I also want to put another two competing theories out there. Both are based on the idea, that despite all appearances, the relationship between GDP and national IQ is a linear one.
The first theory decomposes the data into three sections: The pre-industrial section with IQs below 80. The middle income trap with IQs between 80 and 95 and the developed world with IQs above 95.
The idea is that each of these sections has it’s own specific IQ-GDP relationship. In pre-industrial countries this relationship is quite weak, a linear fit with minimal slope. Then the relationship becomes very robust in countries that have the ability to adopt some of the innovations created by the developed world. As we have seen, a reason for this robustness might be that here the reverse causality is strongest. Again, this can be fitted by a linear function, maybe with a short transition phase. In the developed world the IQ-GDP relationship again loses strength, because all these countries not only create new innovations, but additionally are capable of immediately adopting any innovation by the other developed countries.
But why is this a better interpretation than the exponential fit?
We have seen that the exponential fit improves the overall correlation significantly. The three section theory says, that this is an artefact of the positioning of the three sections and not an attribute inherent to any of the sections.
The preindustrial section has a significant IQ-GDP correlation of 0.469, the exponential fit reduces it to 0.418. The developed section has a significant correlation of 0.599, which is reduced to 0.566 by the exponential fit.
Only the middle income section sees a slight increase of the correlation from 0.780 to 0.805. And even that slight curving might be explained away by these sections not being completely pure.
What the three section theory tells us, is that for preindustrial countries an IQ point is worth just 125 dollars. For the middle income countries its 1488 and for the developed countries 1886. The difference between the developed countries and the middle income countries is in that respect smaller than it seems, because the line of best fit in the developed world is not particularly robust. Instead the major difference seems to be an extra 10,000 dollars afforded to the developed countries, which may be due to being ahead of the curve in technology.