Thursday, April 09, 2015

The Rhythm Method and Population Growth Rates

In the process of composing a recent post, I did some rough calculations on the probability of pregnancy from a randomly timed act of unprotected intercourse. It occured to me that the same calculations are relevant to a different question—the effect on population growth rates of the Catholic position on contraception.

Catholic doctrine, as I understands it, permits the use of the rhythm method, avoiding intercourse during the woman's fertile period, but regards all other forms of contraception as sinful. Critics argue that adhering to that rule results in rapid population growth in Catholic countries, which they view as a major cause of poverty. In evaluating that argument, it is important to recognize that how useful a form of contraception is depends on what you are using it for. Contraception intended for family planning, to hold down the number of children to the number a married couple want to produce, does not need to be as reliable as contraception intended to permit an unmarried woman to have regular intercourse with no significant risk of pregnancy. 

As best I could tell by a little online research, there are about four days during a woman's cycle when intercourse has about one chance in four of leading to pregnancy, with a much lower chance on a few more days. Imagine that a married couple is having intercourse twice a week, with no attempt to avoid the wife's fertile period. That should, on average, produce a pregnancy about every four months, hence reproduction at almost the biological maximum. 

Suppose they are Catholics trying to hold down the number of children they produce by avoiding intercourse during the wife's fertile period. They do not do a perfect job of calculating the fertile period and keeping track of it, so one month a year they end up having intercourse during it. The result is one pregnancy about every four years. A woman cannot get pregnant when she is already pregnant and fertility is substantially reduced while she is nursing an infant, which reduces it to about one pregnancy every five years. About 15-20% of pregnancies end in miscarriage, so that makes it about one child every six years. 

Fertility starts to drop in the early thirties, declines faster in the late thirties. Since this is a back of the envelope calculation, I will assume that a woman marries at twenty and becomes infertile at forty. One child every six years for twenty years produces, on average, three and a third children. I am considering the situation in a relatively poor society, so about a third of children will die before they reach reproductive age. We are now down to each couple producing just over two adult children, hence a population growing very slowly—well below one percent a year.

I have left out a variety of complications. Some births produce twins, pushing the number up a little. Some husbands or wives are infertile and some women never marry or marry late, pushing it down a good deal. But the bottom line seems to be that, while other forms of contraception are more convenient, in particular make it easier to control the timing of births, the rhythm method is adequate to give married couples who want to have children a reasonably effective way of controlling how many they have.

Suppose we view Catholic doctrine not as moral philosophy but as social engineering. The obvious interpretation of the ban on other forms of contraception is that it is designed to discourage non-marital sex by making it unacceptably risky, while permitting married couples to engage in an adequate level of family planning.

This leads to another question—why have birth rates in at least some poor Catholic countries been much higher than my calculations suggest? One possible answer is that most using the rhythm method are doing it incompetently, either through careless calculation or inadequate willpower. Another, and I think more plausible, answer, is that most couples in such societies chose to have large families.

That fits with my view of a similar issue in a different context. Back when contraception and abortion in the U.S. faced significant legal barriers, the most prominent argument for legalizing them was to prevent "unwanted children." The implicit assumption was that most births to unmarried women were unintended, would not have occurred if the women had access to adequate contraception or, if that failed, legal abortion. As someone put it, "mistakes cause people."

If that assumption was correct, legalized abortion and the widespread availability of contraception should have led to a sharp drop in the non-marital birthrate. What actually happened was the precise opposite. In 1965, when Griswold v. Connecticut established a constitutional right to access to contraception (for married couples, but a case a few years later extended it to the unmarried), the rate of births to unmarried women in the U.S. was below 8%. It is currently about 40%.

The obvious conclusion is that births to unmarried mothers, for the most part, are not and were not unwanted. That explains why they did not fall. A possible explanation of why they instead rose can be found in an old article by Akerlof, Yellen and Katz or, in a less elaborate mathematical form, in Chapter 13 of my Law's Order (search for "Akerlof").


Karie, the Regular Guy's Extraordinary Wife said...

I have a small problem with your use of "the rhythm method" as it is an out-of-date term that describes using a calendar to count the days of fertility. The current method of family planning espoused by the Catholic Church is called "Natural Family Planning" and has to do with charting a woman's cycle by symptoms and by temperature readings (called the sympto-thermal method). A woman can predict with great accuracy when she is most likely to be fertile and when she will not be. It does take practice but can be taught from a young age (on-set of puberty) and will help women to know their own bodies and even help their doctors diagnose any fertility problems should they occur. I have had five children on this method. Only the last one was an "oops". Considering I have been using the method almost 20 years I think that's a pretty good fail rate.

Contraceptives also have the problem of suggesting to people that they can control their fertility. It allows offspring to become objects of desire rather than an outpouring of love. It has led to the "need" for abortion, IVF, and surrogacy and a host of other problems which the Catholic Church calls "The Culture of Death".

I know it sounds dramatic but this is a culture that believes it can control and eliminate suffering, but seems to be causing more rather than lessening it.

Dave Orr said...

People who work in this field think about this in a couple of different ways, but for contraception in particular, they track desired fertility, which is how many children a woman wants, and unmet need, which is how much unfilled demand there is for contraception.

Both those things vary across regions and times, and both matter a lot. It's worth noting that desired fertility negatively correlates with economic success, with the explanation being that as you become richer, children become more expensive and less valuable (because their marginal economic productivity is large when you're very very poor, and negative once you're rich enough).

None of that really much effects your point about catholic social engineering, but those might be useful terms if you want to know more.

David Friedman said...


How solid is the negative correlation? I remember reading an exchange long ago between Gary Becker and someone on the subject. Becker's claim was that if you controlled for contraceptive knowledge by looking either at a society where nobody had it or where everyone had it, the correlation reversed.

If you think of children primarily as productive goods, your argument works, but if you think of them largely as consumption goods, one might expect a positive income effect. And controlling for everything else that correlates with income might not be easy.

Unknown said...
This comment has been removed by the author.
Unknown said...

@Karie I think David's point was in relation to developing countries. It might be reasonable to assume that many poor people in developing countries have no access to thermometers. Whilst there are other indicators to watch out for, temperature is one of the better predictors of ovulation. If true, then it is likely that the method promoted in developing countries is the rhythm method.

Jonathan said...

The genetic imperative is to produce as many children as possible. However, what people want is to have children at will and not otherwise.

Assuming that genetic engineering will eventually give people control over what they are, I predict that in the far future both men and women will be totally infertile by default, but will be able to switch on when they want to: the reverse of the current situation. I don't know how long it will take to get there, but at least I have a view of the destination.

Whenever that happens, incidentally, teenage sex will cease to be a problem, and people will gradually stop worrying about it.

David Friedman said...

"teenage sex will cease to be a problem"

I think you are making the same assumption, in the context of teen sex, that I rejected in the context of non-marital sex more generally. Teen sex will still be a problem when a teen wants to have a baby and her parents don't want her to.

Power Child said...

@Dave Orr:

You said "It's worth noting that desired fertility negatively correlates with economic success, with the explanation being that as you become richer, children become more expensive and less valuable..."

This strikes me as a flawed explanation, and doesn't specify whose economic success, and whose desire for children, we're talking about.

Wealthy men often want lots of kids.* They can afford them, and because of their success and stability they don't have trouble attracting women who will bear all those kids for them.

Wealthy women, meanwhile, are more likely to be career-minded and feministic, and thus not only are they not as maternal by nature but they will also tend to see childrearing as getting in the way of not only their careers but their career-driven identities too.

*Lots of kids means lots of people to carry on your prestigious name, and it's an unmistakeable marker of success and vitality because it indicates to others that women want to bear lots of your children. I'm guessing the effectiveness of the marker decreases with each additional wife though.

Jonathan said...

"Teen sex will still be a problem when a teen wants to have a baby and her parents don't want her to."

Yes; but, if having a baby becomes a matter of completely deliberate choice, it's not the sex that's the problem -- it's the decision to have a baby.

Aaron said...

Sexual rates very greatly. Twice a week might be a fine average, but some couples slip into once-a-month or fewer territory, and some are multiple times a day. This is a variable that isn't accounted for in your calculations. If a couple is guaranteed to hit the edges of the fertile period, quite a bit more babies will be born.

onyomi said...

Could it not be that, by removing much of the cultural stigma against premarital sex, contraception, on net, ironically increased the number of unintended, out-of-wedlock pregnancies?

mdavid said...

Imagine that a married couple is having intercourse twice a week, with no attempt to avoid the wife's fertile period. That should, on average, produce a pregnancy about every four months, hence reproduction at almost the biological maximum.

The problem with this is that women are more sexually driven (with men they are attracted to) during their fertile period. Nature knows what it's doing here.