The economist article makes it seem like there's a lot of rigorous empirical evidence behind this result, but it is a fundamentally theoretical result.
Basically, the authors come up with a toy model that, given a long list of assumptions, produces the reported result.
They then test these results by running a simple cross-country regression with no time dimension and a sample size of around 300.
I don't place much stock in these kinds of studies. Empirically speaking, there are just too many confounds in cross-country studies for them to be convincing. Theoretically speaking, the assumptions are highly unrealistic for all the reasons that have been said before. With a little bit of ingenuity, these models can be made to say just about anything.