Actually, they are. The birth rates in the USA/Canada and Europe have fallen to their lowest levels ever, less than 2 children per family.
And the rate continues to fall. These first world countries are not producing enough children and are, in fact, dying out. Slowly but surely.
I would say no to that. They're not dying out. They can always get population in from other countries if there is a lack of human beings. And this happens so often does it not. To the extent that it becomes difficult for others to enter the country so often.
Maybe culturally, there are different values. And the immigrants often times absorb some or a good portion of those values for better or worse from the Country they immigrate to. While they bring in their own values to the country and this can be seen in their community.
So in terms of child birth rate, there are always children being born who become citizens of that particular country. These children sometimes go back to their home country to be schooled back home so that they can come back for work or study opportunities later on.
Who doesn't want to live in a first world country who isn't from there. Where I'm from, almost half the people? maybe more. But if you're talking about the native population of the said first world country then it's a different story altogether.
Maybe people don't want that responsibility to raise a family and suffer that way. Not all are called for that life. And so many all over the world do a bad job in raising kids anyway. That many such as myself feel whether it is that necessary. This is something which is of my point of view.
Paul says it is better not to marry in His letters in the New Testament. Jesus Himself says that. So if someone is a Christian and unmarried and has no kids and is able to accept that life, maybe He or She should. Unless God has another plan for them and if God did He would reveal it to them.