POPULATION PROJECTIONS
Session 2 - Background & first
steps
Ben Jarabi
Population Studies & Research Institute
University of Nairobi
1
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
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
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
Demographic Balancing Equation
 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
 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
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”
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
8
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
9
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
10
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
11
Projection – Linear growth

Assumptions:
 Growth rate is constant
 Change is only experienced at the end of
unit time
 Compounding takes place at specified
intervals
12
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
13
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
14
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
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
n
L x 5
n Lx
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
Cohort component method
Population below age 5:





The pop. below age 5 at the end of the 5year 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
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)
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
……..
……..
……..
……..
……..
……..
……..
……..
x - x+5
5Lx
5Px
* 5L15/5L10
5Px-5
* 5Lx/5Lx-5