"During the 2000s, highly educated women had higher fertility rates than women with intermediate levels of education. Importantly, this is a result of a substantial increase in fertility among women with advanced degrees who increased their fertility by 0.7 children, or by more than 50%"
"What can explain the rise of fertility among highly educated women during the period that saw the largest increase in the labour supply of highly educated women? We argue that the growing income inequality over the past three decades created both a group of women who can afford to buy services that help them raise their children and run their homes, and a group who is willing to supply these services cheaply."
They don't mention anything about birth control, which I found interesting.