Uncertainty Wednesday: More on Sample Correlation under Fat Tails


This post is by Continuations by Albert Wenger from Continuations by Albert Wenger


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Last Uncertainty Wednesday, I wrote about how sample correlations are not meaningful under fat tails. Today I want to continue this line of argument in the specific context of the claimed relationship between country IQ and GDP. There is strong evidence that the distribution of GDP growth rates is in fact fat tailed

Why look at growth rates instead of absolute numbers? Because the whole argument has to be a dynamic one and not a static one. We can best see this from the following illustration, which shows the extraordinary growth of China’s and India’s per capita GDP.

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Over an 8 year period China’s per capita GDP nearly doubles and India’s grows by 50%. At the same time major developed economies such as the US and the EU are essentially flat.

When you then combine this with the large number of people in those countries, you can see the

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rise of China and India in the global total GDP rankings (ignore the projections into the future, but watch how China and India are not on the chart at first and then climb rapidly):

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This level of dynamism is easily possible when growth rates are fat tailed. But it also means that any static sample correlation on country IQ and GDP is completely useless. You either have to concluded that country IQ can change quite rapidly (which makes it a useless measure) or that GDP growth isn’t related to it in a meaningful way after all. Personally, I believe both to be the case, i.e. the former is an ill-defined measure and the latter is determined by changes in government and economic systems.