I am currently reading both Poor Economics and Factfulness, and two seemingly contradictory statements jump out at me.
From Factfulness, and I am kind of taking this statement out of context, but it suggests that there is a quantity-quality trade-off between family size and children's educational level (independent of whether the mother is more educated):
Educated mothers decide to have fewer children and more children survive. More energy and time is invested in each child’s education.
Rosling, Hans. Factfulness (p. 69). Flatiron Books. Kindle Edition.
However, from Poor Economics, the authors also discuss studies on the same issue, and seem to suggest that there is no relationship at all:
Of course, these three studies alone may not be the last word, and there is certainly a need for more research, but for now, our reading of the evidence, contrary to what Sachs argues in Common Wealth, is that there is no smoking gun to prove that larger families are bad for children.
Banerjee, Abhijit. Poor Economics: A Radical Rethinking of the Way to Fight Global Poverty (p. 110). Perseus Books Group. Kindle Edition.
I understand that more research needs to be done on the "quantity-quality" trade-off. Poor Economics provides reference to the three studies it examined that found no trade-off, while I found a few studies online that supports the trade-off.
All the references I have seen so far are single-country studies. Is there a cross-country studies, across wide cultural and income regions, that can shed more light on this family-size effect? what are some of the latest development in this research?