How can son preference persist?

In much of North Eastern India, there are 915 or fewer girls for every thousand boys - a sex ratio of more than 1.09 boys per girl. The persistence of such high sex ratios is puzzling, because it violates Fisher's Principle.

In most species, the ratio of males to females is approximately one to one. Fisher's principle explains why. In a society with fewer females than males, females achieve, on average, greater reproductive success than a typical male. Accordingly, any inheritable tendency that predisposes parents to producing females spreads. The number of females rises until, eventually, equality between males and females is restored.

So how can son preference persist?

One answer is population growth, combined with human institutions. Typically, men marry women who are younger than they are. Suppose that, every year, there are 9 girls born for every 10 boys. Given males' greater vulnerability to disease, this translates to say 9.5 women for every 10 men, by the time that people reach reproductive age. Now suppose the population is growing at a rate of 2 percent a year, men at age 28 at women marry at age 20. 

The relevant gender ratio is not between men and women of the same age, but between men and women 8 years younger than they are. In our example, taking into account the 2 percent growth rate, there are 9.5*(1.02)⁸ or eleven marriageable 20-year old women for every ten marriageable 28-year-old men. By varying the age gap between men and women, a growing population can readily accommodate imbalanced gender ratios. 

This is not merely a theoretical possibility. In a recent working paper, Hippolyte d’Albis and David de la Croix calculate a "missing brides" index. Taking into account age at marriage, fertility rates and sex ratios (all of which they take as given), they find that, in the high-growth Asian countries, groom to bride ratios are significantly lower than the ratios of boys to girls in the population. For example, in India, the marriage index is 1.043 grooms per bride, while in Pakistan the marriage market slightly favours males. Son preference only starts having an extreme effect on marriage markets when it is combined with low population growth and a preference for young brides: the most severe marriage market imbalances these authors document are in South Korea (1.194), China (1.139), Singapore (1.134) and Japan (1.092). 

Population growth and marriage institutions make son preference sustainable in some parts of South Asia. But what explains its persistence in East Asia, where it is leading to such large marriage market imbalances?

Until recently, son preference did not have disastrous consequences for reproductive success. Human cravings for sugar and fat did us no harm as long as we lived in an environment where these commodities were hard to obtain. These tastes only became a problem with the development of the modern food industry, with its Cheetos and potato chips, cokes and frappuccinos. In the same way, son preference made life miserable for millions of girls and women. Girls named Nakushi or "Unwanted." Girls who grew up being told "Raising a daughter is like watering your neighbour's garden." But it did not prevent girls from being born, or most of them from growing up and having children of their own. 

For ideas about son preference to change, they will must begin to have serious negative consequences for those who hold them. Even then may evolve only slowly.

A fascinating paper by Lena Edlund explores how such a change might happen, and its potentially adverse consequences for women. Edlund makes four eminently reasonable assumptions. First, parents prefer having unmarried sons to having an unmarried daughter. This does not require any resort to "culture". Men, on average, earn more than women, so an unmarried son brings more income into the household. Second, parents prefer to have a married son to a married daughter. If married children reside close to the husband's family, this is reasonable enough - and most societies, to avoid consanguinity (in-breeding), adopt either a "with husband's family" or "with wife's family" rule. Third, she assumes that parents prefer a married daughter to an unmarried son - people want to be grandparents. Finally, she assumes that when a woman is choosing a mate, "social position and wealth are important components of attractiveness" - but her model allows for the possibility that men, too, find status attractive.

Edlund's model predicts social stratification - low status parents will choose to have daughers, high status ones will have sons. Why? All else equal, parents prefer sons - married sons are better than daughters, unmarried sons are better than unmarried daughters. This creates a surplus of men in the marriage market. When men are in excess supply, the low status, less desirable ones will remain unmarried. Low status parents start to realize that any son they produce would not be good husband material, but observe that brides are hard to find. To avoid being burdened with a "leftover male", low status parents will, in Edlund's model, choose to have daughters. 

When there are excess males, the higher a man's status, the better his probability of marriage. High status parents, knowing that any child they produce will be a hot catch in the marriage market, are free to produce sons, and will do so - after all, a married son is better than a married daughter. Eventually an equilibrium is established, with low status parents producing daughters, and high status ones producing sons.

Edlund's dystopic vision is of a world where girls are raised in poor, low-status families, with less access to education and other resources, while boys are raised in plenty. She leaves it up to the reader to imagine what this would mean the relationships between husbands and wives, for girls' educational opportunities, for the status of women in society as a whole.

Her model avoids making strong assumptions about "culture". In her world, men have no objection to marrying higher status women. This fails to capture one of the sadder aspects of the Chinese marriage market: the poor prospects of highly educated, successful women. A story in a recent New York Times article particularly hit home to me:

Finding a Chinese spouse can be even more challenging for so-called leftover women, even if they often have precisely what the shengnan [leftover men] lack: money, education and social and professional standing. One day in the Temple of Heaven park, I met a 70-year-old pensioner from Anhui Province who was seeking a husband for his eldest daughter, a 36-year-old economics professor in Beijing.

“My daughter is an outstanding girl,” he said, pulling from his satchel an academic book she had published. “She’s been introduced to about 15 men over the past two years, but they all rejected her because her degree is too high.”

(It should be noted, however, that a male aversion to approaching more educated females is not a uniquely Chinese phenomenon - Hitsch, Hortaçsu and Ariely report something similar in this AER paper). 

Edlund images a world where, if "sex choice were freely available and the technology perfect, sex ratios might balance" - but the balancing would come through low-status parents choosing to have girls and high-status parents choosing to have boys.

What Edlund does not account for, however, is psychology. Overconfidence bias means that people mis-perceive their actual social status. In particular, people who are towards the bottom of the income distribution still perceive themselves as middle-class. Every parent's firm (but, in some cases, utterly misguided) belief that their son is not that loser who will end up alone and unmarried is another possible explanation of the persistence of son preference.

Modern sex selection technology has only been available for a relatively short period of time. It is only in the past few years that it has begun to have a noticable impact on marriage markets. If something can't go on forever, it won't. Let's hope that this is the case for son preference, or daughter preference, or any other kind of discrimination against children. 

Note: the discussion of Lena Edlund's work here has been revised and updated.

Comments

[Nick Rowe]

That interaction between Fisher's Principle, population growth rate, and age differential is really neat. Not sure if the geneticists would buy it though, if sustained population growth at any speed is a recent phenomenon?

[Colin Percival]

One question I've never seen answered in all the discussions about "missing girls": How many of them are the result of sex-selective abortion?

On the face of it this seems like a strange question -- just compare the birth ratio to the "normal" birth ratio -- but the gender of offspring is not simply a roll of the dice. Older parents are well known to have dramatically more female children, and researchers have also found correlations with stress (higher maternal Cortisol = more girls), beauty (more attractive mother = more girls), and income (wealthier father = more boys).

Certainly sex-selective abortion happens; but I haven't seen enough evidence to convince me that we can rule out the possibility that societal changes are resulting in *natural* changes in the birth ratio as well.

[Frances Woolley]

Nick - it is, isn't it, and it predicts that the situation in China will get increasingly insane for quite some time. The geneticists have various models where the Fisher principle doesn't hold - see e.g. Hamilton, W.D. (1967). "Extraordinary sex ratios" - it's a huge field of study. Surprisingly complicated, but kind of fun for an economist who is interested in marriage markets, as it's much the same thing.

[Frances Woolley]

Colin - we can't rule out the possibility that natural changes in the birth ratio are occurring. They probably are - birth ratios change in response to lots of environmental conditions. But we can rule out the possibility that natural changes are the only thing going on. This is especially true in India, in particular, where larger families make better tests possible.

The standard test is to compare families where the first child is a boy with ones where the first child is a girl. There's a recent paper by Almond, Edlund and Milligan that does this for Canada. For families with recent S. Asian background, having a first born girl significantly increases the probability that the second child will be a son. The effect is less strong in families which have been in Canada for more generations. It's hard to think of any conceivable biological process that would produce this result.

Also, the timing is off for it being natural changes - the changes in China especially are so huge, and have coincided almost precisely with the introduction of ultrasound+abortion.

[Frank Restly]

Curiousity,

The presumption is that all children are born in wedlock, that males age 16-27 either are abstinent or use birth control by social convention, government mandate, or religious dictum.

[mpledger]

The problem in India is that people are expected to marry within (or close to) their caste so same status people marry same status people.

You'd expect the value of women to increase with scarcity but people get inventive when resources are scarce. There was a case in India where the husband's brother was unmarried so he shared his wife with him.

If you believe all the "beautiful mothers have more daughters" stuff then you might be interested in
Of Beauty, Sex and Power
http://www.stat.columbia.edu/~gelman/research/published/power5r.pdf

[Shangwen]

Fascinating stuff as always. One of the things that researchers or journalists often speculate about is whether societies with excess males will become more violent--that should be happening now in China and India if that's the case, and I don't know if it is. There is some scepticism about this. Of course there is another correcting feature to look forward to: suicide is demographically most present in males 40-55, and among unmarried men of that age even more so. Since selective abortion began around 1985, it would also be reasonable to speculate that a large wave of male suicide would start around 2020 in those countries. That would be a more brutal version of Fisher's principle. So the problem of excess adult males in those countries may be one that only lasts 30 years rather than 60.

On the other hand, there's no reason to think that such a salient epidemiologic event would dissuade continuing selective abortion, indeed it may worsen it.

Thanks for writing about this, despite Stephen's brutal campaign of repression to silence you!

[Shangwen]

Also interesting, a number of the countries with excess males (China, SKorea, Japan) are already in the top 10 for suicide rates in medium to large countries.

http://en.wikipedia.org/wiki/List_of_countries_by_suicide_rate

[Frances Woolley]

mpledger "The problem in India is that people are expected to marry within (or close to) their caste so same status people marry same status people"

Yes and no. Men can marry down, women can't marry up, and so this means that individual marriage markets, especially at the top end of the caste system, can still operate very much in men's favour despite what appears to be sex ratios skewed in women's directions. There's some interesting research that looks at this in connection with dowry payments (this is a puzzle - why can dowry payments persist and even increase in the presence of growing sex selection).

Shangwen "One of the things that researchers or journalists often speculate about is whether societies with excess males will become more violent"

I know, and it's a bit tedious. I think this is something of an overstated worry for China for a couple of reasons. First, the "leftover males" have moms, who will cook for them and care for them and generally exert a civilizing influence. They're not like the young adult lions who get kicked out of the pride and go out and create havoc while looking for a place to set up a pride. Second, video games. The potential for displacement is absolutely huge.

But when I talk to my Chinese male students, who are often recent immigrants, I do get a sense that some are struggling with what it means to be a man.

mpledger "people get inventive when resources are scarce" - should that be "people" get inventive or "men" get inventive. Let's hope that young Asian women get inventive and work out some way to capitalize on their increased value!

[Guillaume]

Very interesting posts Frances, I thoroughly enjoyed them.

[Chris J]

This is rather disturbing. It does re-enforce the idea that gender equality (or at least an attempt at it) is important for society to be stable and prosper.

I remember learning in first-year Canadian history that women's suffrage came first to the prairies (and the plains states in the US) because families needed women's contributions in order to survive. This seems to jive with your statement "For ideas about son preference to change, they will must begin to have serious negative consequences for those who hold them. Even then may evolve only slowly."

[Wonks Anonymous]

Robin Hanson rounds up studies on gender ratios & violence:
http://www.overcomingbias.com/2012/01/sex-ratio-violence.html

[Rachel Goddyn]

I am wondering if China will look to North Korea as a source of marriageable woman.

[Frances Woolley]

Guillaume, thanks!

Rachel - I think that's already happening. Also if youth is valued in women - so women over 35 (say) are considered to be "not marriageable" - any country with an inverted population pyramid will have a shortage of "marriageable" women. So S. Korea, which has had below replacement fertility for a while, will also look to N. Korea as a source of marriageable women. Meanwhile savvy Canadian guys will tap into the supply of beautiful, successful professional Chinese women in their late 30s.

Wonks, thanks for the link.

Chris J - interesting.

[Giovanni]

"Suppose there is a unbreakable social norm that, for example, a woman cannot marry a man who is taller than she is."

By "unbreakable social norm" you don't mean a law or government regulation, right? You mean something more informal, perhaps even tacit. Some standard of behaviour to which people in a society reflexively adhere because it has been drilled into their heads from the time they were little kids. Something people in another society might find incomprehensible or downright silly. In other words, an idiosyncratic and contingent element of...er...culture.

[Nick Rowe]

"“My daughter is an outstanding girl,” he said, pulling from his satchel an academic book she had published. “She’s been introduced to about 15 men over the past two years, but they all rejected her because her degree is too high.”"

I've been thinking about this, trying to figure out the underlying model.

It would be true to cite the cliche that men are afraid of marrying a woman who is higher status than themselves, (and having a PhD would mean high status, presumably especially in China?). But that doesn't explain *why* men would be afraid. That fear could be very rational. Given hypergamy, where women want to marry a man of higher status than themselves, any man who marries a high status woman risks being despised by her family and friends, and ultimately by the wife herself, as a loser ("couldn't she have found someone better than him?"). If men don't care about status, only looks, but don't want to be despised as a loser, marrying a higher status woman is a bad risk, with no upside for the man. He would need massive amounts of "game" to give himself higher perceived status and make it work, and any man able and willing to do that amount of game could probably do better anyhow (in his eyes).

I can't quite figure out the exact model. Some sort of cross between the Market for Lemons and Groucho Marx, to explain why the market would fail to clear.

There was a news story recently about some Chinese tycoon offering massive amounts of money to find a man who would marry his daughter. And man who accepted that offer would be signalling he's a loser. It wouldn't be worth it, unless you're a loser.

The Obsidian blogs about trying to persuade african american women (who vastly outnumber aa men in education) to consider men who don't have degrees but who do have solid jobs.

[Nick Rowe]

I'm stuck in spam! (Feminist spam filter!)

[Frances Woolley]

Nick "But that doesn't explain *why* men would be afraid."

Yup, as Giovanni says, it gets back to "culture" which is fundamentally unsatisfactory.

There is the external social status/signalling thing, for sure (too hungry to work out that out right now, will think about it).

One could also write down a model of marriage where each person's say in household decisions, or each person's share of the surplus generated by the marriage, was a function of their outside options/voice/income, etc.

There's this sociological literature on "doing gender" - about how people will turn somersaults to make it seem as if they're conforming with standard gender stereotypes, because breaking the rules e.g. that father/husband knows best, that the husband is the provider, is so psychologically costly. This is also the story behind that Akerlof/Kranton literature on identity. (Who was that person who wrote that post about culture being a lousy explanation? Do we know her?)

About the tycoon's daughter - she actually came across quite well in the media interviews afterwards - saying "I'm touched that my Dad has done this, it's kind of him and it shows how much he loves me, but my girlfriend and I are very happy together, so please don't bother to apply."

[Giovanni]

Lemons? Signalling? Yikes! People...put down the textbook and back away from the blackboard!

I’ve got to use my Canadian hoser voice for this.

“Seems like a real nice girl…smart, educated, attractive, nice even. But I know the score here. There aren't a lot of men of her own income/education/status-group available and a lot more like me. If she marries me it’ll only be because she wants an insurance policy in case Dr. Right doesn’t come along. And if and when she should find her Knight in Shining Armour - of which there is some decent chance, considering the circles in which she travels - I’m out on my proverbial kung pao and back to Square Zero. On the other hand, if she could somehow credibly commit (where’d I learn that phrase?) to our marriage then it’d be a different story and I might consider it. But divorce laws being what they are, there’s no way I could count on her staying with me. Besides, why would I want to live with somebody reminding me every day that I'm the miserable SOB standing between her and True Happiness. So, me being kind of risk-averse (again with the $10 words...what the hell!)…think I’ll call up the factory girl next door and see if she wants to go for American food.”

[Jim Sentance]

Someone mentioned the odds of a second child being male if the first was female and so on. I'm wondering about the chances of a second child period given what the first is.

Also wondering what the bias is in various migration numbers. Are there serious imbalances in the number of males versus females moving here and the, between countries and urban/rural. And are the volumes enough to create or offset imbalances.

[Jacques René Giguère]

Colin Percival
In his famous book Sperm Wars

http://www.amazon.com/Sperm-Wars-Infidelity-Conflict-Bedroom/dp/1560258489/ref=sr_1_1?s=books&ie=UTF8&qid=1364496569&sr=1-1&keywords=sperm+wars

http://en.wikipedia.org/wiki/Sperm_Wars

Robin Baker even had the arguments, that in Britain, rich men wives had more sons but that their mistresses had more girls.

[Frances Woolley]

Jim "Someone mentioned the odds of a second child being male if the first was female and so on. I'm wondering about the chances of a second child period given what the first is."

Another way of assessing whether or not there's son or daughter preference is to look for "stopping rules." You must know some family that had 3 or 4 or 5 children of one sex, then finally had one of the other, and then the parents stopped? So, yes, if there is strong son preference and a desire for small families, then first born sons would be more likely to have no younger siblings, and first born daughters would be more likely to have younger siblings. Stopping rules are a bit harder to test for, as family size will be correlated with age of parents and income, which may in turn influence the gender of the children.

[Frances Woolley]

Giovanni - cut out the taller women part. Didn't need it. Better without resorting to "culture" as an explanation.

[Jim Sentance]

On stopping rules, my parents gave up on getting me a sister after three brothers.

[Jacques René Giguère]

Jim Sentance: my parents stopped trying for a girl after six boys. Her rationale for a daughter: after each new boy was presented to her, her answer was "Oh no! Not another one for the war!"
In the end , she had produced 6 potential draftees...

[Giovanni]

Frances,

My point wasn't that invoking cultural explanation should be avoided at all costs. Rather, I think it is perfectly acceptable - and, at times, indispensable - to invoke cultural factors in social research. The point is to be scientific about it - be clear as to what you mean, develop a way of measuring the thing that makes sense, recognize the correlations that might exist between the cultural factor and other potential determinants, apply an appropriate method to assess its relative importance.

I agree that simply chanting "culture, culture" is worthless, as worthless as it would be to say "economic reasons" to explain why the unemployment rate has gone up. I also agree that showing some element of culture helps explain behaviour should never be taken to imply the immutability of that element - doing this involves a huge logical leap. But I can also imagine instances of perfectly sound research showing - say, by comparing the documented experiences of different societies - that changing certain elements of culture is very hard.

[Frances Woolley]

Giovanni, so we aren't so far apart then.

Jacques Rene, Jim - I wouldn't know, having only sisters. I think there's something liberating about growing up in a single sex family, less pressure to conform with gender stereotypes (perhaps).

[Phil H]

Nick said:
"I can't quite figure out the exact model. Some sort of cross between the Market for Lemons and Groucho Marx, to explain why the market would fail to clear."

Wasn't Noahpinion just blogging about this? Could it possibly be that personal relations aren't well explained by a market?

Before we attempt any kind of explanation, though, it would be useful to know if there is anything at all to explain here. The "phenomenon" of "leftover women" certainly gets a lot of press in China, but that's because the media here has a rather grotty tabloid mentality. No-one seems to know if there actually is a problem for women with high levels of education who want to find husbands, because there are no good figures out there.

Right now, in the absence of much more information (for example, on exactly what factors mediate the difference between sex ratios and bride/groom ratios; what factors cause sex ratio imbalances in the first place; etc.), this is all more of a Rorschach test than serious enquiry. Even explanations which avoid "culture" in favour of individual demand still end up invoking "culture" - why do Japanese men want younger brides? It's just what They want. The discussion is icky all the way through.

[Jacques René Giguère]

Frances: 5 ( the sixth was much younger) young males all trying to out alpha each others is a good work-out for future life but can we call that liberasting?

[Peter T]

Frances - you might want to read the relevant bits of Sarah Blaffer Hrdy's book Mother Nature. Selective infanticide is quite common - and was very common in some parts of India. But the preference for sons is not universal - higher-ranking Rajput clans and some others strongly preferred sons - because daughters could marry up, but not down (so at the very top, here there was no higher rank available, daughters were very scarce indeed). The lowest castes preferred daughters (and demanded bride-price, not dowry). Son preference is much less marked or even non-existent among Christians, Dalits, Bengalis and in South India. The differences go back to caste rules and marriage rules.

So, in India, you can explain son preference by reference to the economic and other incentives structured by caste and sub-caste. But then you have to explain the structure - why caste is such a pervasive feature of Indian life. And for this, you go to, eg Louis Dumont's Homo Hierarchicus. And you are back with "culture" - in a very sophisticated form.

In China, with its patrilineal clans, village alliances and so on at the base, you still have to explain why patrilineality is the dominant form - unlike, say Europe (where it was historically much more mixed). And, again, you are back with "culture" - the persistence of patterns from the deep past that structure incentives.

[Frances Woolley]

Peter T - thanks for those references. Culture in a very sophisticated form is just fine!

There has to be some rule - patrilineality, matrilineality, or a mix. Perhaps it's just arbitrary - the flap of a butterfly wing causing...? Stigler and Becker would want to use the weather or environment or some kind of deep structural factor to explain it (see, for example, this paper by my former colleague Ingela Alger that explains the strength of family ties in various places by the harshness or otherwise of the environment http://www1.carleton.ca/economics/ccms/wp-content/ccms-files/algerweibull10.pdf).