In my previous post, I tried to unravel life expectancy curves. The comments on this post were fantastic (thank you, readers!). They were so good that I decided to share some of the readers’ information and reply to a request.
First, I was asked if the mortality rates follow a “bath tub” shape. If you have taken a course on reliability, you have seen hazard rates. Many processes and widgets have a “bath tub” curve, meaning that there is some break-in failure (this is what a warranty is for), there is an extended period of time with a low incidence of failure during a widget’s useful life, and then there is wear-out failure. People are like widgets in this regard. Below is the CDC’s recent mortality estimates for men and women as a function of age. Do to low infant mortality rates, there isn’t much of a tub there, but mortality does decrease for the first 10 years of life for girls and boys (using reliability terms, this is break-in failure). After the age of 10, the mortality curve for boys dramatically rises and diverges from the curve for girls.
The bathtub curve for mortality
Second, the link between women’s life expectancy and childbirth is quite real. The figure below from the Red Blog (courtesy of Hans Rosling) captures international life expectancy rates as a function of the number of children a country has, on average. Michael also points out that the growing life expectancy disparity between men and women reflects this: “As family sizes grow, life expectancies drop. It seems to me that the widening gender gap from 1920 onwards tends to support your notions about childbirth reducing female life expectancy.” Hans Rosling talks about this figure in the must-see video at the bottom of this post.
Smaller families = longer lives
David Smith found an entire article about life expectancies in England in 1550-1800. Life expectancies were between 35-40. The figure below is not differentiated between gender, but it is indeed fascinating. The article itself discusses childbirth quite a bit, although not so much on the relationship between childbirth and life expectancy. They note that lower life expectancies were caused by poverty and lack of nutrition, which in turn encouraged people to have fewer children.
Life expectancy in England
The following video of Hans Rosling talking about life expectancy over time is a real treat.
Punk Rock Operations Research 
January 27th, 2012 at 12:33 pm
Here is a lot of mortality data for you to play with: http://www.mortality.org/. It needs a registration, but it isn’t onerous.
If you take the logarithm of the mortality rates (which is what us demographers usually do), you should see a more pronounced bathtub effect. If you superimpose several years of the same population, you can see it get lower. Another nice graph is to take the logarithm of the death rate at a given age on the y-axis and the year on the x-axis, for a single population. If you superimpose several ages (do age 0-5, 20-25, 40-45, 6-65, and 70-75) you will see the different rates of mortality change highlighted (infants have a much faster decline etc.)
Finally a note on the relationship between mortality and fertility. This is the topic of Demographic Transition Theory: http://en.wikipedia.org/wiki/Demographic_transition. It would be simplistic to say that “drops in fertility lead to drops in mortality” or vice versa. There are two main ideas that people think about their relationship: (1) Lower mortality means parents need to have fewer kids in order to have x number of survivors. Here mortality change causes fertility change. (2) The conditions that produce lower mortality (public sanitation, safer jobs, etc) also produce more expensive children (education and a later entry to the workforce) so fertility drops. Here social conditions cause both. Fertility drops generally follow mortality drops in time, so causality doesn’t work in the fertility -> mortality direction.
Also, higher poverty is usually associated with *more* children, not fewer (so the relationship described would be, ahem, wrong). Perhaps the referenced article makes a good case, but that relationship is the opposite of what they teach in Demography School.
Fishing causes for demographic trends is really hard (e.g. lower childbirth -> lower mortality), since so many things are happening at once (higher nutrition, sanitation, education, war, social norms about birth control/ withdrawal, etc, etc).
(I think mathematical demographers and OR types is a synergy waiting to happen….)
January 27th, 2012 at 12:41 pm
Thanks, @Fork. Your claim that “higher poverty is usually associated with *more* children, not fewer” is correct. There are two issues here. Here are my non-expert opinions.
1. In England, I think the lower life expectancies that occurred during periods of poverty are caused by increased mortality in children (if people have fewer children but they survive, life expectancy would stay the same or go up). So we are in agreement there.
2. What you are talking about is an aggregate analysis of many countries. In England specifically, this author noted that fewer women had children during periods of widespread poverty. This figure of England, however, represents a single country changing over time, resulting in a localized response to the economy. Here in the US, the fertility rate has dropped in the past few years since the recession began. So, I think you gave the right answer to a different question, but you may know better here since I have not gone to demography school.
Thanks for the link to more mortality info. I can’t wait to get started.
January 27th, 2012 at 12:56 pm
Thanks @Laura,
1. Yes.
2. This is interesting. I think about it in terms of long- and short- term relationships (a structural change versus a response holding structure constant). Long term poverty (Afghanistan) usually creates higher fertility usually, since it changes the equilibrium structure in terms of costs and benefits of children. Short term poverty (a recession in the US) usually pushes fertility down in well developed countries.
The control on population in pre-transition populations (and all non-human populations) is believed to be “Malthusian” — population leads to food shortages, food shortages lead to mortality, mortality leads to a drop in population. In post-transition populations (France in early 1800s led the way, btw), fertility drops are the way population is controlled.
More summary datasets can be found here: http://www.prb.org/Publications/Datasheets.aspx
(I think the above is appropriate for a blog, but if you want to contact me offline, I would be interested. I could reply this weekend. I am ABD in this stuff and think we should be working with OR folks a lot more than we do…)
January 27th, 2012 at 1:38 pm
@Fork: Thank you for the references and comments. You are awesome.
January 27th, 2012 at 5:31 pm
Life expectancy v. fertility may be a case of proxying: poorer countries (which may be more likely to have both higher child mortality rates and greater use of child labor) may tend to have both higher fertility rates and lower lifespans (due to general quality of living issues, not specifically due to fertility).
Also, I’m not sure higher marriage rates would close the male-female life expectancy gap, which I attribute to nagging (which primarily goes in the direction of female nagging male, and probably increases after marriage).
January 28th, 2012 at 3:51 pm
Great post. I like the bathtub graph. I always think about that when I hear people suggest that life expectancy will eventually be 130 years or something asinine like that. The increase in life expectancy that has occurred over the years has resulted from what actuarial textbooks call “the rectangularization of the life curve.” That is to say, the right hand side of the bathtub has become increasingly more vertical over time. But the de-facto limiting age for human life is and has always been something like 110–cases of people living beyond that age are exceedingly rare. So when someone says that technology will make us live forever, I like to point that out 🙂
January 28th, 2012 at 8:51 pm
@Mike N: Thank you for your insights here. I hadn’t thought about what a limit on life expectancy would be.