Why Is There A Catch-Up Effect?
When Western societies started to industrialize and move from poverty, growth was relatively slow. While GDP statistics were usually not collected, most modern estimates of growth during that era suggest that growth wasn't that much higher than growth today.
By contrast, growth in countries that now industrializes, such as China and before it many other East Asian countries have been much higher than in Western countries. Does that mean that East Asian policy makers are much wiser than 19th century Western policy makers? No, at least not necessarily.
The key reason why they industrialize so much faster than the first countries that industrialized is instead the catch-up effect. As the name suggests, this effect is involved with poorer countries catching up to richer countries. When the first countries industrialized they were the richest countries, and so they couldn't catch up to anyone, hence they didn't benefit from the catch-up effect.
But why does the catch-up effect occur? Mainly for two reasons. One is the fact that poorer countries today have all the modern Western technology available, and can thus go from pre-industrial technology to late 20th early 21st century technology almost immediately, enabling a far faster technological advance than was available in 19th century Western countries, something which in turn implies a much faster increase in productivity.
The other key reason is trade. When Western countries were at a similar stage of development, they didn't have large export markets in wealthier countries, and thus couldn't specialize in producing goods for those markets where they had a comparative advantage, as those markets didn't exist. By contrast, China for example, can specialize in producing for large export markets labor intensive goods where they due to their low wage levels have a comparative advantage.
If somehow it was possible to stop all technology transfer and if Western markets had been closed, China and other East Asian countries would have likely not grown any faster than 19th century Western countries did.
Another way of looking at the catch-up effect is to imagine two individuals that are equally talented, motivated and so on, but that one of them lives in New York in 1810 and the other lives in New York in 2010. Since the person living in 1810 didn't have access to computers, phones, TVs, subways, cars etc., and since the number of people he could have worked with and for was much smaller (both due to a smaller overall population in New York, America and the World, and even more importantly due to much worse transportation and communication systems), it is quite obvious that the person living in New York in 1810 would have a much lower standard of living than the person living in New York in 2010, despite not being intrinsically better.
In this analogy, 19th century Western countries are like the person living in New York in 1810 while China and other East Asian countries are like the person living in New York in 2010. The reason why the latter have it so much easier than the former are not really that they are really intrinsically better than the former, but that the latter work in a much more favorable environment with better available technology and larger markets that they can trade with.
Note however, that the catch-up effect is obviously not sufficient to achieve high growth. If a country is sufficiently mismanaged then they will remain mired in poverty despite the existence of modern technology and large open foreign markets. That is the case for nearly all countries in Africa as well as in varying degrees in certain Latin American, Middle Eastern, Asian and Eastern European countries. But if a country is relatively well managed than they will thanks to the catch up effect leave poverty much faster than was possible for a similarly well managed country in the 19th century and early 20th century.