Well, there has been a long running and, in terms of reduced numbers in the population, scheme in China. And the numbers talked about there are huge - ie impact on a global level.
For the relative consumption of populations is not static - when I was young China was still under Mao and consumption was very low. Capitalist China's consumption explosion was then unthinkable. I should imagine there will be such shifts in the future - it takes decades, but so does the impact of population.
Population control is always the elephant in the room - it's a direct contradiction to the UN Convention on Human Rights in terms of freedom to found a family. Because it does come down, eventually, to enforced control if an actual difference is to be achieved. The reasons for wanting children, and how many children are wanted and how many are actually had is even more slow moving - and after the impact of the first availability of contraception doesn't seem to decrease much. But if your children are your pension, and many children do not survive, then you'll keep having them until you have two or three strapping, family oriented teenagers - it's the prudent thing.
In China, when the Government became involved, it led to fertility quotas, forced sterilisations and forced abortions, plus fines and other sanctions. That was the level of means required to achieve the end.
Without compulsion, the effects will remain uncertain; with compulsion, it is surrendering control of bodily functions to the state (and the Chinese example impacted on women far, far, far more than on men).
Personally, I think this is an area best left to charitable endeavour and bodies such as UNICEF. There is a lot of good work done in this area, and it can readily supported in choice of charities to which one chooses to donate.