This is a great post from Jared Bernstein on income inequality that I wish you'd hear more. He writes:
"This sounds, and is, a bit weedy/wonky, but it’s a point that needs
to be taken more seriously among economists, journalists, and policy
makers who focus on trends in family income: it’s not necessarily
correct to adjust incomes for family size, because family size is
endogenous to economic conditions."
You would think this would also be of interest to people who talk about inequality a lot - like Don Boudreaux and Steve Horwitz - who also (I assume) agree with Bryan Caplan's enthusiasm for children and population growth.
When the earning potential of a family declines the size of that family is going to decline too, in response to the reduced earning potential. That endogenous response is going to understate shifts in earning potential if you adjust for family size, because families are accommodating to their income stream.
You don't just have to imagine the poorest families to see this, although it's a group we often focus on. Kate and I probably would have had kids three years ago or so if I didn't have plans to go for a PhD. We're not going to wait until I'm all the way out, but we definitely didn't want a toddler around when our income stream took a temporary nosedive*.
I've adjsted family income for family size in analyses before, but it was typically because I wanted to control for the resources of a given family. Even that, of course, has endogeneity problems but since neither family size nor family income was an outcome I was interested in it wasn't quite as big of a deal. But if you're looking at trends over time this could be very important.
* - in my earlier post on ability to pay, a lot of people talked about poor people accessing credit. Kate and I aren't even poor - what do you think the bank would say if I just went up to them and asked for a loan because we're having a kid and we really just need to make up the tens of thousands of dollars I lost by leaving the Urban Institute. I don't think I'd get it. They'll give me a loan for an actual underlying asset, like my house, but not for that. Credit rationing and credit constraints are real, and I was surprised how many people just appealed to accessing credit markets in the comment section of that post.