Strangely what waton said is the premis of the movie Idiocracy.
Educated couples waiting too long to start a family or choosing not to have children at all meant the poor and uneducated were the only ones breeding which eventually leads to a dystopian future world populated by the seriously vacuous and stupid.
It's a comedy of course and the issues it raises although absurdly reduced for comedic entertainment are intruguing complex modern issues.