Wednesday, March 08, 2017

Division Rules and Assortative Mating

 [Warning: This post assumes the reader understands the Principle of Comparative Advantage. Those who don't will find an explanation here.]

Assortative mating is the pattern of like partnering with like. A standard example is the tendency of men with college degrees to marry women with college degrees. It came up in a talk I recently heard in the rather different context of the tendency of elite law firms to have partners at similar levels of ability. To an economist familiar with the principle of comparative advantage that looks like the opposite of what we would expect, which started me thinking about why, in different contexts, assortative mating would or would not happen.

Consider a greatly simplified model of the marriage market in a world with the traditional division of labor between household and market production but without the traditional sexual division of labor. The world contains four people, two men and two women. One of the men and one of the women are high income earners—think of them as the college graduates. The other two command lower incomes on the market but are equally good at running a household. The two high income earners can each make $100,000/year, the two low income earners can each make $40,000/year. Any of them can produce household services, cooking, laundry, rearing children, whose cost if purchased on the market would be $60,000/year.

With assortative mating, the two high income earners marry each other. Both work, they purchase household services and are left with $140,000/year. The other pair also marry,  one works and one stays home, and they have an income of $40,000/year. The combined income for the two couples, net of the cost of buying or producing household services, is $180,000/year.

Suppose, instead, that each high income earner marries a low income earner. The high income earner works, the low income earner stays home. Combined income of the two couples, again net of cost, is $200,000/year.

The pattern is a familiar one in the context of trade. One partner has a comparative advantage in earning income, the other in household production. Dividing who does what accordingly can make both better off. The implication of that simple model is that men with college degrees should marry women without them and women with college degrees should marry men without them. That is not what actually happens. Why?

In the case of marriage, there are a number of possible explanations. Many couples meet in college. Educated men and women may get along better with educated partners. Educated men and women may prefer that their children be reared by an educated housewife or househusband.

I want to offer another explanation which is not limited to marriage, one that suggests why pairing would be assortative in some contexts, possibly including law firms, and not in others.

Add one more assumption to my model—that the income of each couple is split evenly between them. With assortative mating, the high earning couple get $70,000 each, the low income couple get $20,000 each. With mixed mating, each individual gets $50,000. As long as income has to be split evenly, the situation is stable, since neither of the high earning individuals would want to switch. Without that assumption it is unstable, since a switch to the mixed mating pattern with a 75/25 division of income in each couple makes everyone better off.

Generalizing from the simple model, we would expect to see assortative mating in contexts where differences among potential partners are large and pairs, or larger groups, are constrained to a roughly equal division, because the loss to the high value partner of having to share equally with the low value partner(s) outweighs the benefit of a more efficient division of labor. We would expect the opposite pattern where potential partners are free to vary the division between them.

Consider again the case of marriage. Husband and wife live in the same house, share the same meals and vacations. That limits, although it does not entirely prevent, an unequal division of consumption. Further, once they have been married long enough to have children they are locked into a bilateral monopoly bargaining situation in which any contract over the division of consumption is largely unenforceable.

Consider next the law firm. A law partnership is a worker run firm, although one where control is limited to a subset of workers. That fact limits the degree to which an unequal division can be maintained among the voting partners. So the prediction is that voting partners will be unwilling to recruit others who are substantially less productive than they are and unable to recruit others who are substantially more productive than they are. They will take advantage of comparative advantage by hiring non-voting members of the firm, whether non-partner attorneys or secretaries, who will receive a different, usually lower, share of the firm's income.  

Finally, consider the issue of immigration. It is in the interest of the population of a high income, high skill country such as the U.S. to admit low skill, low income immigrants due to the usual principle of gains from trade. For people who understand the relevant economics, the chief argument against doing so is that poor people will come not to work but to collect welfare. The solution offered by supporters of free immigration, the solution I offered more than forty years ago in my first book (Chapter 14), is that welfare should not be available to new immigrants. The response to that solution is that immigrants will eventually become citizens, at which point they will vote for income redistribution in their own favor. Hence, it is argued, we should admit skilled immigrants from India and China to work in Silicon Valley but not unskilled Mexicans to pick crops.

How accurate the final step in the argument is in the real world of 21st century America is not clear, but its logic is the logic I have offered for when assortative mating will or will not happen.


Anonymous said...

One other major factor: highly-skilled persons want their children to inherit a similar level of skill. Mating with another highly-skilled person is more likely to accomplish this than mating with a low-skilled person.

szopen said...

Another possibility is that assortative mating has nothing to do with economy, but with biology. After all, the pairs are not just paired based on income, but they are also more similar on several other axes.

Salemicus said...

The (alleged) rise of assortative mating has happened at the same time as home production has been de-emphasised. So the complementarities in production that you talk about have become less important, and penalise assortative mating less.

But you should also consider complementarities in consumption. It's not just that the pair are sharing a level of consumption, but the nature of that consumption is going to be shared too. And it's possible that has become more important over the same period. If I want to enjoy most of my consumption in terms of status goods like living in Manhattan, expensive holidays, etc, then I need to marry someone who thinks the same way.

albatross said...

There may be other benefits to like associating with like:

a. Pleasant interactions--it seems like it's more pleasant overall to interact with people who are about as bright as you are. Shared culture, stories, jokes, interests, and concerns are possible when you're all on more-or-less the same level.

b. There are benefits to having everyone in the office be reasonably bright. In some sense, any tools, software, instructions, rules, etc., at your workplace that apply to everyone need to be geared toward the least intelligent. It's possible that there are some global benefits when you don't have to keep mechanisms around in your workplace that will work out well for someone of below-average intelligence, because all your employees graduated from high-end schools.

Andy C. said...

The fact that mixed pairs have higher overall compensation seems to be off-point to me. Each individual choosing a mate is going to be advantaged by getting a highly compensated one. The highly compensated people in the marriage pool are going to have the strong negotiating position, and each individually will be better off seeking a highly compensated mate. The less-well compensated are often left with each other to marry. Total income is down, but each acts in their own best interest.

David Friedman said...


I think you are missing the possibility of side payments. The highly compensated person can offer the less highly compensated an uneven division of benefits that is still better for him than the deal he could get if matched with another less highly compensated person.

Andy C said...


I certainly missed the possibility of side payments to change the individual economic incentives. However, after consideration, I think they are not important in marriage in the US. Except in wildly disproportionate power situations like a mail-order bride, or in small traditionalist sub-cultures, I see a world of marriages where husbands usually earn a lot more and wives spend more of the money. And this is not just delegating the grunt work of shopping to a housewife -- the women have great say in the composition of spending. Bathrooms and kitchens are typically of much greater concern to women than men, and the cost of homes is driven up because they get their druthers. All generalities -- but don't they match your life experience as well?

David Friedman said...


I believe the paragraph of my post that starts "Consider again the case of marriage" is making precisely that point–that in the context of modern marriage there are serious limits on the unequal division of income, which helps explain the existence of assortative mating.

Ilíon said...

Should any of Mr Friedman's readers be interested, I have used Mr Friedman's link to his explanation of 'comparative advantage' as the starting-point of a mini-rant against 'protectionism'.