In economics of economic growth, it is often seen that countries have catch-up growth, called the advantage of backwardness. We can see this in OECD using GDPpcppp numbers. 
However, looking at the world at large for the same period (2000-present), the picture is not so clear. R2 dropped from 52% to 9%. Looking at the plot, most of the dots that didn't grow as expected are Africans. It's another example of OECD fallacy, one can get substantially wrong ideas about how the world works by only looking at a subset of mostly European, above average countries.
We can see the role of national intelligence here. A simple way is just splitting the data into some groups. Higher IQ countries show much stronger convergence, and the low IQ countries grow quite slowly. This is essentially the story of how Asian tigers had strong economic growth starting poor, including China.
These slopes also show us the interaction effect. Economic growth is the fastest if you are both poor and smart, since you can quickly copy and adopt others' technology and improve upon it. We can plot this model indirectly this way.
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