One of the great comic writers or journalists of the past century might not be thought of as quite the place to find an economics lesson, nevertheless it is so:
"This is the first time a newspaper article was started in brackets. Innovation, you see. The homeric task of creation. Bringing into being a thing hitherto not here, much more exhausting than building pyramids in Egypt."
And there we have the explanation of why the poorer countries should be growing faster than the richer. For we lucky enough to be in those rich countries are up and around the limits of the technological envelope. For economic growth to occur we have to do that homeric creation thing, work out how to add more value through some process or another.
The poorer countries - a useful definition of being poorer being not at that limit of the technological envelope - can copy what is already being done elsewhere to add value and thus growth is easier. Or at least should be easier.
In one sense this is what has been happening these past few decades as our beloved neoliberal globalisation has been spreading. It should be true that poor countries grow faster than rich. It should be that global inequality falls as this happens. Back when we were trying to plan that global economy, to plan those local and poor economies as so many did, it wasn't happening. It's since we've stopped that planning and direction, allowing markets to take much more of the strain, that what should have been happening has been.
Or as we might put it, that neoliberal globalisation has been more about not doing things to stop it than anything else.