Understanding changing populations with the cohort-component method

Written by Jessie Saeli, edited by Nicole R. Smith and Rachel J. Bacon


When governments set out to design long-term projects and plans, they need to know how many people those future projects must accommodate. Many turn to demographic projections to provide data on future population sizes and make-up. The cohort-component method (CCM) is commonly used by the government and academia to create these demographic projections.

In a CCM projection, the target population is divided into categories called “cohorts”, which may grow or decrease at different rates. Dividing the population into cohorts distinguishes individuals into groups based on well-known differences and allows demographers to perform calculations with millions or billions of people without overloading their computers.

But what about the limitations of CCM? Wouldn’t the strict division between cohorts create unrealistically rigid categories?

CCM strikes a balance between simplicity and complexity, but technological breakthroughs open the door to implementing new methods and achieving nuanced projections.

This article will provide a crash-course on the cohort-component method, evaluating its strengths and highlighting its weaknesses. The next two articles in this series will explore how computer simulations compare to CCM and what it takes to replicate population projections in a microsimulation.

What is a cohort?

cohort is a group of people who are identified by fixed characteristics based on a starting period.

For example: one cohort could be those who were born female in 1990–2000; another could be those who identified as Christian in 1980.

Because cohorts are determined by these starting characteristics, demographers are “following” the same group over time, regardless of if those characteristics change later, such as if one of the 1980s-born Christians converts to Buddhism.

Using cohorts to divide the population into many distinct groups allows demographers to distinguish how and why different groups in the population will change over time. However, this method can result in an unwieldy number of cohorts.

A demonstration is in order:

1.

Demographic projections begin with a particular geographic region and a goal, such as projecting how the religious composition of Norway will change over time.

Change in population size is determined by three factors: how many babies are born (fertility), how many people die (mortality), and how many people enter or exit that geographic region (migration).

Dividing the population into cohorts allows demographers to apply different rates of demographic change based on real-world data. For example, mortality rates are usually higher for older cohorts than for younger cohorts.

Now let’s create our cohorts. All CCM projections begin by dividing the population by age and sex to define basic cohorts at the beginning of the projection.

Age can be divided by groups as small as several months, but generally projections use 5-year groups. Here, let’s use simple 10-year groups. Sex is always divided into male and female, in order to correlate with female-specific fertility rates.

This gives us a manageable 20 cohorts.

2.

Next, let’s add religious (non)affiliation. This will multiply our existing number of cohorts by the number of religions that we choose to include. The base population for each religion (and nonreligion) is determined by censuses or surveys.

Let’s include the five major world religions and the unaffiliated: Christianity, Islam, Buddhism, Hinduism, Judaism, nonbelief. This will multiply our previous number of cohorts by 6.

Remember, however, that religious affiliation is not so simple. For example, people can identify with multiple religions. Unfortunately, CCM cohorts must be strictly divided: an individual cannot “belong” to more than one cohort.

To account for people with multiple religious affiliations, we could create a set of new cohorts for “multiple religions.” However, doing so wouldn’t allow us to specify to which multiple religions those people adhere, so it wouldn’t add any useful nuance. For the sake of simplicity, we must forego accounting for people with multiple religious affiliations.

Our number of cohorts is multiplied by 6.

Now we have 120 cohorts.

3.

Finally, let’s include a necessary nuance to our projection of religious composition: religiosity.

Facets of religiosity — such as how seriously someone takes their religious belief, how often they attend religious services, or whether they believe in the supernatural — are used to indirectly determine religiosity, or strength of belief. We use this data to assign one of three levels of religiosity: strong, medium, or weak.

This goes one step beyond current projections of religious change by organizations such as Pew, which create religion cohorts by affiliation alone.

Adding three levels of religiosity multiplies the number of cohorts by 3.

Wow! That’s 360 cohorts! Adding just one more factor increased the number of cohorts by 240.

And we didn’t include smaller religious beliefs, different denominations or sects within religions, or different types of nonbelief (such as atheism or agnosticism)! We also excluded people who adhere to multiple belief systems.

Although we will stop here, many demographic projections would also include other relevant factors, such as race, ethnicity, and education level. Even if we use only two cohort-divisions for each characteristic (e.g. white and non-white, high-school educated or less), that results in 2,160 cohorts!

Any additional features that we add to our population projection multiplies the number of cohorts. Although this increase begins small, soon it becomes sizeable.

So why divide the population into thousands of cohorts? Why not make projections of the total population? Dividing the population into cohorts allows for the fact that, in general, different fertility, mortality, and conversion rates apply to different groups within the population.

For example, applying fertility rates only to female cohorts — rather than to the population as a whole — makes a difference in populations where there is a disparity between the number of men and womenReligious people tend to have more children than nonreligious people and fertility rates differ between different religions.

Even a small difference in fertility can have a large impact over time. Distinguishing between a multitude of cohorts enriches the information demographers can glean from these projections.

How does the Cohort-Component Method create population projections?

A set of four calculations are used to determine population change in a standard CCM projection. These calculations operate by applying the three factors of population change — fertilitymortality, and migration — to each cohort or group in the population.

Our projections additionally account for religious change, where people switch between religions and change their religiosity levels.

The projection period is the time over which the population projection is extended, for example, from 2020 to 2050. This chunk of time is divided into smaller projection intervals, such as 1-year, 5-year, or 10-year intervals. The four calculations are applied at each projection interval for the length of the projection period.

Each cohort has a starting population, called the baseline population.

The animation below visualizes how the four calculations affect the baseline population of birth cohorts over several projection intervals.

U.S. population by age and gender, 1960–2060, Population Reference Bureau

Each birth cohort moves up in age and decreases in size according to how many people that age die (mortality) or migrate in or out of the region. The new youngest cohort’s size is determined by how many babies are born during that projection interval (fertility). The populations of the cohorts after the four calculations are applied become the new baseline populations for the next projection interval.

The first calculation concerns how many members of each living age cohort will survive the current projection interval. This number is determined by the survival ratio: the percentage of people in each cohort who survive to the end of the interval.

These percentages are based on real-world statistics of how many people die annually (mortality) and may differ for each cohort.

Future mortality statistics are predicted based on current and past information. Demographers also assume that life spans will increase due to improvements in health thanks to advances in medical technology and quality of life.

In the United Nations’ estimates for female life expectancy in China, life expectancy increases in all cases, although at different rates. Life expectancy before 2020 represents real-world data, but after 2020 the single line disperses into an array of estimated gray and red lines.

These projections for life expectancy are used to create “probabilistic” population projections, providing governments and policy-makers with various possible futures to consider.

After determining how many people survive the projection interval, net migration is added to or subtracted from the remaining population. Net migration is the difference between the number of people who immigrate to that geographic region and the number of people who emigrate out.

In nations with lower fertility rates, immigration helps maintain a steady population. For example, thanks to immigration, population growth has remained stable in high-income countries from 1950–2020 despite lowering fertility rates.

Source: Conrad Hackett, Twitter

This interplay between migration and fertility exemplifies the importance of distinguishing the three factors of mortality, migration, and fertility. How these three factors individually impact population growth or decline can be individually explored.

Next, we calculate how many births will occur.

First, we determine the average of the female population of each age group. The baseline population before the first two calculations (mortality and migration) is averaged with the population after these calculations. This accounts for the fact that some women may give birth to children but die or migrate before the next projection interval. Age-specific fertility rates — the average number of children born per woman — are then applied to that average female population.

Fertility is impacted by age. Therefore, younger populations with a higher percentage of young women will grow more quickly than a population with fewer young women. Finally, births are divided into boys and girls. This determines the base population for the new youngest cohort.

As with mortality and migration rates, future fertility rates must be assumed based on expected trends. Since fertility rates have been decreasing in recent decades, they are assumed to continue decreasing into the future.

In the final calculation, mortality and migration rates are applied to the youngest cohort — those births generated in the previous step.

After these four steps: 1) mortality, 2) migration, 3) fertility, 4) infant mortality and migration, are applied, the base population for the new projection interval has been determined.

These four calculations are then repeated for the next projection interval, using the previous population as a base for projections over the following interval, until the final target year in the projection period has been reached.

The total number of calculations necessary for a population projection is 4 times the number of projection intervals. If we assume projection intervals of ten years to match our ten-year age cohorts, then a projection from 2020–2050 will have three projections intervals.

Applying this to our final number of cohorts (360) results in 4,320 calculations.

Applying this to the cohort breakdown including race, ethnicity, and education level (2,160 cohorts) would result in 25,920 calculations!

Religious Change

Adding religion to a standard CCM requires calculations beyond the four we already described, because religious affiliation and religiosity are characteristics that frequently change among individuals. In addition to fertility, migration, and mortality, the number of people affiliated with any particular religion (or none at all) changes through religious switching.

This can be conversion from one religion to another, a nonreligious person converting to a religion, or a religious person becoming nonreligious. Another calculation would be required to determine changes in religiosity.

Because the mechanisms of religious switching are not well understood, CCM projections can make the safe assumption that rates of religious change will remain the same. That is, these projections impose rates of religious switching, rather than attempting to incorporate possible causes or influences affecting religious switching.

CCM projections do not — and cannot — explore why people switch religions.

In particular, CCM projections fail to account for the influence of family and social networks, even though these have been shown to have a profound influence on stability and change in religion over one’s lifetime. Including networks would require tracking individuals, to account for interactions with other individuals in different cohorts.

Photo by Kevin Bluer on Unsplash

Because CCM only distinguishes monolithic cohorts, it fails to represent influential interactions among family or social network relations.

The limitations of the cohort-component method

Dividing the population into distinct cohorts allows demographers and policy-makers to visualize how the age, sex, religion, and other characteristics of the population will change in the future and what demographic factors will influence this change.

However: CCM relies on strictly defined and divided cohorts. Predicted future fertility, mortality, and migration rates apply to cohorts based on limited assumptions that observed trends will continue.

Increasing the number of cohorts and expanding assumptions to include rates of religious switching and change, quickly becomes an unmanageable set of calculations.

The strength of CCM lies in its straightforward and simple calculations. Increasing the number of cohorts is antithetical to this simplicity.

But what if we embrace this complexity and model each individual person in a population, specifying their unique characteristics and freeing us to test assumptions that aren’t bound to a fixed population rate?

Our next article will explore using simulations to explore just that, showing how such models build fine-tuned methods and produce nuanced results.

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