2 Ain't Enough

I read a post on Substack the other day and the poster used the number 2. And I pointed out there that… 2 ain’t enough.

What am I talking bout? Demographics, my Dear Watson! Demographics!

2.2

It is tempting to think that if every couple has two children, then the society will reproduce itself. It makes sense, no? Two people have two people who have two people…

2 → 2 → 2 → 2…

But, alas, demographics does not deal with pure math. Demographics deals with real people and so the number you’re actually looking for is 2.2.

You see, unfortunately, those two children that the couple had do not always grow up and havre children. Sometimes they die in infancy, sometimes they die in childhood, sometimes they die in war before they marry… or even a woman dies before she had both of her scheduled children!

And there are those who are infertile, both male and female. So two do not always lead to two which lead to two which lead to two. The modern math (ie in an age without massive infant mortality, war, famine, plague, etc) is that two needs to lead to two point two, which then leads to two, which then leads to two point two, etc.

2 → 2.2 → 2 → 2.2…

0 ≠ 2

And then you have those who choose not to marry, not to have children. They have zero children. And yet we often miss them when thinking about the ‘average being two’ (or, as we have seen, more than two). But we need to remember… TFR means that every woman has to have that many children… or that the women who don’t need to be made up for by the women who do.

When we look around, when we are standing in our church our in Walmart and see the couple with two children, and we think that they are almost there! That they are just short of reproducing! But we forget that we just passed another couple with zero children, or a woman not even married. Which means the next couple we pass, who has three children, may not have enough children for us to reach even 2.2!

Let’s run the numbers. Let us suppose that for every one hundred couples in our society, fully fifty percent of these decide not to marry or not to have children. (We have already included those who can’t have children in our 2.2). What does that mean for the other fifty couples? It would mean that in order to achieve a TFR of 2.2 the TFR of the women who do have children would have to be… 4.4!

100 (couples) → 50 (childbearing couples) → 50 (childbearing women) → 220 (children) → 100 (couples, surviving to age of reproduction)

Or if it is clearer:

100 women → 50 women willing to have children → 220 (children) → 110 (girls) → 100 (girls who survive to age of reproduction)

Cohort

Now we come to a bit of tricky math. A bit of math that, in general, our ancestors would never have had to do. You see, the way that demographics have worked in pretty much all of the past (monogamy and war would distort this) is that today’s women have today’s children, and today’s children become tomorrow’s women. The whole thing was kind of like an escalator: with each new kid popping out of the machine at just the right time and the preceding steps going upwards like all the other steps.

But unlike an escalator, the steps are not all the same size. Going back to our two-point-two analysis in the beginning, for a society to even reproduce itself, the bottom steps have got to be bigger than the top ones. And as the steps slid upward, they got smaller and smaller until they vanished altogether.

The ordinary way that this gets represented is with a pyramid. A broad base with a slightly smaller next step on top of it, and then a slightly smaller one, all leading up to the top. Historically, this pyramid has represented population growth, but it would also work, if needing to be exactly balanced, for a society that merely reproduced itself.

(The ideal pyramid would be smooth all the way down, but nothing human is smooth. However you can plainly see the slope from the eighty five year olds to the zero year olds, and the overall pyramid shape.)

But recently our pyramid has gotten out of shape. The bottom of the pyramid, the very bottom, which represents new children, is smaller than some of the steps above it. And as the escalator has moved upwards, to mix our metaphors, we have reached the point where the small steps include child-producing women.

(Note, the above images were taken from the Wikipedia. Notice the date on the later one: 2020. So you will have to project this pyramid 25 years upward… with the gap that started at year 35 now starting at year 60, and the low point that shows at 25 now being year fifty, and the diminishing numbers at year zero now being peak fertility of year 25!)

Now, in the past, what has been happening is that the steps which represented childbearing women produced the steps which represented children. And so, if we were to take away all of the other stops except these two sets. We would see that the two-point two number representing the child step is just that little bit bigger than the child-bearing woman's step. But in the past, all of those steps were part of a pyramid.

But if we replace the normal pyramid shape with our modern non-pyramid pyramid shape, with its dramatically smaller child-bearing women step, along with the smaller children step that it would produce, and then add the rest of the pyramid back in, we would see that the ‘children’ step was not big enough to support the pyramid.

(So, keeping in mind the 2020 problem, the green line represents the children that would be produced if the women of childbearing age were to ‘normally’ reproduce. The black lines (which extend off this screen) represent the number that would be needed for an actual pyramid. The difference is the demographic gap that is so catastrophic).

The problem here goes under the word ‘cohort’. The problem is that the child-bearing cohort is too small to fit into its place in the overall population pyramid. So it’s not good enough that the child-bearing cohort merely produce the number of children that would work in an ordinarily shaped pyramid. It must produce a vastly oversized number of children in order to rebalance the pyramid.

Multiplicative

Sp of we start with the need for 2.2 in a normally shaped pyramid, and then we realised that that 2.2 might need to become as hight as 4.4 once we translate it into the number of women who are actually willing and able to have children, we then have to multiply that 4.4 to make up for whatever deficit our diminished child-bearing size requires.

So when we look around and see the happy family with one boy and one girl we need to realise that in the face of our demographic death spiral, they don’ cut it. They don’t even come close.

Normia

Let us invent a country. We will call it ‘Normia’. Here’s what their population pyramid used to look like:

Age Population (rounded)

80+ 10 million

70-79 11 m

60-69 12.1 m

50-59 13.3 m

40-49 14.6 m

30-39 16.1 m

20-29 17.7 m

10-19 19.5 m

0-9 21.4 m

So here we see that for every retiree 70+ years old there are 7.39 people in the working age cohort (20-69).

Now, instead of fooling around with a whole lot of fancy math lets just take the exact same population pyramid with a greatly reduced TFR over the last forty years.

Age Population (rounded)

80+ 10 million

70-79 11 m

60-69 12.1 m

50-59 13.3 m

40-49 14.6 m

30-39 11.7 m

20-29 9.4 m

10-19 7.5 m

0-9 5.9 m

This pyramid gives us 4.7 working age people per retiree.

And not let us consider the child-bearing cohort problem. In the first pyramid the number of women between the ages of twenty to forty was 16.9 million. The number of children between zero to twenty years old was approximately 40 million; which gives us a ration of 2.4 children per child bearing woman.

If were now take that same 2.4 number and use it on our updated, modernised population pyramid we would end up with 25.2 million children… or a deficit of 14.8 million children. If, on the other hand, the modern child-bearing cohort were to attempt to adequately fill the bottom of the pyramid, their number would have to be not 2.4 but 3.89. And that’s the average! That’s ignoring women who can’t have children, don’t get married, refuse or choose not to have children… The burden on those who can have and do choose to have children would be much higher.

(The discerning reader will notice a difference between the 2.2 TFR needed to sustain a modern population and the 2.4 number we quote above. There are two reasons for this:

1. We made this pyramid up, we did not calculate it in great detail.

2. Because women do not all have their children all at the same time in some clutch at some exact age in her life, but instead has them spread out over various years and thus ages, some of the older children would no doubt have come from women outside of our ‘child-bearing cohort’, and the younger portion of that cohort (say, the 21 year old woman) has not had all of her children yet.

However, while both of those issues are true for this chart, and thus it does not represent an exact and detailed mathematical analysis… the problems it presents are absolutely true.)

And the problem gets worse as the escalator continues upward. The upper steps start becoming filled with older people, and the lower steps with fewer and fewer working age people to support them… and the entire economy.

This problem is also exacerbated by a lack of political will to deal with the issue. Just this week I read that the government of France, which recognizes the problem that their pension system represents as their people age into it without younger workers, has just had to drop any plans for dealing with it… as none of the political parties are willing to touch it.

2 B or not 2 B

In the short term, this is a political problem. The numbers will look worse and worse for various government problems, and the potential short term solutions fewer and fewer and more and more desperate.

But in the long run, this is an existential problem. A problem that, if not dealt with, will lead to the actual destruction of countries and peoples that do not deal with it.

Note: If anyone is tempted to think ‘well, we will just import workers’, see my “Math of Fertility” post below.

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Thanks again, God Bless, Soli Deo gloria,

Von

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