There's no tradeoff between 'quality' and quantity of kids

One of the key elements of human capital theory is the idea of a trade-off between having more, lower 'quality' kids and fewer higher 'quality' kids. That is: having more children and having less money to spend on their education, healthcare and so on, leaving them with less human capital (anything that makes their labour more valuable), or having fewer kids and having more money for all those things. You can have two high-achievers or ten low-achievers, the theory would go.

We know there was a demographic transition first in Northwest Europe then in all developed countries and even now some developing countries. This saw fertility crash down to where it stands now—only about replacement value (and much lower in some places like Japan and Russia). One theory holds that this explains part of the industrial revolution: parents have fewer kids but invest more in the ones they do have, leading to more smart tinkerers, scientists, skilled workers and so on—and faster growth and more wealth.

A new paper from two of my favourite economic historians, Gregory Clark of UC Davis, and his regular co-author Neil Cummins (I blogged on some of his other work earlier) of the LSE, tackles this question by looking at the mindblowingly productive surnames database they have already mined to effectively overturn the entirety of existing social mobility research.

The paper, entitled "The Child Quality-Quantity Tradeoff, England, 1750-1879: Is a Fundamental Component of the Economic Theory of Growth Missing?" (pdf, excerpts), fits into the usual Clark/Cummins mould. It's well-written, clear, filled with hugely interesting tidbits, and it overturns popular but flawed views. Here they argue that the Industrial Revolution and gigantic rise in wealth and living standards since the 1700s (or even the 1600s) cannot be down to a quality-quantity trade-off in kids because kids in bigger families had life outcomes indistinguishable from kids in smaller families.

A child quantity/quality tradeoff has been a central to economic theorizing about modern growth. Yet the evidence for this tradeoff is surprisingly limited. Measuring the tradeoff in the modern era is difficult because family size is chosen endogenously, and family size is negatively associated with unmeasured aspects of family “quality.” England 1770-1880 offers an opportunity to measure this tradeoff in the first modern economy. In this period there was little association between family sizes and family “quality”, and if anything this association was positive.

Also completed family size was largely randomly determined, varying in our sample from 1 to 18. We find no effect of family size on educational attainment, longevity, or child mortality. Child wealth at death declines with family size, but this effect disappears with grandchildren. The switch in England in the Industrial Revolution to faster growth rates thus seems to owe nothing to declining family size.

This isn't quite true for wealth, as they say; spreading inheritances among 10 siblings meant less for those 10 than if they had been five or two. But by the next generation (grandchildren of the original parents) this difference evaporated entirely. Isn't this a surprising fact when people claim that the children of the rich turn out rich because of the cash they inherit? It's just very very hard to pass wealth on through human capital investments (this seems to be one of the key truths of economics).

Most economics papers are not worth reading the whole way through but here I would definitely recommend it.