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.