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POPULATION PROJECTIONSPOPULATION PROJECTIONS

Session 3 - Establishing the base Session 3 - Establishing the base populationpopulation

Ben JarabiBen Jarabi

Population Studies & Research InstitutePopulation Studies & Research Institute

University of NairobiUniversity of Nairobi

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

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Types of ErrorsTypes of Errors ContentContent

Age mis-reportingAge mis-reporting

DigitDigit preference preference

CoverageCoverage

Omitting a unit that should have been Omitting a unit that should have been

includedincluded

Including a unit more than onceIncluding a unit more than once

Including a unit that should not have been Including a unit that should not have been

includedincluded

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Evaluation - RationaleEvaluation - Rationale Age structure is very important with Age structure is very important with

respect to planning for respect to planning for social and economic social and economic

necessitiesnecessities in human life in human life

Knowledge of age structure essential to Knowledge of age structure essential to

the the analysis of fertility, mortality & analysis of fertility, mortality &

migrationmigration

Errors by age & sex are Errors by age & sex are replicated & replicated &

repeatedrepeated in pop. projections - in pop. projections - hence the need

to evaluate and adjust where necessary

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Detecting errors – age reportingDetecting errors – age reporting

Age misreporting may be suggested by Age misreporting may be suggested by

irregularities evident in indices or irregularities evident in indices or

graphsgraphs

Population pyramidPopulation pyramid

Age and sex ratiosAge and sex ratios

Cohort comparisonCohort comparison

Summary indices of “irregularities” in Summary indices of “irregularities” in

age structure or in age-sex structureage structure or in age-sex structure

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Evaluation - Evaluation - Digit PreferenceDigit Preference

Frequently used indices for detecting digit Frequently used indices for detecting digit

preference:preference:

MyersMyers

Whipple’sWhipple’s

BachiBachi

RamachandranRamachandran

They provide not only an They provide not only an overall idea of the overall idea of the

extent of age misreportingextent of age misreporting but also but also

indicate the indicate the preference for certain ending preference for certain ending

age digitsage digits

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Evaluation - Age RatiosEvaluation - Age Ratios

Age ratios for 5-year age groups are Age ratios for 5-year age groups are

used as indices for detecting possible used as indices for detecting possible

age misreportingage misreporting

Normally age ratios are expected to Normally age ratios are expected to

be similar throughout the age be similar throughout the age

distribution, and all of them should distribution, and all of them should

be close to a value of 100be close to a value of 100

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Evaluation - Age RatiosEvaluation - Age Ratios An age ratio is defined as:An age ratio is defined as:

    55PPxx

55ARARxx = 100 = 100

1/2 (1/2 (55PPx-5x-5 + + 55PPx+5x+5))

  where: where: 55ARARxx = age ratio for ages x to x+4  = age ratio for ages x to x+4 

55PPxx = population at ages x to x+4 = population at ages x to x+4

The larger the departure of this ratio from The larger the departure of this ratio from

100, the larger the error100, the larger the error

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Evaluation -Evaluation - Sex RatiosSex Ratios

The level of the sex ratios depends on the The level of the sex ratios depends on the

number of male and female births and on number of male and female births and on

the mortality of the populationthe mortality of the population

All populations have more male than female All populations have more male than female

births, and so the sex ratio at the early ages births, and so the sex ratio at the early ages

is expected to be slightly over 100is expected to be slightly over 100

Since mortality is usually higher for males Since mortality is usually higher for males

than females, the sex ratio is reduced than females, the sex ratio is reduced

continuously up to the oldest agescontinuously up to the oldest ages

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Evaluation - Evaluation - Sex RatiosSex Ratios A sex ratio is defined as:A sex ratio is defined as:

    55MPMPxx

55SRSRxx = 100 = 100

55FPFPxx

  where: where: 55SRSRxx = sex ratio for ages x to x+4  = sex ratio for ages x to x+4 

55MPMPx x & & 55FPFPxx = male & female populations, = male & female populations,

respectively, at ages x to x+4respectively, at ages x to x+4

The larger the departure of this ratio from 100, The larger the departure of this ratio from 100,

the larger the errorthe larger the error

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The Age-Sex Accuracy IndexThe Age-Sex Accuracy Index The UN suggested a The UN suggested a joint accuracy index joint accuracy index to to

summarize the age & sex ratios summarize the age & sex ratios

The index of The index of sex-ratio score sex-ratio score (SRS) is (SRS) is

defined as: defined as: The mean difference between sex The mean difference between sex

ratios for the successive age groups, averaged ratios for the successive age groups, averaged

irrespective of signirrespective of sign

The index of The index of age-ratio score age-ratio score (ARS) is (ARS) is

defined as: defined as: The mean deviation of the age The mean deviation of the age

ratios from 100 percent, also irrespective of ratios from 100 percent, also irrespective of

signsign

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The Age-Sex Accuracy IndexThe Age-Sex Accuracy Index

Based on empirical relationships between Based on empirical relationships between

the sex-ratio scores and the age-ratio the sex-ratio scores and the age-ratio

scores, the following index is defined as scores, the following index is defined as

the the joint score joint score (JS) or age-sex accuracy (JS) or age-sex accuracy

indexindex

JS = 3xSRS + ARSM + ARSFJS = 3xSRS + ARSM + ARSF

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The Age-Sex Accuracy IndexThe Age-Sex Accuracy Index

The age and sex structure of a The age and sex structure of a

population will be:population will be:

accurateaccurate if the joint score index is under 20 if the joint score index is under 20

inaccurateinaccurate if the joint score index is if the joint score index is

between 20 and 40between 20 and 40

highly inaccuratehighly inaccurate if the index value is over if the index value is over

4040

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Correcting for Age MisreportingCorrecting for Age Misreporting

SmoothingSmoothing techniques have techniques have

frequently been used for correcting frequently been used for correcting

data for age misreporting data for age misreporting

These techniques involve the These techniques involve the

application of a formula to the application of a formula to the

original dataoriginal data

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Correcting for Age MisreportingCorrecting for Age Misreporting

Smoothing techniques may be classified Smoothing techniques may be classified

into 2 categories:into 2 categories:

Those which accept the population in Those which accept the population in

each 10‑year age group & separate it each 10‑year age group & separate it

into two 5‑year age groups into two 5‑year age groups without without

modifying modifying the total population sizethe total population size

Those which smooth the 5‑year age Those which smooth the 5‑year age

groups and groups and modify slightly modify slightly (either up or (either up or

down) the population being smootheddown) the population being smoothed

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Smoothing MethodsSmoothing Methods

Methods that preserve the original total:Methods that preserve the original total:

The Carrier‑Farrag and Karup‑King‑NewtonThe Carrier‑Farrag and Karup‑King‑Newton

The Arriaga formulaThe Arriaga formula

Arriaga’s “strong smoothing”Arriaga’s “strong smoothing”

Methods that alter the total slightly:Methods that alter the total slightly:

The United Nations methodThe United Nations method

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Smoothing MethodsSmoothing Methods

There is no generalized solution for all There is no generalized solution for all

populationspopulations

The technique to be used will depend on the The technique to be used will depend on the

errors in the age and sex distributionserrors in the age and sex distributions

While, as Arriaga and Associates (1994) note, While, as Arriaga and Associates (1994) note,

differences in results across procedures are differences in results across procedures are

small, a decision to use strong smoothing small, a decision to use strong smoothing

should not be taken lightlyshould not be taken lightly

The whole age distribution need not be The whole age distribution need not be

smoothed if only part is considered smoothed if only part is considered

problematicproblematic

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Evaluation and adjustmentEvaluation and adjustment

ExerciseExercise

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Inputs - Base PopulationInputs - Base Population A population by sex & age is required to serve A population by sex & age is required to serve

as the base population for the starting date of as the base population for the starting date of

the projectionthe projection

Usually, the base population is taken from the Usually, the base population is taken from the

latest available censuslatest available census

Census enumerations are not always perfect - Census enumerations are not always perfect -

the reported data on age and sex may be the reported data on age and sex may be

affected by errors – affected by errors – hence the need for hence the need for

adjustmentadjustment

Where necessary, move the adjusted Where necessary, move the adjusted

population from a given date (e.g. a census population from a given date (e.g. a census

date) to another date (e.g. midyear)date) to another date (e.g. midyear)