There have been a flurry of articles lately on the cost of raising an American child, including a NYT blog post. This old news to students of demography, I remember reading about this back in the 80s. In agricultural societies children are a net economic gain, in industrial societies the gain is less, and in post-industrial societies they are a net negative for parents.
I should add, by the way, that traditional evaluations of the cost of children underestimate the cost. They assume a healthy neurotypical child. A special needs child is vastly more expensive, and approximately 5-10% of post-industrial children are relatively disabled by 'autism' (whatever that is), low average IQ, schizophrenia, affective disorders and the like.
So this is old material, but I don't recall a theoretical framework explaining why child raising takes a larger and larger proportion of income as a society becomes wealthier. The answer, of course, is Baumol's cost disease.
Child raising is one of those tasks with minimal productivity increases. Indeed, as output requirements rise to meet the narrowing demands of a post-labor economy, productivity may be negative over time. Certainly much of the cost is related to education and health care, two domains with notoriously slow productivity growth. Baumol's work teaches us that as overall productivity and wealth increase, relatively low productivity labor will consume increasing fractions of total income.
This seems to be an obvious insight, but a cursory Google search didn't find any articles or posts connecting demographic transitions with Baumol's Cost Disease. Until now.