Monday, 29 February 2016

Assortative outcomes

The effects of assortative mating are finally starting to hit the mainstream. Here's the New York Times on growing class divisions driven by stronger assortative mating:
The Don Drapers of the world used to marry their secretaries. Now they marry fellow executives, who could very well earn more than they do.

With more marriages of equals, reflecting deep changes in American families and society at large, the country is becoming more segregated by class.

“It’s this notion of this growing equality between husbands and wives having this paradoxical effect of growing inequality across households,” said Christine Schwartz, a sociologist who studies the topic at the University of Wisconsin-Madison.

...Assortative mating is the idea that people marry people like themselves, with similar education and earnings potential and the values and lifestyle that come with them. It was common in the early 20th century, dipped in the middle of the century and has sharply risen in recent years — a pattern that roughly mirrors income inequality in the United States, according to research by Robert Mare, a sociologist at the University of California, Los Angeles. People are now more likely to marry people with similar educational attainment — even after controlling for differences between men and women, like the fact that women were once less likely to attend college.
So far so good. And they get this part right too:
Researchers say the rise in assortative mating is closely linked to income inequality. The two have increased in tandem, Dr. Schwartz, the sociologist from the University of Wisconsin, said: “People who are married tend to be more advantaged, and on top of that, more advantaged people are marrying people like themselves, so those people tend to be doubly advantaged.”
If the base model in your head is like mine, outcomes like income and employment depend on the interaction of ability and effort. Ability depends on genetic endowment and, to a lesser extent, childhood environment - at least within conventional bounds. If childhood environment is terrible, it'll munt ability. But otherwise, Caplan's results on the effects of environment hold.

The large story of the 20th Century, in America, is then one of sorting. America had huge gains in the early through mid 20th Century as agricultural productivity improved. Fewer kids were needed to take over farms, and fewer smart kids stayed in small towns. Agglomeration and the big cities ramped up. Now, agriculture is again very skilled, requiring exceptional management ability over very large operations. But it needs far fewer people.

You had huge income mobility over a broad meritocratic sorting period. But that sorting is now largely done.

Couple that with much stronger assortative mating you get lower income mobility, stronger class differences, and much stronger regional heterogeneity. Where the class differences also turn into partisan assortment, things start looking not so nice.

If every child's base endowment is the parents' mean with some reversion to population mean, then stronger assortative marriage drives greater real heterogeneity in child endowment. That can be compounded by that those parental endowments will also cash out into greater environmental heterogeneity. But there's an increase in the amount of income inequality you should expect: the closer the world is to pure meritocracy based on ability and effort, the more inequality you're going to get when assortative mating strengthens and where ability is heritable.

As fun aside, consider that the change in inequality in New Zealand is rather muted compared to the change in the US. If it's due in part to that New Zealand disproportionately sees out-migration at the higher end of the ability distribution, we should not be so quick to celebrate.

But where does the Times take it?
The effects could become more pronounced in future generations. Studies tell us that parents’ income and education have an enormous effect on children’s opportunities and achievements — and children today are more likely to grow up in homes in which parents are more similar than different.
That's largely an environmental story.

It's not entirely wrong, and it does make the case for school funding in America being more like school funding in New Zealand, with a strong egalitarian lean in the per-student funding scheme.

When I play with the Ministry of Education's funding formulas, our kids' school would get about 66%* $1000 per student more government funding if it were Decile 1 (poorest) rather than Decile 10 (richest). This is a baked-in part of New Zealand's system that is constantly missed: everybody talks about how high-decile schools get way more in parent donations, nobody mentions the strong progressivity of the government's funding formula.** If you grow up in a poor neighbourhood, your school's funding depends a lot less on the localised tax base. And school funding can matter.

But ignoring the role of trait heritability would be a huge mistake. You'll wind up underestimating how well some schools in poor communities are performing, overestimating how well schools in some rich communities are performing, and overestimating the extent to which any of it can be affected by transfers.

  • Cargo Cult Reading: In which books in the home is a better signal of what parents have passed down through their genes than of home environment.
  • Assortative Mating. In which people are Lancasterian goods and we all get the best spouse we can afford given our characteristics. 
  • Cinderella Men: assortative mating dynamics at the bottom of the distribution
  • Genetic Performance: Heritability of academic outcomes and test scores.

* The Ministry's calculator here is on the operational grant, not on staffing. So the percent difference will be much smaller than I'd initially written. Thanks to Chris, in comments, for the correction. He's also dead right that lower decile schools can't use funding to attract and keep better teachers, or at least not through pay.

** On this one, work by Chris Ball and others is great. They show how measures of inequality would change if you accounted for goods and services provided by government for free to everybody. But even that understates the case: they there take education spending as the average amount spent per student across the whole system rather than recognising the strong by-decile differences in school funding.

In the table below, market income is your pay; disposable income is your pay net of taxes and transfers; final income starts with disposable income and adjusts for the value of government-provided services like education. You'd shave a bit more off that final number if you accounted for that poor schools get dramatically more public money than rich schools. Remember: when folks quote Gini on market income as argument for greater redistribution, they're trying to deceive you. Existing redistribution mechanisms have to be accounted for when thinking about this stuff: final income then is the better measure.

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