The document discusses population projections using the cohort component method. It involves projecting a base population forward over time using assumptions about fertility, mortality, and migration. The key steps are: (1) projecting survivors in each age-sex cohort using survival ratios, (2) estimating births based on fertility rates and female population, (3) applying survival ratios to estimate population under age 5, and (4) accounting for migration. This allows calculating the population in each future time period based on the components of population change.

1. POPULATION PROJECTIONS
Session 2 - Background & first steps
Ben Jarabi
Population Studies & Research Institute
University of Nairobi

2. Population change
• 4 basic components of population change:
– Births
– Deaths
– Inmigration
– Outmigration
• Excess of births over deaths results in natural increase
• Excess of deaths over births results in natural decrease
• The difference between inmigration and outmigration is net
migration

3. Population change
 Closed population
 A population for which immigration and out
migration are nil, e.g., the population of the world
as a whole
 Population growth depends entirely on the
difference between births and deaths
 Open population
 A population in which there may be migration
(international)
 The growth of an open population consists of
natural increase and net migration

4. Demographic Balancing Equation
 The principle of the balancing equation:
 In any time interval, the pop. of a country can increase or
decrease only as a result of births, deaths and movements
across the country's boundaries
 Births & immigration add to the pop., & deaths and emigration
subtract from it
 If data are available from 2 censuses, and the numbers of
births, deaths and in- and out-migrants are known, then the
equation must balance exactly, if all the data are perfectly
accurate

5.  Pop. change = (Births - Deaths) + (Immigrants -
Emigrants)
 Pt = P0 + (B -D) + (I-E)
where: P0 = initial population
Pt = population after time t
 Worldwide, natural increase is the most important
component of overall population change over time
Demographic Balancing Equation

6. Demographic Balancing Equation
 Each component of population change can be expressed as
an absolute number, or more commonly, as a rate
 A rate always has 3 components: a numerator, a
denominator and a time period
 The denominator for the calculation of an annual rate is the
estimated mid-year population
 Demographic rates are ordinarily calculated per 1,000
persons per year

7. Growth rate
• Rate of Natural Increase (RNI) = CBR –CDR
– RNI is expressed as a percent (%) & is often used as the
measure of the annual rate of population growth
• Intrinsic Rate
– A constant growth rate of a population with fixed mortality
and fertility schedules - resulting in a “stable population”

8. 8
Projection - Definition
A population projection is:
– An extrapolation of historical data into the future
– An attempt to describe what is likely to happen under certain
explicit assumptions about the future as related to the
immediate past
– A set of calculations, which show the future course of
fertility, mortality and migration depending on the
assumptions used

9. 9
Projection – Linear growth
• Implies that there is a constant amount of increase per
unit of time
• A straight line is used to project population growth
• It is expressed as Pt = P0 + bt
where P0 = initial population
Pt = population t years later
b = annual amount of population change

10. 10
Projection – Linear growth
Assumptions:
– Growth rate is constant
– Change is only experienced at the end of
unit time
– Resultant change (i.e. interest) does not
yield any change

11. 11
Projection – Geometric growth
 The growth assumes a geometric
series
 It is expressed as
Pt = P0 (1+ r)t
where P0 = initial population
Pt = population t years later

12. 12
Assumptions:
 Growth rate is constant
 Change is only experienced at the end of unit time
 Compounding takes place at specified intervals
Projection – Geometric growth

13. 13
Projection – Exponential growth
• This is the equivalent to the growth of an investment
with compound interest
• Growth is constant, but compounding is continuous
• It is expressed as Pt = P0(ert)
where P0 = initial population
Pt = population t years later
r = annual rate of growth
e = base of the natural logarithm
2.71828

14. 14
Projection - Definition
A population projection is:
– An extrapolation of historical data into the future
– An attempt to describe what is likely to happen under certain
explicit assumptions about the future as related to the
immediate past
– A set of calculations, which show the future course of
fertility, mortality and migration depending on the
assumptions used

15. Cohort component method
• Data required
– Initial (base) population by age and sex
– Assumptions on mortality - survival ratios by age and
sex
– Assumptions on fertility - ASFRs
– For an open population, assumptions on international
migration

16. Cohort component method
Computational steps:
– Project forward the base pop. in each age group in order to
estimate the number still alive at the beginning of the next
interval
– Compute the number of births for each age group over the
time interval, and compute the number who survive to the
beginning of the next interval
– Add migrants and subtract emigrants in each age group or
compute the number of births to these migrants during the
interval, and project forward the number of migrants and
number of births that will survive to the beginning of the
next interval

17. Cohort component method
Population aged 5 years and over:
– Obtain the survivors at the end of each projection
interval (except for the open age group) by
multiplying the survival ratio to the number of
persons at the beginning of the interval,
remembering to move the result one row down. In life
table terms, nLx specifies the mid-year pop. between
age x and x+n. Therefore, the survival ratio, the
proportion of persons surviving from age x to x+n, is
given by xLx+5/xLx (& Tx+5/Tx for the open age group)
– The number of survivors in the open age group is
obtained by adding the survivors from the preceding
age group to the survivors of the open age group
xn
xn
L
L 5
xn
xn
L
L 5

18. Cohort component method
Population below age 5:
– The pop. below age 5 at the end of the 5-year projection
interval consists of children born during the interval
– To obtain this pop., it is first necessary to compute the
number of births by sex occurring during this interval and
then apply survival ratios to this pop.
– The number of births is calculated from the ASFRs, the
number of women in the childbearing ages and the sex
ratio at birth
– The female population exposed to this fertility schedule in
each age group is the mean of the initial pop. & the
projected pop. since both groups contribute births to the
age group 0-4

19. Cohort component method
Population below age 5:
– Total births = n/2∑(fP + fP’)*ASFR, where fP and fP’ are
initial and projected female populations respectively
– Male births = Total births * SRB/(100 + SRB), where SRB =
Sex ratio at birth
– Female births = Total births * 100/(100 + SRB)
– 5P’o = Births * survival ratio (i.e. 5Lo/5lo)

20. Cohort component method
Age nLx nPx nPx+5
0-4 5Lo 5Po B* 5Lo/5lo
5-9 5L5 5P5 5Po * 5L5/5Lo
10-14 5L10 5P10 5P5 * 5L10/5L5
15-19 5L15 5P15 5P10 * 5L15/5L10
…….. …….. …….. ……..
…….. …….. …….. ……..
x - x+5 5Lx 5Px 5Px-5 * 5Lx/5Lx-5