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Fertile Myrtle and the Most Important Statistic...In the World!

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

Dr. Eric Gaze
Director of the QR Program
Bowdoin College

Numb: In 2007 there were 4,317,119 babies born in the U.S.

Number: In 2007 there were 4,317,119 babies born in the U.S. meaning 14.18 births per person or 69.5 births per 1,000 child-bearing women.

Numbest: In 2007 there were 4,317,119 babies born in the U.S. meaning 14.18 births per person or 69.5 births per 1,000 child-bearing women, defined as a women aged 15-44 years old. At this point in time the average woman in the United States can expect to have 2.12 babies over the duration of her child-bearing years. Preliminary data for 2008-09 suggest these rates are falling for the first time in this decade exactly as the economy has experienced a downturn.

Calling something the most important statistic in the world certainly is an attention grabber! George Friedman in his book, The Next 100 Years, makes this bold claim about the total fertility rate, which is derived from the birth/fertility rate. Simply put the total fertility rate measures how many babies every woman can be expected to have over her lifetime, on the average. Right now the total fertility rate in the United States is 2.1 babies per woman over her lifetime. This is one of those statistics that is easy to grasp on first glance but devilishly complicated once one stops to think about it. For starters how in the world would someone actually go about calculating this number? The birth/fertility rate is trivial by comparison, just take the total number of babies born in a given year and divide by the total number of people or child-bearing women. There is a little confusion out there regarding the difference between birth and fertility rates, as discussed below, but their calculation could not be more straightforward (assuming of course someone has bothered to count all the babies/people/child-bearing women for you!). The accepted definition of "child-bearing woman" is any woman aged 15-44 years, although our tables will immediately contradict this definition and extend this age range a bit. This does not do much harm, since women outside this range rarely have children, but is disconcerting to those of us who appreciate a good definition!
The National Vital Statistics Reports [NVSS] published the following table:

Table 1. Number of births, birth rates, fertility rates, and total fertility rates, by race and Hispanic origin of mother: United States, 1990, 2000, and 2001

[Birth rates are live births per 1,000 population in specified group. Fertility rates are live births per 1,000 women aged 15–44 years in specified group. Total fertility rates are sums of birth rates for 5-year age groups multiplied by 5. Population enumerated as of April 1 for 1990 and 2000 and estimated as of July 1 for 2001. Rates for 2000 and 2001 have been revised for this report and may differ from final rates previously published.]

Gaze Birth Rate Table 1 Image

Notice how the Total Fertility Rate is ostensibly given as total number of births per 1,000 people: "sum of birth rates," when we shall see they actually sum the fertility rates for this statistic. Thus the 2,034 is implying 2.034 births per woman over her lifetime, in the United States in 2001. The reason the total fertility rate can claim to be the most important statistic in the world is that it answers a very interesting and pertinent question.

How many children must every woman have over her lifetime to maintain a stable global population?

This is a good question that I personally never thought about before, and one that is fun to ask your students to answer while working in groups. To some the answer comes readily with a little mental effort and seems obvious, every woman must have 2 children over her lifetime in order to replace herself and her mate. There are subtleties involved however which can lead many of the groups to go round and round without coming to a consensus. Most importantly, the sex ratio, male to female, of the offspring needs to be 50-50. An "Amazonian" world where there are only 5 male births for every 95 female births, will certainly lead to a population explosion, just as only boy babies is a certain road to extinction. It is interesting to think about how the 50-50 sex ratio is optimal from an evolutionary standpoint. Actually, don't think about that, I'd like to see if my students can figure it out and maybe publish an article. Our world has a slight preponderance of male babies and thus the answer needed for a stable population would have to be above 2. Another complicating factor is infant mortality rates. If many females die before they have a chance to contribute their 2 babies then that should raise the number even more, unless of course many boys are dying as well which might offset the replacement rate; but the boys all will die sometime so maybe that doesn't matter. Yikes! Most demographers would answer the question with a total fertility rate of 2.1 babies per woman over her lifetime needed on our planet right now to maintain a stable global population.

It is necessary that we are talking about global rates so that immigration does not factor into this as it does for populations of individual countries. The United States is one of the only first world countries which actually has a total fertility rate close to the magic 2.1 with Iceland being the other exception for obvious reasons...(what else is there to do?). Most European nations hover around 1.3 babies per woman over her lifetime, but immigration has thus far kept these populations growing for the most part. Italy is a notable exception with a current annual growth rate of -0.019% and a projected population in 2050 to be 20% less than it was in 2000 (www.nationmaster.com). Russia is also experiencing population decline due to a lack of willing immigrants with an annual growth rate of -0.474%, putting it 229th out of the list of 236 countries in this category! The "Iron Curtain" tourism campaign just never took off for them. This brings us to the burning question of what is the current total fertility rate for the world? In 2009 it is estimated to be 2.8 babies per woman globally. In 1970 the rate was a whopping 4.5 babies per woman over lifetime! This is a massive 40% drop, and has led to headlines such as "Heading for Extinction" in the March 23, 2009 USA Today. Pundits refer to this now as the "Birth Dearth" and public policy advocates like George Friedman are predicting that countries will begin actively seeking immigrants in the very near future to work for the aging resident populations.

For the children being born into the aging first world countries, this is going to present them with fantastic opportunities. There is going to be less competition to get into the best schools and jobs will be so plentiful that governments will need to recruit labor from less developed nations! This sounds like something out of Malcolm Galdwell's bestseller, Outliers, which tries to make the point that success is due to a lot more than just being born with certain talents. It comes mostly from hard work and rare opportunities that we take advantage of, like being born in the Great Depression. This is so counter-intuitive even to myself as I write this that it explains why Galdwell's books are so popular. Yes being born in the Great Depression was fortuitous! It was fortuitous chiefly because so few other babies were born during this period that these children moved through life with less competition and more attention to their own development. They were like an inverse baby boom, the baby busters, just as this generation of babies is shaping up to be. Imagine if the global total fertility rate actually falls below 2.1, the replacement threshold. Population pressures on the environment and dwindling resources will all be lessened! We might actually be able to afford waterfront property again!

So how is this most important statistic in the world actually calculated? Table 1 gives us the instructions for how to calculate the total fertility rates using age specific data from Table 2, by summing "birth rates for 5 year age groups multiplied by 5." Birth rates, we recall, are babies per 1,000 people, but we want babies per woman so we need to use what they call the fertility rate not the birth rate.

Table 2. Births and birth rates, by age, race and Hispanic origin of mother: United States, 1990, 2000, and 2001

[Rates are per 1,000 women in specified group. Population enumerated as of April 1 for 1990 and 2000 and estimated as of July 1 for 2001. Rates for 2000 and 2001 have been revised for this report and may differ from final birth rates previously published.]

Gaze Birth Rate Table 2 JPEG

Notice how the rates for each year are actually the fertility rates in Table 1 above but here are referred to as birth rates, so even the experts can screw up and add to the confusion surrounding these numbers! If we add the fertility rates in the table for the age specific groups below, and multiply by 5 we do indeed get the number 2,034 that we saw in Table 1. Let's think for a bit about why this makes sense. We are trying to calculate how many babies a hypothetical woman would have if she were to live her entire child-bearing years with the given fertility rates for 2001. She of course cannot do this because as soon she ages one year the fertility rates will all change, which is why she is hypothetical. So she spends her years from 10-14 with the chance of having a baby in any of those years given at 0.8 to 1,000 which is a 0.08% probability. Thus a million of these women will contribute 800 babies per year or 4,000 over the 5 years. I am using a million women so we have nice big whole numbers to work with, not messy decimals. From 15-19 years of age these million women will contribute 45,300 babies a year, for an additional 226,500 babies over the 5 year period:
 Baby Ratio per 1, 000, 000 women

Gaze Birth Rate Table 3 JPEG

Continuing in this fashion we get the sum:

Baby Sum per 1,000,000 Women

Notice how the 5 year fertility rate is assumed constant for each age group although for 15-19 year-olds they do break it down further for us with 15-17 year-olds having a rate of 24.7 comparing to 18 and 19 year-olds' 76.1 babies per 1,000 women each year. Can you figure out how they got the 45.3 for the entire 5 year cohort in this age group?
Now since the preceding has been so simplistic I would like to close with a paradox, the "Demographic-Economic" paradox to be precise. It is best illustrated with the following graph showing the inverse correlation of total fertility rate and a country's Gross Domestic Product per capita. It's a real chicken and the egg scenario. In order for less developed nations to advance economically they need to slow down their birth rates, but the best way to slow down birth rates is to become more developed. As Karan Singh aptly put it: "Development is the best contraceptive."

Fertility Rates w/ GDP per capita (Medium Size)

Sapere Aude!

[NVSS] Ventura, Stephanie, Hamilton, Brady, Sutton, Paul; Revised Birth and Fertility Rates 2000 and 2001, National Vital Statistics Reports; Vol. 51; No. 4; Feb. 6, 2003; Centers for Disease Control