It’s well established that many ethnic group differences exhibit what is called a Jensen Effects, or a correlation between g-loadings and the magnitude of the group differences. It’s also well established that a test’s g-loading indexes its heritability coefficient. There is a perfect correlation between g-loading and the variance in a trait explained by genetic as opposed to environmental influences. This implies that, on average, environmental effects will induce ant-Jensen Effects. This situation appears to render difficult common environmental explanations for ethnic group differences. As noted before:
Obviously, a Jensen Effect could be environmentally accounted for, but the point is that an accounting for must be done, since only a subset of environmental influences can induce such an association and since the simplest environmental model would predict an anti-Jensen Effect (for example, as on the Flynn effect). To render more clear this latter statement: by the simplest environmental model, the environmental factors causing a group difference would be a random sampling of the within group cognitive affecting environmental factors, factors which, on average, have a greater influence on the less heritable, less g-loaded sub tests. That is, a random sampling of environmental differences would not be expected to cause a Jensen Effect, an effect which represents a correlation between within population genetic influences on tests and group differences. Thus, when a Jensen Effect is found, some environmental explaining is needed.
I also noted though that there were some ambiguities with regards to the relationship between environmental effects and Jensen Effects, such to make the reasoning above uncertain. Specifically, I noted that no one that I was aware of had actually discussed the association between g-loadings and specific biometric environmental components i.e., shared and unshared environment. I hypothesized that perhaps shared environment alone could induce a Jensen Effect and therefore that the Jensen Effect on ethnic group differences could readily be explained in terms of shared environmental differences. To explore this issue further, I lackadaisically reviewed the literature and came up with k=1 study, Luo et al. (1994), which recorded g-loadings and subtest variance components. These are listed below along with the correlation between these components and g-loadings.
As it can be seen, the Jensen Effect for heritability was modest to strong positive, for shared environmentality it was weak to modest positive, for unshared environmentality it was strongly negative, and for shared + unshared environmentality (i.e., environmentality) it was, of course, the inverse of that for heritability. So it’s probably correct that shared environmentality doesn’t tend to produce strong positive Jensen Effects. But, nonetheless, it seems to be the case that shared environment produces very different effects from unshared environment, which is interesting to know, at least, as far as these things go. Generally, the association specifically between shared environment and g-loadings warrants further exploration as this environmental component seems to be the more promising one when it comes to (environmentally) explaining clearly intergenerationally transmitted ethnic group differences (since environmental intergenerational transmission is by definition a shared environmental effect).
In short, when you decompose the association between g-loading and environmentality (1-h^2), you see that the strong negative correlation is being driven by unshared environment (e^2) as opposed to shared environment (c^2) or as opposed to by both components equally. While shared environment probably doesn’t induce strong positive Jensen Effects and therefore probably can’t explain the Jensen Effects on ethnic group differences, the effects that it seems to induce i.e, a weak to modest positive one, is not, at least in my opinion, such that a difference in shared environment can be definitively ruled out as a plausible candidate for explaining the highly g-loaded nature of ethnic group differences — if that makes sense.
Luo, D., Petrill, S. A., & Thompson, L. A. (1994). An exploration of genetic g: Hierarchical factor analysis of cognitive data from the Western Reserve Twin Project. Intelligence, 18(3), 335-347.