It's a vicious cycle, but historically what we've seen is that drops in birth rate follows economic growth, not vice versa.

Poor economic conditions tends to mean parents rely on children for both work and for care in old age, and also correlates to lack of access to education on family planning as well as lack of access to contraceptives.

There are arguments to be made about precise cause and effect, but this pattern has been known for a long time; pretty much every developed country went through it, and almost all developing countries are on their way through the same pattern (almost all have seen birth rates drop dramatically, to the point the world is heading towards dropping population numbers within the next century).