Define the Policies of Education
Universal education--particularly universal education of girls--pays a two-fold benefit. Investments are more likely to be productive with a better-educated workforce to draw on; therefore investments are more likely to be made. Educated women are likely to want as a minimum as much education for their children and to have relatively attractive opportunities outside the home--and so birth rate is likely to fall.
It is indeed the case that developing countries of the world appear, for the most part, to be going through demographic transition faster than economies of today's industrial core did in the past 3 centuries. Therefore current estimates of the world's population in 2050 are markedly lower than estimates of a decade ago. A decade ago projected global population in 2050 was 16 billion or more; today it is 12 billion or less. This is in part at least because of rapid expansions in educational attainment in today's developing economies.
A high level of educational attainment also raises the efficiency of labor both by teaching skills directly and by making it easier to advance general level of technological expertise. A leading-edge economy with a higher level of educational attainment is likely to make more inventions. A follower economy with a higher level of educational attainment is likely to have a more successful time at adapting to local conditions innovations and inventions from the industrial core of the world economy. How large these effects are at macroeconomic level is uncertain. That they are there nobody doubts.
East Asian economies particularly provide illustrations of how uncorrupt and well-managed developmental states can follow macroeconomic policies which accelerate economic growth and convergence. These economies which have provided incentives to accelerate demographic transition and boost savings and investment have managed to close the gap concerning the world economy's industrial core faster than anyone would ex ante have believed possible.