Rich countries are having more children. The evidence doesn't say whether rich people in rich countries are having more children, or poor people in rich countries, or whether it's all sections of society in rich countries.

(I interpreted the title initially to mean that rich people were having more children.)

"No doubt all these social explanations are true as far as they go, but they do not address the deeper question of why people’s psychology should have evolved in a way that makes them want fewer children when they can afford more."

I've always explained this as so (I have no evidence for any of this): 1. People in different social classes have different inherent desires in life. Some people simply want a family and have no other ambitions. 2. Lower class people (or people that have more children on average) have a harder time delaying gratification on average. Delaying gratification is a skill very beneficial when attempting to be successful and is related to the ability to think ahead and visualize the future. Having this ability instills different desires in a person and may detract a person away from parenthood due to truly understanding how much of a commitment children actually are (20+ years of your life, hours a day). Having this ability also helps one realize the difficulty in caring for many children.

In Australia you get $4000 for having a child. No questions asked : produce baby, get cash. This has done wonders for the birth rate. It's actually a response to the problem of the baby boomers : they know they need more workers to pay taxes to look after them, and encouraging babies now will pay off in 20 years time when baby boomers are retiring in record numbers.