TLDR; The magic number is around 2.3, not the 2.0 you might expect, results in a stable population.

This is an exploration of what ‘births per woman’ means, and how it is measured. A key topic here is population. Key to discussion about population is population *growth*, which is most commonly analysed from ‘births per woman’. *But what is ‘births per woman’*? Answer: not quite what you might expect, which means a small adjustment is required for interpreting births per woman when predicting population growth?

- Not quite what you might expect.
- Towards calculating the ‘Perfect’ Statistic
- What Exactly is Births Per Woman?
- Interpreting Birth Rates expressed as Birth Per Woman
- The Magic Number: 2.2 to 2.4.
- What Drives The Fall in Births Per Woman?

## Not Quite what you might expect

It sounds simple. Take a large sample of women, and measure the number of children they have. How else can you calculate ‘births per woman’? This simple formula can work as a statistic for a large period time, but year to year or even over 10 years, becomes impossible to measure. Consider over a long period, say, between the years 1700 and 2000. Woman who had the potential to have children prior to 1700, as well as those who may still have children after the year 2000 need to be excluded from the sample and the compete data party belongs to an different time interval. This excludes most living women from being part sample in the early 1700s, and most living women for the year 2000 and the years before. A woman must have all of her possible childbearing years within the sample period. Still in this case, there is a lot of data.

But what if we take a shorter span of time? Clearly, if we assume a maximum possible number of childbearing years as, for example, being 35 years, then with a sample time of 35 years, only the women born in one exact year could be part of the sample. With women living over 60 years, this would be 1/60th of the population. And even then, it takes 35 years of collecting data to have an answer, and during that time birth rates may change.

To be practical, another way of measuring data is required.

## Towards the Perfect Statistic

The perfect statistic would ‘current annual population growth rate’, a factor we could use to know the *current* rate the population is growing. With a complete yearly record of births and deaths, we can calculate change in total global population, but since the births would be people in the current year, and the deaths on average represent people born around 70 years ago, the figure gives a comparison of two groups of people separated by almost 70 years, and born to very different population counts. Even if birth rates were now well below replacement levels, we would still expect births from the current over 7.5 billion people to be greater than they were in 1950 when the global population was 2.5 billion.

We wish to current trends from year to year, not just trends comparing people a lifetime apart. What is the birth rate of the current generation, not the difference in number of children in the current generation, to the number of children 2, 3 or even 4 generations before.

For each person born today, how many children will they have? If we knew, for each person born, how many people will replace that person in the next generation, and exactly how long each generation would represent, then we would have a generation factor, which divided by the number of years in each generation, would give our perfect per annum figure.

The challenges include:

- there are two parents for each child, so number of children relates to two parents, not ‘each person’
- there no children per ‘two parents’ number as adults can have children with different partners
- children do not directly replace their parents as there is an overlap
- people have children at a wide variety of ages, meaning collecting data could take many years
- accidents and illness can shorten lives and preventing people becoming parents

The first step in solving these problems it to consider children of one gender only, then divide by two since there are almost equal numbers of men and women. Women are the logical gender to choose, as women are unlikely to have children without realising it, and are present at birth allowing easier collection of statistics.

However, tracking women over their entire lifetime is not only impractical, it would also yield confusing data. To calculate data for birth rates applicable for the year 1950, should we include all women of child bearing age during 1950? Obviously many of those women have not necessarily had all their children yet. Some had their children over a decade earlier, so their statistics could be no longer relevant.

The end result is the best statistic we have is ‘births per woman’. This is a practical figure which can be calculated from the data collected in a single year, but there are some limitations.

## What Exactly is Births Per Woman?

Births per woman, is perhaps even more confusingly also labelled ‘fertility rate’, or ‘total fertility rate’.

Since actually tracking women over their lifetime would produce out of date information and require huge samples over long periods of time, this number, is the number of children for an *imaginary* woman who passes through her reproductive life subject to *all* the age-specific fertility rates for ages 15–49 that were recorded for a given population in a given year.

This is a calculated figure, that is practical to collect, and as useful as possible, but is skewed to be higher than ‘births for every woman who was born’ as the number is accurate only for women who live their entire reproductive life. The figure can be calculated from simply recording all births for a given year, together with the age of the mother for each birth.

I state the label ‘fertility rate’ is confusing, because to me ‘fertile’ suggests ability to reproduce. This risks confusion of ‘capability to have children’ with ‘decision to have children’. A society where less 18yr old women are having children does not necessarily mean 18yr old women are becoming infertile.

Note ‘births per woman’, need adjusting for allow for the fact that not all children reach even that 49 years of age of the statistic, to have their full allocation of children, and some will not even reach an age to have any children. At current mortality levels, this means between 2.1 and 2.5 depending on health environment, is the level of ‘births per woman’ required for an exactly sustainable population.

## Interpreting Birth rates as Birth Per Woman

To get the population growth per annum figure, first subtract from the ‘births per woman’ the appropriate figure to allow for deaths prior to reaching full children potential, then divide by two correcting for men and women to get the ‘per generation’ population growth. Than figure should then be divided by the ‘average age when giving birth’ to provide the average ‘generation’ duration, then you have the annual population growth rate.

## The Magic Number: 2.2 through 2.4.

At what number of births per woman would a population with zero immigration/emigration be stable?

The divide by 2 above is clear, as this is required because very close to 50% of people are women. There are two reasons the number is not an exact 2.0.

- There needs to be an allowance for child mortality.
- There needs to be and adjustment for women who do not survive their entire number of fertile years.

Firstly, not all children will become adults and have their own children. The ‘magic’ number would need to be adjusted so that at least 2 of those children get to become adults, and get to have their expected number of children. When

Secondly, and more complex, the calculation of divide births by the ‘average age when giving birth’ only matters works for calculating births in a given year, and in the long term you would think would project the number of children a women would have, but to have that number of children, the woman must continue as a fertile woman for the entire period, and not every one does.

The women that do go through all their fertile years capable of having children need to have a few extra children to compensate for those who die or become infertile, slightly increasing the number over than needed to allow for infant mortality.

How much the number must be increased beyond 2.0 is not exact, as death and illness rates vary over time, making the statistic a little fuzzy. Some optimistic people believe we could enable reduce infant mortality and enable enough women to exist trouble free through their fertile years for the number to eventually become 2.1 or even lower, but estimates for the current rate range between 2.2 and 2.4 as the correct answers for zero population growth.

A very good source of data is worldbank.org. The link provide is interactive and shows data as at 2018 at a level of 2.415. This is 0.215 the level of lower estimates for ‘births per woman for stable population’, but back the data also shows that in 2002 the figure was 2.644. From 2002 to 2018, the rate dropped by 0.229. If the rate continues on the current trend, then births per woman would be below 2.2 by 2034. So depending on which level is chosen between 2.2 and 2.4, that level should be reached between 2020 and 2034.

## What Drives The Fall in Births Per Woman?

In the 1950 and 1960, there were some dire predictions about global population. Unless population growth slowed dramatically – there would be dire consequences!

Strangely, humanity effectively heeded these warnings. Countries such as Singapore, Bangladesh and China have all taken government action to reduce population growth, but similar countries without government action achieved similar outcomes.

I have recently seen articles where authors claim alarms of overpopulation have always been false alarms, but we do not know they were false because humanity, for whatever reason, did take evasive action. Like telling the driver you must not have needed to put on the brakes because when you did put on the brakes we did not crash. **Humanity put on the population growth brakes, and may well have avoided a crash, as if birthrates had remained at 5 per woman, we would have over twice the current world population today, with over 14 billion people**.

But why did birth rates fall?

There are lots of theories, and many of these accurately provide some of the factors. But I have seen no one theory that seems to explain it all. We just do not know with certainty what all of the factors are.