Actually, fertility rates below 2.11 children per woman result in shrinking population due to deaths before puberty, and yes, that's with modern health-care.
We in the USA our doing our part. We have a very high infant mortality rate, ranking in there with some of the third world countries. I know this fact defies conventional wisdom, but it is a fact. The theory for this is that many parents are too ignorant to avail themselves of pre-natal health care.