Sunday, April 7, 2013

Sex Ratios, Savings Rates, and Princeton Women

I'm sure by now just about everyone has read the letter to the editor in the Daily Princetonian, written by Susan Patton, called "Advice for the young women of Princeton: the daughters I never had." Her advice, in short, is to "Find a husband on campus before you graduate" because "you will never again have this concentration of men who are worthy of you." It is controversial advice, to say the least, and has sparked a veritable deluge of reactions by bloggers, journalists, and even Princeton alum economist Edward Glaeser.

By curious coincidence, a new NBER working paper appeared the same month as Patton's letter that takes her basic reasoning to more extreme implications. The paper, by Qingyuan Du and Shang-Jin Wei, is called "A Theory of Competitive Savings Motive." Patton, like the economists, has a model in her head of marriage as a two-sided market, in which both sides (males and females) act strategically to find an optimal match. The premise of Patton's advice, and of Du and Wei's paper, is that sex ratio imbalances in a pre-marital cohort affect the bargaining power of each gender, which in turn influences their optimal strategies.

In countries like China, where there are many more young men than young women, men (or households with sons) raise their savings rates to improve their relative standing in the marriage market. Du and Wei model this competitive savings motive and use simulations and cross-country data on savings rates, sex ratios, and other control variables to estimate its magnitude-- which they find to be very large. Not only does an imbalanced sex ratio cause a country's savings rate to be higher, it can also affect the global economy, since, given a world interest rate, a country with a more balanced ratio wants to save less than a country with an imbalanced ratio, so capital flows from the imbalanced-ratio country to the balanced-ratio country. As the authors explain:
When the country with an unbalanced sex ratio is large, this could have global ramifications. In particular, as the sex ratio rises, the world interest rate becomes lower. Other countries with a balanced sex ratio could be induced to run a current account deficit. Calibration results suggest that the sex ratio effect could potentially explain about half of China's current account surplus and the U.S. current account deficit.
In China, the sex ratio imbalance is a drastic and horrifying demographic fact, as Du and Wei explain:
In many economies, parents have a preference for a son over a daughter. This used to lead to large families, not necessarily an unbalanced sex ratio. However, in the last three decades, as the technology to detect the gender of a fetus (Ultrasound B) has become less expensive and more widely available, many more parents engage in selective abortions in favor of a son, resulting in an increasing relative surplus of men. The spread of technology started in the early 1980s and accelerated quickly afterwards...The strict family planning policy in China, introduced in the early 1980s, has induced Chinese parents to engage in sex-selective abortions more aggressively than their counterparts in other countries. The sex ratio at birth in China rose from 106 boys per hundred girls in 1980 to 122 boys per hundred girls in 1997.
Susan Patton, the Princeton mother, refers to a quite different sex ratio imbalance, one that afflicts Princeton women in particular:
Men regularly marry women who are younger, less intelligent, less educated. It’s amazing how forgiving men can be about a woman’s lack of erudition, if she is exceptionally pretty. Smart women can’t (shouldn’t) marry men who aren’t at least their intellectual equal. As Princeton women, we have almost priced ourselves out of the market. Simply put, there is a very limited population of men who are as smart or smarter than we are. And I say again — you will never again be surrounded by this concentration of men who are worthy of you... As freshman women, you have four classes of men to choose from. Every year, you lose the men in the senior class, and you become older than the class of incoming freshman men. So, by the time you are a senior, you basically have only the men in your own class to choose from, and frankly, they now have four classes of women to choose from. 
If smart women "can’t (shouldn’t) marry men who aren’t at least their intellectual equal" and also can't marry men who are younger than them, but smart men can marry younger, less educated women, then smart women find themselves up against an effective ratio that is not in their favor once they leave college. (As Hanna Rosin points out, for every two men who receive a B.A. in the United States, three women will do the same.) Young men and women in China cannot escape the imbalanced ratio, so they adjust their financial behavior to improve their marital outcome, taking the ratio as given. In other words, it's an exogenous variable in their optimization problem. Princeton women, in contrast, do not need to take an unfavorable sex ratio as given; it is a choice variable in their optimization problem. They can choose to benefit from a better ratio by marrying while they are still at Princeton, when vicinity and youth work in their favor. (Presumably they could also benefit from a better ratio by not getting so gosh-darned well educated that they "price themselves out of the market," is an unspoken implication--but I'm sure she does not intend to advise this.) (Also presumably they could enter PhD programs in economics and have a few more years of smart men in high concentration, but I'm sure she does not intend to advise this either.)

I'm not a Princeton woman, but I am smart, and a newly-wed, and an economist.  So I do more than my fair share of thinking about love and marriage and markets, though not (usually) simultaneously. I met my husband in my first year of graduate school (he was already out of school), but I don't think my newly-acquired optimization-problem-solving skills had anything to do with it. It certainly wasn't part of my plan. I think the marriage-as-market concept is useful on a macro level, because in the aggregate there are indeed consequences of imbalanced sex ratios, so papers like Du and Wei's are interesting and important. Demography is real, culture is real. They can be usefully incorporated, at least to some degree, into models. But I don't know how useful the marriage-as-market concept is on a personal advice level, from a mother to the "daughters she never had." It sounds funny and odd, just as it does when the economists try to factor love and emotions into the equation-- not their comparative advantage. Here's a gem from the paper:
Everyone is endowed with an ability to give his/her spouse some emotional utility (or "love" or "happiness"). This emotional utility is a random variable first period with a common and known distribution across all members of the same sex, and its value is realized and becomes public information when the individual enters the marriage market.

I would be more than happy to get advice from older female alumni from my college or grad school. But instead of life-optimization tips through an economist's lens, I'd much rather have the kind of advice that Patton thinks young women don't need. "For years (decades, really) we have been bombarded with advice on professional advancement, breaking through that glass ceiling and achieving work-life balance. We can figure that out," she claims. I have not been bombarded with that type of advice at all, (and don't expect to run across a model for optimizing work-life balance any time soon.) Those topics are precisely the areas where I think advice is still welcome and needed.

We didn't meet at Princeton.


  1. That's a great picture (and a great way to end an econ article)!

  2. Great post! The article on sex ratios and savings rates is really interesting.

    Also, I love this:

    "Also presumably they could enter PhD programs in economics and have a few more years of smart men in high concentration, but I'm sure she does not intend to advise this either."

    That would make an interesting advice column: "The PhD -- the new MRS degree."

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