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1. 1
POPULATION PROJECTIONS
Session 3 - Establishing the base
population
Ben Jarabi
Population Studies & Research Institute
University of Nairobi

2. Population Age-sex Structure
 Age-sex structure is a map of a population’s
demographic history
 Although all modern censuses collect
information on age and sex of a pop., the
data often contain errors because some
people do not know their true age while
others do not report their age accurately

3. 3
Types of Errors
 Content
 Age mis-reporting
 Digit preference
 Coverage
 Omitting a unit that should have been
included
 Including a unit more than once
 Including a unit that should not have been
included

4. 4
Evaluation - Rationale
 Age structure is very important with
respect to planning for social and economic
necessities in human life
 Knowledge of age structure essential to the
analysis of fertility, mortality & migration
 Errors by age & sex are replicated &
repeated in pop. projections - hence the need
to evaluate and adjust where necessary

5. 5
Detecting errors – age reporting
 Age misreporting may be suggested by
irregularities evident in indices or
graphs
 Population pyramid
 Age and sex ratios
 Cohort comparison
 Summary indices of “irregularities” in
age structure or in age-sex structure

6. 6
Evaluation - Digit Preference
 Frequently used indices for detecting digit
preference:
 Myers
 Whipple’s
 Bachi
 Ramachandran
 They provide not only an overall idea of the
extent of age misreporting but also indicate
the preference for certain ending age digits

7. 7
Evaluation - Age Ratios
 Age ratios for 5-year age groups are
used as indices for detecting possible
age misreporting
 Normally age ratios are expected to
be similar throughout the age
distribution, and all of them should be
close to a value of 100

8. 8
Evaluation - Age Ratios
 An age ratio is defined as:
5Px
5ARx = 100
1/2 (5Px-5 + 5Px+5)
where: 5ARx = age ratio for ages x to x+4
5Px = population at ages x to x+4
 The larger the departure of this ratio from
100, the larger the error

9. 9
Evaluation - Sex Ratios
 The level of the sex ratios depends on the
number of male and female births and on
the mortality of the population
 All populations have more male than female
births, and so the sex ratio at the early
ages is expected to be slightly over 100
 Since mortality is usually higher for males
than females, the sex ratio is reduced
continuously up to the oldest ages

10. 10
Evaluation - Sex Ratios
 A sex ratio is defined as:
5MPx
5SRx = 100
5FPx
where: 5SRx = sex ratio for ages x to x+4
5MPx & 5FPx = male & female populations,
respectively, at ages x to x+4
 The larger the departure of this ratio from 100,
the larger the error

11. 11
The Age-Sex Accuracy Index
 The UN suggested a joint accuracy index to
summarize the age & sex ratios
 The index of sex-ratio score (SRS) is
defined as: The mean difference between sex
ratios for the successive age groups, averaged
irrespective of sign
 The index of age-ratio score (ARS) is
defined as: The mean deviation of the age
ratios from 100 percent, also irrespective of
sign

12. 12
The Age-Sex Accuracy Index
 Based on empirical relationships between
the sex-ratio scores and the age-ratio
scores, the following index is defined as the
joint score (JS) or age-sex accuracy index
 JS = 3xSRS + ARSM + ARSF

13. 13
The Age-Sex Accuracy Index
 The age and sex structure of a
population will be:
 accurate if the joint score index is under 20
 inaccurate if the joint score index is
between 20 and 40
 highly inaccurate if the index value is over
40

14. 14
Correcting for Age Misreporting
 Smoothing techniques have
frequently been used for correcting
data for age misreporting
 These techniques involve the
application of a formula to the
original data

15. 15
Correcting for Age Misreporting
 Smoothing techniques may be classified
into 2 categories:
 Those which accept the population in
each 10-year age group & separate it into
two 5-year age groups without modifying
the total population size
 Those which smooth the 5-year age
groups and modify slightly (either up or
down) the population being smoothed

16. 16
Smoothing Methods
 Methods that preserve the original total:
 The Carrier-Farrag and Karup-King-Newton
 The Arriaga formula
 Arriaga’s “strong smoothing”
 Methods that alter the total slightly:
 The United Nations method

17. 17
Smoothing Methods
 There is no generalized solution for all
populations
 The technique to be used will depend on the
errors in the age and sex distributions
 While, as Arriaga and Associates (1994) note,
differences in results across procedures are
small, a decision to use strong smoothing
should not be taken lightly
 The whole age distribution need not be
smoothed if only part is considered problematic

18. 18
Evaluation and adjustment
Exercise

19. 19
Inputs - Base Population
 A population by sex & age is required to serve
as the base population for the starting date of
the projection
 Usually, the base population is taken from the
latest available census
 Census enumerations are not always perfect -
the reported data on age and sex may be
affected by errors – hence the need for
adjustment
 Where necessary, move the adjusted
population from a given date (e.g. a census
date) to another date (e.g. midyear)