Timescale for the catch-up of developing economies

Right now, the world is going through a dramatic economic transformation, whereby previously poor subsistence economies such as Brazil, China, India etc are rapidly catching up with the West's standard of living, with growth rates of 5-10%. This is largely attributed to successful government policy, abandoning things like central-planning and import-substitution, instead embracing property rights and market economies.

However, I'd like to explore why this is happening at the time it is. To my mind, it seems to be because it's a couple generations after decolonisation. During that time, a whole host of new states were created, often with political leaders that had never experienced government before. That meant the first generation of independence leaders basically ran economic policy poorly, causing stagnation. One generation later, people looked at the few countries that had done it right (Singapore, Japan, Taiwan etc) and copied them, thus the boom.

Do people agree with this analysis? If so, would the great catch-up always happen 40-50 years after decolonisation, even if decolonisation had happened in, say, in the 1920s and 30s rather than than the 60s and 70s?
 
most the emerging markets economy did not try to follow the examples you set above but decolonization that happened earlier and have the same effect right which economic growth but earlier seems unlikely
 
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