in the top five centiles of cognitive ability worked as farmers, shopkeepers, blue-collar workers, and housewives-a situation that necessarily prevailed a century ago, given the occupational and educational distributions during the early 1900s - these relationships between the cognitive ability of parents and children had no ominous implications. Today, when the exceptionally qualified have been so efficiently drawn into the ranks of the upper-middle class, and when they are so often married to people with the same ability and background, they do. In fact, the implications are even more ominous than I just described because none of the numbers I used to illustrate the transmission of cognitive ability to the next generation incorporated the effects of the increased educational homogamy of recent decades. In any case, the bottom line is not subject to refutation: Highly disproportionate numbers of exceptionally able children in the next generation will come from parents in the upper-middle class, and more specifically from parents who are already part of the broad elite. (pages 66-68, my emphasis)
This line of argument does not align well with much of the current political rhetoric in the UK about social mobility. However, it seems quite likely that the UK will experience the same trend towards cognitive homogamy. It may be less marked than in the US where there has been a clear elite grouping of universities since the 1960s using a standard set of admission tests, the SATs (Scholastic Aptitude Tests). But, as posted here before, there are well-known rankings of British universities and, very recently, there is increasing use of admission tests to supplement A-level results.  Again, the existence in the UK of elite grammar schools and independent schools pupils concentrate on the academic A-levels appropriate for the best universities may cloud any comparison with the US.

A technical point which intrigues me is that if the offspring of the two 135 IQ parents have an expected IQ of 121, that will be the mean IQ of the children of such parents. What is the nature of the statistical distribution of the offspring’s IQ? Is it, like IQ in the population as a whole, normally distributed (the “bell-curve”, see below) or skewed in some way? If it is a normal distribution, what is the standard deviation (SD)? In my experience, sometimes the children of such parents are just as clever as their parents (if not more). But if symmetry applies, others must be as far below 121 as 135 is above ie 107.  Again, experience, which is not of course the same as objective statistics, leads me to doubt it.

Although it is primarily about the US, I hope to come back to another aspect of Murray’s book in a future post. I would certainly urge anyone interested in British society to read it for the insights it provides into how things could develop here.

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