# Population Lag: The Pipeline

For any change in birthrate, there is a significant ‘lag’ before the population change reflects the birthrate.  This is why we have the paradox where countries with family sizes that suggest the population should contract, actually have growing populations.

To demonstrate I have made a simple model.  In this model  of the imaginary country ‘Imaginania’ (population approximately 10million in the year 2000), birth rates in the year 1900 are at a level consistent with developed countries at that time.  Then, from 1965, the model then uses the new birthrate typical of developed countries in the late 20th century and up until the present.

The models is simplified, but I suggest still very useful. So what happens to population with this model?

As expected, the number of people born each block of five years from 1900 until 1965 becomes a larger number. Then from 1970 until now a progressively smaller number are born each year.

The three ‘yellow blocks’ represent the population pipeline for 1970, 2000 and 2015.  People enter the pipeline at birth, and exit when they die.  So the pipeline for any given year stretches back from that year to the average life expectancy number of years ago. Starting from the right side of the pipeline, the people born in the previous 5 years, then to the left of those the next oldest on to the very oldest at the left of the pipeline being those born longest ago.

Using the model, by totalling each sector within the ‘yellow area’ or ‘pipeline’ reveals that ‘Imaginania’ has a total of just under 4 million people in 1900 (not illustrated), and as shown, 8 million in 1970, 9.6 million in 2000 and 9.8 million in 2015.  Even though the birth rate is modelled as below replacement level from 1970 through to 2000, the population continues to climb.

This is the principle of the ‘lag’.  The peak population group is those born in the block ‘1965’, and aged 0-5 in the year 1965.  The total population in 1970 is the 1970 group (0-5 year olds), the 1965 group (now 5-10 year olds),  the 1960 group (10-15 year olds) through to the 1900 group (70+ year olds).  To move from 1970 to 1975, we add the new 1975 group as the new 0-5 year  olds, and each other group moves through the pipeline and becomes 5 years older, with a group of the size of the 1900s group leaving the pipeline and the statistics. Even though the group for 1975 is smaller than the previous 1970 group, the population is still increasing in total the group dropping out is the 1900 group.  This pattern continues as the pipeline slides through to 2000.  Ever smaller groups are added to the pipeline on the right, but as these new groups remain larger than the groups dropping out of the pipeline on the left, the number of people in the population pipeline continues to grow.  In the second transition, from 2000 to 2015, the population is still growing, but has almost levelled off.  Continue this model through to 2050, and the model shows the population of the ‘Imaginania’ would fall back to around 9 million.

# The ‘Real World’.

This model predicts growth for a country with no net migration.  The results are for the population excluding immigration,  however most developed nations are significantly impacted by migration.  These countries fall into one of two categories: people exporters or people importers.  Basically this is the ‘old world’ (exporting people) compared to the ‘new world’ (importing people).  Old world countries of Europe (such as the UK, France, Germany etc), throughout the growth age exported significant numbers of people to the  new world countries in the continents of North and South America and Australia/New Zealand(Oceania).

So for most countries, we need to then apply adjustments to a model such as the model for ‘Imaginania’, however Japan comes to mind as a country with relatively low migration.  In fact figures for Japan track extremely closely to those Imaginania (only around 10x larger).  This was neither intended or planned.  The model started working on a target population of 10 million and working backwards this resulted in a population back at 1900 of 4 million. In fact Japan basically moves from 40 million in 1900 to 100 million in 2000.  However there is some coincidence to this as many factors of real world Japan are not modelled.  Also, Japan has had lower birth rates than typical for developed countries or those used in the model, which is one reason the model still has an almost flat but still growing population in 2015 whereas Japan has actually already entered population decline.  But Japan is certainly close enough to suggest the model works for a case such as Japan.

However, for most countries, the model predicts only what would happen without migration.  Such data is still extremely useful in prediction how migration must be adjusted to counter underlying changes or how overall population growth will change in the absence of changes to migration numbers.