I’ve narrowed down the classes of possibilities. And restated the problem:
Environmental influences which cause a group difference can be: Common or unique (influences which affect IQ in both populations or influences which affect IQ in one or the other population ), variable within or uniform within (influences which vary between individuals within the populations or which do not), variable between or uniform between.(influences which variably affect individuals in one population relative to another or which uniformly affect individuals in one population relative to another). This gives us 8 imaginable classes, of which 4 are internally inconsistent (e.g., by the above taxonomy, an influence can not be both common in both populations and uniform within populations). After removing these we are left with 4 classes, two involving common influences and two involving unique influences. The classes involving unique influences are: unique, uniform-within, uniform-between and unique, variable-within, variable-between. These classes can be ruled out because:
Unique factors. With regards to unique versus common influences, a group difference can be caused by influences that vary within both groups, and so are common to both, or, in principle, by influences that vary uniquely between groups. Rowe et al. (1994) summarizes this issue:
It is conceivable that the causal processes leading to average levels would be different from those creating within-group variation in behavior. This possibility is real in the mathematical sense in that averages and correlations are statistically independent. However, for this alternative to hold requires also that minority-unique Factor X contributes to average level but does not contribute to variation among individuals… However, this argument—influences on means separate from those on individual differences—is a strong one because it requires nearly equal exposure to and influence of the unique causal mechanism in all exposed persons…
What’s novel about unique influences is that they are unconstrained by within population heritability. It is solely because of this property that we are making the common/unique distinction.
Unique uniform factors. Now, there are really two classes of unique influences: Unique uniform and unique variable influences. With the first class, the influence does not vary among individuals within the group affected – and because these influences don’t vary among individuals within the affected group, they have a uniform effect on individuals between groups. As such these factors are both uniform within and between groups. It’s rather difficult to think of examples of these in the case of Blacks and Whites in the US, but some examples are more obvious between generations (e.g., iodine fortified salt and fluorinated water). These are influences for which the vast majority of individuals in one groups (e.g,, people born in the 2000s) are exposed to and for which the vast majority of individuals in the other group (e.g., people born in the 1800s) were not. With regards to Black and Whites in the US, these are theoretically implausible for the following reasons:
(1) African-Americans are not affected uniformly, relative to Whites, as the difference between Blacks and Whites is conditioned on the color (and Negro appearance) of the former but not the latter. As such, the cause of the mean difference between Blacks and Whites can not, at least fully, be said to be unrelated to the cause of the differences within the Black population, which is what a uniform factor X hypothesis proposes.
(2) While there are mean environmental differences between the groups, there are no apparent ones which are invariant in one or the other. This situation is most clearly seen when comparing children of Black, White, and mixed parentage. For example, in the nationally representative NLSY 97, biracial individual scores 0.46 SD below monoracial Whites, and 0.49 SD above monoracial Blacks on the highly general intelligence loaded AFQT (Gullickson, 2004); owing to convention, these “mixed” individuals are classified as Black and constitute 10% of the “Black” population. These mixed race children do not appear to uniformly inhabit an environment either distinct from Whites and in common with Blacks or distinct from both Whites and Blacks. Given the continuum of differences between Whites, biracial individuals, Caucasian appearing Blacks, intermediate appearing Blacks, and Negro appearing Blacks and given the apparent absence of uniform environmental differences, these types of factors are implausible.
Unique variable factors. The second class contains influence with vary within the affected population. In the case of the Black-White differences, this class contains hypothetical influences such as: Black culture, the effect of racism, and minority caste system. Such types of influences have frequently been evoked. For example, Scarr (1982) postulated “Blacks culture” as the unique influence stating:
As I have noted in several papers, the Factor X to which Jensen refers is none other than cultural differences in child-rearing styles, values, and emphasis on skills though to be desirable for children to learn.
This was said in response to a statement about the constraints of within population heritability. Now the specific cultural differences mentioned are not mostly uniform across the Black population (e.g., upper and lower class African-Americans), so they are best classified as unique variable influences. The problem with this class is that such influences should alter the IQ-environment/kinship correlation matrices between populations. Unique influence which causes one groups to differ from another will not leave the patterns of correlations between IQ and other variables untouched (assuming that there is variability within the affected population), just as poking on a balloon will not leave the material surrounding the indentation unstretched, Yet Rowe et. al. 1994 analyzed the correlation matrices between Blacks and Whites in six studies and found them to be statistically identical. Two of the studies included good indices of cognitive ability, the National Longitudinal Survey of Youth and the Richmond Youth Project . Rowe et al. concluded:
Our main result was that developmental processes in different ethnic and racial groups were statistically indistinguishable. Developmental process refers to the association among variables in these groups and to the variables’ total variances. This conclusion held for the examination of six data sources, containing a total of 3,392 Blacks, 1,766 Hispanics, and 8,582 Whites, and in one data source, 906 Asians. The patterns of covariances and variances were essentially equal when one ethnic or racial group was compared with another; moreover, this structural similarity between ethnic or racial groups was no less than that within random halves of a single ethnic or racial group.
Given the above, unique variable influences, as with unique uniform influences, do not seem to be promising candidates for explaining the group differences in the US.
References: Gullickson, 2004.; Rowe et al., 1994. No More Than Skin Deep: Ethnic and Racial Similarity in Developmental Process; Scarr, 1982. A reply to some of professor Jensen’s Commentary. In: Race, social class, and individual differences in IQ.
 For those two studies, the following variables were looked at: (NLSY) Mother’s education, Age of child, HOME Cognition, HOME Emotion, School self-esteem, Self-worth, Math achievement, Reading recognition, Reading comprehension, Problem behavior; (Richmond Youth Project) Participation with father, Supervision by father, Overall GPA, Mother’s education, Participation with mother, Supervision by mother, Peer orientation, IQ, Standard self-report, delinquency. Official offenses to 1967.
Common influences. The two classes involving common influences are: common, variable-within, variable-between and common, variable-within, uniform-between. Influences which are uniform within a group are, per our taxonomy, classified as unique. Unlike these, common influences, as they vary within group, are constrained by heritability estimates.
Variable-between and uniform-between influences differ in terms of the distribution of the environmental effect. In the former case, the effect is not distributed equally — some members of a population are affected more and some less — and in the latter case it is. In both instances there is variance within groups. To illustrate: We could imagine a situation such that the # of books a person has influences intelligence. And that the correlation between the # of books and IQ is 0.2 and that the standard deviation of the # of books is 1. And that for both of the groups in question, Blacks and Whites, the # of books is normally distributed. Now, further, we could imagine an initial condition in which both groups started out with the same average number of books. If 5 books were later confiscated from every Black individual, in our situation, depressing each individual’s IQ by 1 SD relative to the individual’s IQ at the initial condition, we would have a uniform-between influence — since Black individuals would be uniformly depressed relative to Whites. In this situation, were we to match Blacks and Whites for the same IQ at the later time, we would find that all Black individuals had 5 less books than White individuals (5 x 0.2 = 1 SD) of the same IQ. Accordingly, a Black individual with an IQ of 115 would be equivalent to White individual who would have had an IQ of 130 where he not deprived 5 books. Alternatively, if the Black population was divided into quarters and 0, 2, 8, and 10 books were later confiscated from each, depressing the quarters 0 SD, 0.4 SD, 1.6 SD, and 2 SD respectively, we would have a variable-between influence. In this situation, were we to match Blacks and Whites for the same IQ at the later time, we would find that some individuals would have 0 less books and some would have 10 less books. Some Black individuals would be affected by the various influences depressing the Black population on average, and some would be unaffected. Now many people assume that the mean difference is due to variable-between influences; they typically don’t suppose that Blacks with an IQ of >115 are afflicted to the same degree that Blacks with an IQ <85 are.
Variable-between influences. Were the influences depressing the Black population variable, then Black individual who had higher IQs would, on average, be less affected, as less affected Black individuals would have higher IQs. Differential sibling regression is an index of depressive influence. If Blacks and Whites are matched for the same IQ, and the siblings of Blacks regress to a lower mean than that to which the siblings of Whites regress, we can reasonably conclude that both the matched Blacks and their siblings are depressed by the magnitude of the differential regression divided by 0.6. (The alternative is to argue that the unmatched Black siblings are depressed but the matched ones are not; the problem with the alternative is readily obvious: Typically, siblings of IQ matched Blacks are found to regress 0.6 SD below siblings of IQ matched Whites, when Blacks and Whites differ on average by 1 SD. Were we simply to posit a uniformly depression of 1 SD, we would get our differential regression of 0.6. However, were we to posit that Black sibs were variable depressed 0.6 SD (by factors which vary within families, of course) we could only explain 0.3 SD of the total depression (0.6 x ½ of our sibs). The other 0.7 SD would have to act either variably or uniformly or through some combination of the two with respect to the Blacks siblings. Whatever way we would get a differential regression of substantially more that 0.6. (e.g., uniform: 0.7 SD x 0.6 + variable: 0.6 SD.). Now, since siblings of IQ matched Blacks do show differential regression (i.e, they regress to a different mean) and since this regression is no less at the upper end of the IQ spectrum than the lower end, we can conclude that the influences depressing the Black population are not substantially of the variable-between sort."
Hence we need to search for common influences which vary within populations which fairly uniformly depress the Black IQ. Now, since these common factors vary within populations, their influences are constrained by within population heritability estimates.
Now enters the problem: The environmental variance within populations is mostly due to within family, unshared influences (e.g., influences which make MZ twins different.) A substantially smaller amount is due to shared influences (e.g., influences which make virtual twins – unrelated children reared together — similar) (1). As Jensen and others have noted, this is a point sociologists refuse to accept. If we choose to, we have to either explain the Black-White difference in terns of the meager shared influences (by adulthood) – or in terms of influences which are unshared by members of families within populations. As for the latter, It’s not readily clear how such can induce fairly uniform differences between families of different populations.
(1) It can’t be argued that heritability estimates are insensitive to shared influences since at younger ages and especially at young ages at lower SES levels, shared influences explain a large portion of variance. The problem is not with the heritability estimates, per se.
There are two possible escapes from the conclusion:.
(1) It could be that adult shared influences, in general, are underestimated
(2) It could be that adult shared influences for one of the two populations in question are
The theoretical grounds for the second possibility is that shared environmentality estimates seem to vary as a function of SES, being greater at lower SES levels (e.g., Tucker-Drob et al., 2011; Harden, 2007), and that Blacks have, on average, lower levels of SES. It is plausible, therefore, that shared influences have a greater impact in the Black population. This escape is blocked, though, by fact that the Black-White difference increases with SES (Rowe, 1994; Jensen, 1998). As a result, consideration can be restricted to upper SES individuals of both races and any race x SES x heritability interaction can be ignored.
If there is to be an escape, it must be along the first path. The major problem here is that the evidence converges on a low adult shared environmentality (Lee, 2009; Bouchard, 2009). This conclusion has been debated though. Nisbett et al., for example, write:
Shared environment effects are sometimes reported to be very low or even zero by adulthood (Bouchard, 2004; Johnson, 2010; McGue & Bouchard, 1998). If shared environment effects were really this low in adulthood, it would prompt pessimistic conclusions about the degree to which interventions in childhood would have enduring effects. One basis for the claim that shared environment effects are zero in adulthood is a review of three studies in 1993 by McGue, Bouchard, Iacono, and Lykken (1993), which has been frequently cited since (e.g., Bouchard & McGue, 2003; Rushton & Jensen, 2005a). But a large range of shared environment effects has been reported. Bouchard and McGue (2003) reproduced the 1993 review figure with its assessment of zero adult shared environment effects, but they also found a shared environment effect in excess of .25 for 16–20-year-olds. Johnson (2010) reported that shared environment effects are zero in adulthood (but did not provide sources) and in the same year reported a study showing that the shared environment effect was .07 for 17-year-olds in Minnesota and .26 for 18 year-olds in Sweden (Johnson, Deary, Silventoinen, Tynelius, & Rasmussen, 2010). Another recent study found shared environment effects of .26 for 20-year-olds and .18 for 55-yearolds (Lyons et al., 2009), and yet another found shared environment effects of .20 for Swedish conscripts (Beauchamp, Cesarini, Johannesson, Erik Lindqvist, & Apicella, 2011). A recent review of six well-conducted studies found shared environment effects in adulthood to be .16 on average (Haworth et al., 2009).
There is some misreporting here by Nisbett et al., though. For example, Haworth et al., 2009 provided shared environment effects of 0.16 for young adults (mean age 17), not adults. That figure is along with the young adult estimates given by Bouchard and McGue (2003) and Johnson et al. (2010) are utterly consistent with the claim that shared environmentality drops down to near zero by adulthood (i.e,., above age 25).
It might be, though, that the shared environmental effects are high enough, in general, to allow for a shared environment explanation of the between race difference. Perhaps, on average, shared environment explains 20% of the IQ variance in adulthood and the adult heritability is, in fact. only 0.55 (h= 0.55, C = 0.20, E = 0.25). (The amount of shared effect between races would have to be massive at 1.1 divided by the square root of 0.2 – but at least an explanation would be possible.) But here again we are constrained by the relation between SES and the IQ differences. Nisbett et al. forcefully argue that heritability is related to SES. So if the average shared effect is 0.2 by young adulthood and adulthood, it should be less for those at the upper SES levels. As a result, consideration can be restricted to upper SES individuals of both races and any shared effects in adulthood can be treated as insignificant.
References: Bouchard, 2009. Genetic influence on human intelligence (Spearman’s g): How much? Harden, 2007. Genotype by environment interaction in adolescents’ cognitive aptitude; Jensen, 1998. The g-factor. Lee, 2009. Review of intelligence and how to get it: Why schools and cultures count, R.E. Nisbett, Norton, New York, NY (2009). ISBN: 9780393065053; Sesardic, 2011. Commentary: An explosion without a bang; Tucker-Drob et al., 2011. Emergence of a Gene× Socioeconomic Status Interaction on Infant Mental Ability Between 10 Months and 2 Years Nisbett et al. 2012. Intelligence: New Findings and Theoretical Developments