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

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

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 4 4 4

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 5 5 5

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 6 6 6

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 7 7 7

8. Evaluation - Age Ratios
An age ratio is defined as:
  Px
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 8 8 8

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 9 9 9

10. Evaluation - Sex Ratios
A sex ratio is defined as:
  MPx
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 10 10 10

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 11 11 11

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 12 12 12

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 13 13 13

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 14 14 14

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 15 15 15

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 16 16 16

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 17 17 17

18. Evaluation and adjustment
Exercise 18 18 18

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) 19 19 19