Lower birthrates follow better education, female emancipation, and equal opportunities. Even those who do not want to use contraception have smaller families now than the 12 or 15 they would have had a couple of centuries ago. You cannot impose population control before there is a good reason for people not to have a large family to help provide for them.
As a nation gets more prosperous and more organised to look after its weaker members, the need for the insurance of many children lessens.
But when the state has taken over the whole role of providing for everyone, cradle to grave, disabled or able bodied, hard-working or idle, the connection between producing children and the family working together to raise them to an age where they can help support the older and younger members is blurred.
I don't advocate leaving children to starve because their parents have no work, or exposing unwanted infants, but I do follow carboncopy's reasoning about China. That is not the way to go - but it did have a result!