Ok, I think I should have written "international scale", I apologize for the confusion.
I don't know of any study on national level, i.e. of families in a single country. The only thing I know of are anecdotes and stories about very poor families having 5+ children.
Basically if you have two groups of American born, collage educated men, with of the same age then income positively correlates with number of children. But, if you compare collage dropouts vs. people that have PHD's then the PHD population makes more money and has fewer kids. So, education is a huge confounding factor.
We went from 14 being a reasonable age to start a family to 24 or even 34 being the 'reasonable age' that's a huge impact. But, ‘wealth’ as an independent factor aka adjusted for age, education, country etc becomes a positive factor.
PS: Historically, starvation also limited family size.
I don't know of any study on national level, i.e. of families in a single country. The only thing I know of are anecdotes and stories about very poor families having 5+ children.