That’s the intuitive justification for an exponential model (each additional increment of intelligence adds a percentage of the previous GDP), but I don’t see how this justifies looking at log transforms.
GDP ~ exp(IQ) is isomorphic to ln(GDP) ~ IQ, and I think log(dollars per year) is an easier unit to think about than something to the power of IQ.
[edit] The graph might look different, though. It might be instructive to compare the two, but I think the relationships should be mostly the same.
It’s worth pointing out that IQ numbers are inherently non-parametric: we simply have a ranking of performance on IQ tests, which are then scaled to fit a normal distribution.
If GDP ~ exp(IQ), that means that the correlation is better if we scale the rankings to fit a log-normal distribution instead (this is not entirely true because exp(mean(IQ)) is not the same as mean(exp(IQ)), but the geometric mean and arithmetic mean should be highly correlated with each other as well). I suspect that this simply means that GDP approximately follows a log-normal distribution.
I suspect that this simply means that GDP approximately follows a log-normal distribution.
This doesn’t quite follow, since both per capita GDP and mean national IQ aren’t drawn from the same sort of distribution as individual production and individual IQ are, but I agree with the broader comment that it is natural to think of the economic component of intelligence measured in dollars per year as lognormally distributed.
GDP ~ exp(IQ) is isomorphic to ln(GDP) ~ IQ, and I think log(dollars per year) is an easier unit to think about than something to the power of IQ.
[edit] The graph might look different, though. It might be instructive to compare the two, but I think the relationships should be mostly the same.
It’s worth pointing out that IQ numbers are inherently non-parametric: we simply have a ranking of performance on IQ tests, which are then scaled to fit a normal distribution.
If GDP ~ exp(IQ), that means that the correlation is better if we scale the rankings to fit a log-normal distribution instead (this is not entirely true because exp(mean(IQ)) is not the same as mean(exp(IQ)), but the geometric mean and arithmetic mean should be highly correlated with each other as well). I suspect that this simply means that GDP approximately follows a log-normal distribution.
This doesn’t quite follow, since both per capita GDP and mean national IQ aren’t drawn from the same sort of distribution as individual production and individual IQ are, but I agree with the broader comment that it is natural to think of the economic component of intelligence measured in dollars per year as lognormally distributed.