The puzzle of declining family size in the face of rising wealth remains.
Since I'm currently steeped in Gregory Clark, let me throw in my two cents.
From Clark, we learn that in England:
1. Prior to the industrial revolution, the number of (surviving) children was higher for people with higher incomes. Clark describes this--misleadingly, in my opinion--as greater fertility among the rich.
2. Population exploded from about 1750 to about 1890.
3. Around 1890, the "demographic transition" set in, and people started having fewer children.
My model of this is that parents want heirs, not children. Until the industrial revolution, you had to have a lot of children in order to make sure that some would survive. On p. 92, Clark writes,
from 1580 to 1800 18 percent of infants died within the first year. Only 69 percent of newborns made it to their fifteenth birthday.
My explanation for the three facts above is as follows.
1. Rich people had more surviving children because they were able to take better care of children. There need not have been more births among the rich--just fewer childhood deaths.
2. With the Industrial Revolution there came a drop in childhood mortality, which took parents by surprise. For a few generations, people had more surviving children than they expected.
3. Once people were used to lower childhood death rates, they cut down on the number of children they decided to have.
I said that Clark's book could spawn a lot of Ph.D dissertations. Proving or disproving my conjecture could be one of them.