So, I’m reading an interesting book due out in the fall from Princeton called The Altruism Equation, about the search for the evolutionary origins of altruistic behavior, and a section dealing with the influence of Thomas Malthus got me thinking about fertility trends and inequality. It’s a pretty well established fact that both within and between countries, wealth and fertility tend to vary inversely with one another. (A review essay I wrote for Reason a little while back considers some of the reasons for that.) Presumably contraception and abortion both make it easier for those differences to become more pronounced, as people who want to postpone childbearing are more able to ensure that they do. And census figures for the U.S. seem consistent with that: The fertility rate for women with household incomes under $20,000 looks to be about 1.4, while it’s closer to 1.0 for women in households with incomes above $75,000. Educational attainment looks to track about the same way. This may be skewed by age, of course, insofar as higher income is likely to correlate with age, which means those women have had more time to bear children. The relatively low fertility rate for women without a high school diploma (1.03), for instance, is presumably just a function of that group’s including lots of 15-18 year olds who simply aren’t out of school yet.

Still—and I’m sure plenty of people have floated this idea before, but it just occurred to me—it seems like this sort of trend would tend to make inequality in a society worse. Say you start out with a simple mini-society of 2000 poorer people and 2000 wealthier people, with respective fertility rates of 1.4 and 1.0. I just did a quick back-of-the-envelope calcualtion, and if I didn’t just screw up the arithmetic, that would give you, within three generations, a poor population of 686 people and a rich population of 250 people. (For folk worried about shrinking populations, by the way, there’s an interesting post at Catallarchy about how a generational shift to delayed childbearing might be artificially deflating fertility rates.)

Two obvious upshots. One, of course, is that the richer parents who had more resources to begin with are also going to be more able to concentrate their investment in their children. But let’s actually ignore that for the time being, and assume away class mobility so we just figure that the children of each class are going to end up with the same relative incomes. You’re still going to get much greater concentration of wealth, because the rich group that used to be half the population is now less than a third.

So pretend the relative incomes of people in the poor group and rich group stay constant across generations; we’ll just say the poor people always have $1,000 each, and the rich people all have $10,000 each. Now say you want to do one of those “Top X percent of the population controls Y percent of the resources” sorts of measures of inequality. Again, I did this super hastily, so I might’ve flubbed it, but what I got was: In the starting generation, where there’s 2,000 people in each group, the total social wealth is $22,000,000, and the top 10 percent (that is, 400 people from the rich group, at $10,000 each) have $4 million, or about 18 percent of the total. In the third generation, I get total wealth of $3,186,000, with the top 10 percent (94 people, still all from the rich group) with $940,000. So the top tenth now have almost 30 percent of the total wealth.

Obviously, this is a grossly dumbed down example, and the simplifying assumptions I’ve made render this an unattractive society in various ways: No class mobility, static earning potential for each member of each class, etc. Still, unless I’ve made some embarassing dumb arithmetic mistake, it’s interesting that you seem to get a big jump in one kind of measure of inequality just as a function of different fertility rates, without any kind of real change in the income dynamics of the society. That is, by stipulation, each person in each group is earning the same amount across generations; there’s no “shift” of wealth in the colloquial sense from poor to rich, but the share of wealth in the hands of the top tenth has grown dramatically.

I’m not sure what, exactly, the upshot of this ought to be—this is not the point in the post where I claim that we therefore shouldn’t be concerned about growing inequality. The most we might say in that vein, I think, is that ceteris paribus, inequality growth that can be traced to some kind of systematic unfairness is worse than other sorts, and at least on face, that’s not involved with inequality that’s just a function of different fertility rates. Of course, you might say the differential fertility itself is the product of unfairness, insofar as the reason the poor are having more children is that their opportunity costs for childbearing are lower, because they don’t have good prospects for going to college and pursusing more remunerative careers if they postpone starting families. (This is not the place to get into whether such differences really are per se “unfair”; let’s just say that there are plausible enough views on which it would be.) Still, to keep our concepts separate, it doesn’t look like this translates into an unfairness to the child generation. Remember, we assumed that each child cohort earns the same as their parents, and that this isn’t affected by family size. So it’s not that any particular child (at least in this imaginary scenario) has a lower earning potential because mom had another kid and, with her resources split, couldn’t send either to as good a school as she might’ve afforded for only one child. None of the kids who would’ve existed in the world where the poor fertility rate was 1.0 are any worse off, incomewise. And, a fortiori, it can’t be that this is unfair to the extra kids who wouldn’t have been born under the lower-fertility scenario

In the real world, where parental division of resources does play a role, it’s still a bit tricky what you’d say about this. Stipulate that the economic circumstances some particular woman faces are unfair, and that it’s because of these that she begins a family earlier, having two children rather than one. If she’d had better economic prospects, she’d have had only one child later, and it would have been better off than either of the children she actually has, both because she’d have more resources to devote to it, and wouldn’t have to split her food/clothing/education/general upbringing budget between two kids. But, of course, that would have been a distinct child. So we’re in one of those situations that Derek Parfit so elegantly proved are notoriously tricky, where we’re dealing with different numbers of distinct future people. So whatever unfairness is involved at the first stage, it’s at least non-obvious that it translates into unfairness to the actual members of the later generations.

Anyway, all this seems to suggest that insofar as we care more about inequality generated by unfair processes (and if we don’t want to say any process that generates inequality is ipso facto unfair) then maybe fertility-differential inequality should be less troubling in that one way than some other kinds. On the other hand, there are a lot of other arguments, both in terms of social stability and subjective satisfaction with one’s lot, for thinking we might want to worry a bit about growing inequality even if we don’t think it was produced by unfairness. So maybe I’d better just refrain from drawing any grand conclusions and toss this out as an interesting potential source of inequality, about which it’s not clear what we ought to think.