# Lesson 8: The Cohort Component Population Projection Method

## Introduction

#### Course Objective

Acquire skills to project the population of a locale by 5-year age groups and sex.

#### Expected Outcome

Ability to use the cohort component method to project the total population size as well as the number of males and females for each 5-year age group for a future date.

The cohort component technique uses the components of demographic change to project population growth. The technique projects the population by age groups, in addition to other demographic attributes such as sex and ethnicity. This projection method is based on the components of demographic change including births, deaths, and migration. The processes or stages of the projection tool are summarized below in Equation 8-1.

### 8.1 About the Cohort Component Method

Equation 8-1:
Cohort Component Summary Equation

To project the total population size, and the number of males and females by 5-year age groups, find the number of people who survive or are expected to be alive in the future. Add to the survived population number, the number of births that take place and the number of net migrants.

There are several approaches to using the cohort component technique. The approach described here is easy to use, and requires minimum demographic information. Isserman (1993) offers planners an alternative way to employ this tool. Isserman's alternative method uses a different approach to input fertility, mortality, and migration data.

Assumption
When the cohort component method is used as a projection tool, it assumes the components of demographic change, mortality, fertility, and migration, will remain constant throughout the projection period. As a forecasting tool, planners can alter the vital statistics and migration estimates to reflect their view of the future. For the purposes of this section, the tool is presented as a projection method.
Strong Suggestion
When making a 10-year projection, it is best to perform two separate projections: a projection for the first 5 years and then a projection for the next 5 years. The result of the first projection is used to perform the second round of the projection. In some cases, planners alter demographic rates to reflect their vision of the future for a locale. For example, they may observe declines in fertility levels and alter age-specific fertility rates using some of the extrapolation tools or ratio methods presented in Lesson 6.
When to Use this Method
Use the cohort component method when population projections by age and sex are needed for 5 years, 10 years or longer periods of time. This projection tool allows planners to examine the future needs of different segments of the population including the needs of children, women in their reproductive years, persons in the labor force, and the elderly. It also allows planners to project the total size of the population. The results can be used in all aspects of local and regional development plans.

### Steps for Using the Cohort Component Method

Step 1: Collecting Information

The cohort component method requires information from both the most recent and the prior census of the locale. Collect information on the number of births during the past 10 years. Ideally information on births should be compiled by the age of the mother so that age-specific fertility rates can be calculated. These rates are used to project the number of births that occur during the projection period. Use the general fertility rate when births by age of mother are not available. A life table or calculated survival rates are also needed.

Step 2: Aging a Population into the Future

The cohort component method takes each age group of the population and ages it over time using survival rates. For a quick review of survival rates, review Lesson 7. For a more detailed explanation, please refer to Shryock and Siegel, or Dr. Suchindran's course, Multiple Decrement Life Tables.

1. Obtain census information distributed by sex and age (usually 5-year age groups)
2. Multiply the base census population of a given age group by survival rates to obtain the population still alive 5 years later
3. What is the number of women aged 25-29 who will be alive in 5 years?
4. Women aged 25-29 alive in 5 years = (population women aged 20-24) (survival rate)

Next, calculate the number of births taking place during the projection interval. Age-specific fertility rates are used to estimate the number of births that take place. The rates are multiplied by the number of women in their reproductive years. The results give an annual number of expected births. They are then multiplied by the projection period, usually 5 years, to obtain the total number of births that take place in the future.

An age-specific fertility rate indicates the probability that a woman in her reproductive years will give birth in a given year.

Use the Sex Ratio equation as shown in equation 8-2 to find the number of male and female babies born.

Equation 8-2
Sex Ratio

Once the number of male and female births has been determined, the results are multiplied by a survival rate to determine how many babies survive into the future as shown in equation 8-3.

Equation 8-3:
Surviving Population

Next add the number of net migrants. This can be a positive or negative number. Obtaining the number of net migrants is a 2-stage process. First, calculate net migration rates. Then multiply these rates by the survived population to obtain the number of net migrants.

### 8.2 Applying the Method

In this example assume that the Ministry of Social Welfare wishes to develop a plan for a women's development and craft center in a small district. The goal is to project the number of women for the district from years 2000-2005.

• Setting up the Table

First set up the table for the projection, as shown in Table 8-1.

 Table 8-1:Projecting the Population of Females for Year 2005 Column 1Age in 2000 Column 2Age in 2005 Column 3Census 2000 Column 4Survival Rate Column 5 Survived Population(Column 3*4) Birth 00-050-45-910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980+ 0-45-910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980-8485+ ---383730062632264834784022409138233474264817061341115511801139951827 0.98090.99040.99340.99760.9960.99380.99160.9870.97950.96730.95120.93220.90360.86530.81650.75050.66340.5426 ---3763.712986.162625.682637.413456.443988.224037.823744.633360.402518.781590.331211.73999.42963.47854.82630.89448.73

In this example a computer spreadsheet program is used because of its speed in multiplying columns of information. The first row in Column 1 shows the births that take place from years 2000–2005. The age groups have been aligned so that women ages 20–24 in year 2000 will be 25–29 in year 2005, as presented in column 2. This first step is important. It helps determine where to put the census data that is required for the projection.

Next supply the census data for year 2000 in column 3. The census information should be provided for the age groups in column 1. Notice that the first cell is empty in column 3. This is where births will be added that take place throughout the projection period. Next, add 5-year survival rates to the table, as shown in column 4.

• Finding the Number of Females Alive in 2005

Once the table has been created and census information and survival rates have been added, it is possible to find out the number of women that survive the next 5 years. Multiply Column 3 by Column 4 to find out the number of females that will be alive in 2005. The results are in Column 5. Notice some of the females in each age group died.

• Adding the Number of Births

Estimating the number of births taking place during the projection period is a two-stage process. First, calculate age-specific fertility rates. To do this, obtain information on the number of births by age of mother for a three year period around the date of the last census taking. If the number of births by age of mother is not available, use regional or national age-specific fertility rates. Demographic and Health Surveys (DHS) are available for most developing countries and provide age-specific fertility rates.

Table 8-2 presents the data table for calculating and adding the number of of births.

 Table 8-2:Calculating Births Column 1Ages Column 2Births 1999 Column 3Births 2000 Column 4Births 2001 Column 5Births Average((C2+C3+C4)/3) 15-1920-2425-2930-3435-3940-44 32447242725810210 273442411250939 3024574162747414 299.67457418260.6789.6711 Column 6WomenCensus 2000 Column7= C5/C6ASFR Column8Survived Women Column9 = C7 * C8Annual Births 264834784022409138233474 0.11320.13140.10390.06370.02350.0032 2637.43456.43988.24037.83744.63360 298.47454.16414.49257.2887.8310.64 annual births total = 1522.8599 births during the projection period = annual births * projection period(1,522.86) (5) = 7,614 female births = expected births * .49(7,614)(.49) = 3,731 Number of projected births = 3,731*survival rate3,731*.9809 = 3659.7379

Column 1 indicates the ages of women in their reproductive years. Columns 2-4 present the number of births for the 3 years surrounding the last census period. An average was taken of the births prior to calculating the age-specific fertility rate ((Column 2 + Column 3 + Column 4)/3)). Why? As indicated in the data, the number of births changes each year.

Once the average of births is obtained, the Year 2000 census data is used for women in their reproductive years to calculate age-specific fertility rates. To do this, the number of births is divided by the number of women in a given age group.

Once the age-specific fertility rates are calculated, they are multiplied by the number of survived women in each age group. The sum of Column 9 provides the number of expected annual births.

To find the number of expected births for the projection period, the number of annual births were multiplied by the projection interval of 5 years. It was also necessary to find the number of female births. To do this, the number of expected births was multiplied by .49 (.49 is based on the use of Equations 8-2 and 8-3).

The final step is to multiply the expected births by a survival rate, which is provided in Table 8-2 (3,731 x .9809 = 3,659.7 projected female births).

• Estimating Net Migration

The last part of the projection involves accounting for population movements in and out of the projection area. Two methods of estimating the number of net migrants will be introduced in this section. Both methods rely on survival rates and census information. First, it is important to be familiar with the definitions for migration and net migration.

Definition:
Migrations are movements across political boundaries that are semi-permanent or permanent in nature. Net migration can be defined as the number of in-migrants minus the number of out-migrants divided by the population exposed to the possibility (or risk) of migration, as shown in Equation 8-4.

Equation 8-4:
Net Migration Rate

K is a constant, usually 100.

Obtaining Migration Information

The process of obtaining migration information has two approaches, the Direct Method and Indirect Measures.

1. Direct Method:
1. Continuous registration system: individuals report their change in residence immediately to a local government office.
2. Use of census information: based on census question of "Where were you living 5 years ago"? In this case, planners compare the place of residence with the place of prior residence.
2. Indirect Measures:
1. Vital statistics or residual method
2. Survival ratio method

Most planners rely on indirect measures for obtaining migration information. This section will present different methods to calculate net migration using indirect measures.

The residual method is shown in Equation 8-5.

Equation 8-5:
Residual Method

In most cases, planners use survival rate methods to estimate net migration rates. The forward and the reverse methods estimate net migration by age and sex. The forward method is shown in Equation 8-6, and the reverse method in Equation 8-7.

Equation 8-6:
Forward Method

The survival rate is multiplied by the prior census population, P °x. The result provides an expected population for the present census period. Subtract the expected population from the present census period, Ptx+t. The difference is assumed to be due to migration. The forward method estimates the number of net migrants at the end of the period and assumes that:

• All migration takes place at the end of the period
• All deaths occur in the community for which the estimates are being prepared, or all deaths are to non-migrants. One problem is that residents and migrants are moving and dying throughout the period.

Equation 8-7:
The Reverse Method

The reverse method uses a slightly different approach. The terminal population (population in the last census) is being revived to the initial census date thereby estimating the number of persons that would have been alive at the earlier date. Then, subtract the expected population from the prior census data. Those persons who cannot be accounted for are assumed to be migrants. The reverse method assumes that deaths occur to people after they migrate. The reverse method produces more net migrants. The differences are greatest at the older ages, where mortality is highest. Most demographers compute both methods and average the results.

Assumption: Both methods of estimating net migration assume that population change not accounted for by fertility and mortality is due to migration.

Population change not accounted for by fertility and mortality may be due to:

• Migration
• Errors in the census counts
• Boundary changes from one census period to the next

Table 8-3 uses the forward method to estimate net migration. This method was selected because its process of estimating migration is easier to understand. Census data were collected for 1990–2000, as well as information on the number of births that occurred in 1990–2000. 10-year survival rates are used to calculate estimates of net migration.

 Table 8-3:Estimating Net Migration Rates Using the Forward Survival Rate Method Column1:1990Ages Column 2:2000 Ages Column 3:10-yearSurvivalRates Column 4:Census 1990 Column5:Expected Population Column 6:Census 2000 Column7:Net Migrants Column8:NetMigrationRate Births1995-2000Births1990-1995 0-45-910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475+ 0-45-910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980-8485+ 0.98920.99620.9980.99660.99480.99420.99320.9910.98640.97850.96610.94630.92080.88550.82650.72810.57820.5524 32262468234623872535333239493144251516741337121813261236112711298951089 3191.15922458.62162341.3082378.88422521.8183312.67443922.14683115.7042480.7961638.0091291.67571152.59341220.98081094.478931.4655822.0249517.489601.5636 30062632264834784022409138233474264817061341115511801139951827545409 -185.1592173.3784306.6921099.11581500.182778.3256-99.1468358.296167.20467.99149.32432.4066-40.980844.52219.53454.975127.511-192.5636 -0.05800.07050.13100.46200.59490.2350-0.02530.11500.06740.04150.03820.0021-0.03360.04070.02000.00610.0532-0.3201

Note: The first two rows in Column 4 show the births that took place from 1990 to 1995 and from 1995 to 2000. In Column 3, the first survival rate is S0-5 for children under the age of 5, and the second rate is S5-10 for children ages 5–9. The remaining survival rates are for a 10-year period.

Notice how the table is set up for this estimation. Ages are put in Columns 1-2 to guide the placement of census information. The survival rates in Column 3 are multiplied by Column 4 to produce an expected population for the year 2000.

To determine the number of net migrants, the Census 2000 population was subtracted from the expected population of Year 2000. To obtain a net migration rate, the number of net migrants in Column 7 is divided by the expected population in Column 5. Some planners take an average of the expected population and the census data and divide the number of net migrants by the average of the two to obtain net migration rates. This is an individual choice.

The net migration rates in Column 8 can be used to estimate the number of migrants that came or left the projection locale. Notice that some of the numbers are negative. Negative numbers indicate out-migration in given age groups. In the later age groups, it can also indicate mortality.

### The Projection

The projection for females for the Year 2005 is provided in Table 8-4. Births were added to Column 3. Net migration rates in Column 6 were used to calculate the number of net migrants (see Column 7). Column 8 consists of the projected population for each age group. It represents the number of net migrants plus the number of population that survived into the future plus the number of births that occurred.

 Table 8-4:Projecting the Population of Females Year 2005 Column1:Age 2000 Column2:Age 2005 Column3:Census 2000 Column4:Survival Rate Birth 00-05 0-45-910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980+ 0-45-910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980-8485+ 3731383730062632264834784022409138233474264817061341115511801139951827 0.98090.99040.99340.99760.9960.99380.99160.9870.97950.96730.95120.93220.90360.86530.81650.75050.66340.5426 Column5:Survived Population Column6:Net Migration Rate Column7:Number Net Migrants Column8:Projected Population 3659.743763.712986.162625.682637.413456.443988.224037.823744.633360.402518.781590.331211.73999.42963.47854.82630.90448.73 -0.05800.07050.13100.46200.59490.2350-0.02530.11500.06740.04150.03820.0021-0.03360.04070.02100.00610.0532-0.3201 -212.3473265.4116391.16231213.14431568.9443812.1030-100.8169464.3361252.3855139.484696.18283.3206-40.670240.655220.20575.173633.5399-143.6408 3447.394029.123377.323838.834206.354268.543887.404502.153997.013499.892614.961593.651171.061040.08983.68859.99664.43305.09 Total: 44839.557

### 8.3 Discussion

The cohort component population projection method follows the process of demographic change and is viewed as a more reliable projection method than those that primarily rely on census data or information that reflects population change. It also provides the type of information needed to plan for services to meet the future demands of different segments of the population.

Like most projection tools, there are disadvantages to using the cohort component method. First, it is highly dependent on reliable birth, death and migration data. Thus, it may be difficult to collect the information to apply this tool. Second, it assumes that survival and birth rates and estimates of net migration will remain the same throughout the projection period. In addition it does not consider the non-demographic factors that influence population growth or decline.

Even though problems exists, this projection method is the most widely used tool by planners since it provides information on the potential growth or decline of a locale by age and sex.

### 8.4 Review Exercises

For a quick review, answer the following questions.

1. When would the cohort component projection method be used?

2. What are the weaknesses of this method?

3. What could be done to check results?

### 8.5 Repeat of Case Studies from Lesson 2

This exercise will review concepts taught throughout the course. Review Lessons 1-8 and then select a case study to answer.
HINT: All three case studies require the use of the cohort component population projection tool.

Case Study 1 Background: Economic Development Planner

Case Study 2 Background: Development Planner with the Ministry of Health

Case Study 3 Background: Land Use Planner: Capital City

### References

George W. Barclay, "The study of mortality," Techniques of Population Analysis (New York: John Wiley and Sons, 1958) 123-134.

Ansley J. Coale, Paul Demeny and Barbara Vaughan, 1983, "Uses of the Tables," Regional Model Life Tables and Stable Populations, 2nd ed. (New York: Academic Press, 1983) 29-36.

Donald J. Bogue, Kenneth Hinze and Michael White, Techniques of Estimating Net Migration (Chicago: Community and Family Study Center, University of Chicago, 1982).

Andrew M. Isserman, "The Right People, the Right Rates," Journal of the American Planning Association59.1(1993): 45-64.

Steve H. Murdock and David R. Ellis, Applied Demography: An Introduction to Basic Concepts, Methods, and Data (Boulder, CO: Westview Press, 1991).

James C. Raymondo, "Survival Rates: Census and Life Table Methods," Population Estimation and Projection(New York: Quorum Books, 1992) 43-60.

Henry S. Shryock and Jacob S. Siegel, "The Life Table," The Methods and Materials of Demography(Washington, D.C.: United States Bureau of the Census, 1973).

Note: The sample life table (Table 5) was produced using an interactive life table provided by Simple Interactive Statistical Analysis and developed by Daan Uitenbroek, of the Netherlands. From the homepage click on Free Spreadsheets.

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