Economic prosperity has had more to do with population control than actual policy in my opinion. As the Western countries prospered, the standard of living rose, and the educaton system mature and became more effective. Literacy spread and with it, the knowledge of family planning.
People from wealthier households are much more likely to have smaller families than people from lower income backgrounds. In countries like Russia and in parts of Eastern Europe, birth rates fell in the modern era because, while they fell on economic hard times, their populations were still well educated.
I would have to think that the current economic times would have to have a bearing on the lower birth rate. It is hard to start a family or add to a family if there is no income to support it.
I imagine that you could say that advanced countries have succeeded in population control. Just about every advanced country in the world has a very low birth rate these days. In fact, you could argue that countries have birth rates that are actually too low.
A good example of this is Japan. Japan's birthrate is so low that its population is going to start declining. This is a problem because there will be too few young people to take all the jobs and to provide money for the retired people.
One final note -- it is not really anything that the countries did that has caused this. People seem to want fewer children as their country gets richer. So the drops in birth rates are not the result of government policies.