SADC Course in Statistics Population Projections - I (Session 19)

SADC Course in Statistics

Population Projections - I

(Session 19)

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Learning Objectives – this session

At the end of this session, you will be able to

• follow the basic approach of demographers in projecting populations forward from the time for which they have data

• explain the component method of projection and its constituent parts

• appreciate the use of life table values as part of the projection process


Seeing the future?

Several methods attempt to look ahead and set a value on future population size or a component thereof. Demographers do not refer to the results as “predictions” as that would imply they believe in the absolute accuracy of the numbers; in fact any future estimate is inaccurate to some degree because of unforeseeable factors.

“Projection” implies taking best available existing information and working out what will happen on a set of stated assumptions.


“Geometric model”

One very simplified approach is to argue:-

Pt = P0(1+r)t where

P0 is the initial population size on which the

projection is based;

r is the constant annual growth rate

Pt is the population after t years.

Example: population of an island is 1500. If annual growth rate is 4%, population in7 years time will be 1500(1 + 0.04)7 = 1974


Other simple models

Of course other “mathematical” models are possible, e.g. arithmetic: Pt = P0(1+rt);

exponential : Pt = P0.ert.

All such models produce not-very-inaccurate short-term projections of the total size of a national pop.n in normal circumstances, but they are not based on using detailed knowledge of demographic make-up, and are too crude adequately to project other features of the population.


“Component methods”: 1

With the same Pt & P0, the basic idea of all

component methods is:-

Pt = P0 + B – D + I – E where

B is the number of births in period of t years

D is the no. of deaths in period of t years

I is the no. of immigrants in period of t years

E is the no. of emigrants in period of t years


“Component methods”: 2

Whether the above is simple or complex depends on how sophisticated the system is for working out components B, D, I, and E.

A worthwhile system takes age and sex into account, and most “demographic” systems make projections one year at a time. Often the projection is labelled by a year e.g. 2010, so demographers work to a mid-year date.


Deaths component

If nPx is the number of persons at mid-year n,

at that time aged x [and less than (x+1)], then – with their birthdays spread evenly through the year – they were on average aged (x+½) at mid-year.

If we set out to express nPx in terms of the

previous year’s existing population,

nPx = n-1Px-1 (1 – n-1qx-½), the q-term indicating

that at mid-year (n-1), the average age of the group was (x- ½).


Deaths: a verbal explanation

People (usually one sex) who were between their (x-1)th and xth birthdays were subject to LT mortality and aged by one year in the year. Their average age was (x-½) at the start of the period at mid-year (n-1), hence the application of qx-½ to take account of

deaths amongst them.

The superscript on n-1qx-½ indicates that we

are assuming deaths rates may change from year to year.


Deaths: separate sexes

If we are specifically talking about one sex, using another superfix is common, e.g. for

females:-

nPx = n-1Px-1 (1 – n-1qx-½)

Despite its formidable appearance note that this formula still just represents applying a LT death rate to an existing population, for each age and sex, each year.

f f f


Migration component

Many countries get some migration information about legitimate passage via an international airport, but with extensive land borders, it is often very hard to measure movement to/ from contiguous states, e.g. unauthorised movements of distress migrants seeking some form of relief/sanctuary.

Below formal methodologies are illustrated with UK information ~ an “easier” case!


Migration: 1

There is a good explanation athttp://www.gad.gov.uk/population/2004/methodology/migrass.htm

of how the UK comes up with figures of net migration for its population projections.

This component can vary unpredictably from year to year e.g. when Poland joined the EU many more young adult Poles than expected took up their new right to seek work in UK. As a relatively wealthy island, UK is better-equipped than many countries to monitor in- and out-migrants.


Migration: 2

For UK, migrants (in- and out-) are defined as individuals who change their country of usual residence for a period of at least a year, so that the country of destination becomes the country of usual residence. Principal UK source of data about them is the International Passenger Survey (IPS), but with corrections for no. of people who change their declared length of stay in or out of UK.


Migration: 3

Only land border is with Irish Republic. The 2 Stats Offices collaborate on agreed net migration [10,000/year net from UK].

Note this equates to about 1 per 6000 of UK population. Estimate to nearest 1,000 is good enough for practical purposes.

No.s seeking political asylum are advised by Gov.t Department handling their cases.


Illustration: UK’s assumed figures

2004-based 02 & 03-based

IPS +145,000 +130,000

Visitor switcher adjustment

+15,000 +10,000

Migrant switcher adjustment

-20,000 -15,000

Asylum seeker adjustment

+15,000 +15,000

I rish Republic -10,000 -10,000

Total +145,000 +130,000

Note that all are to nearest 1000 only.


Geographic disaggregation

UK has figures for England, Wales, Scotland, Great Britain, Northern Ireland, and UK –

{GB = E + S + W}; {UK = GB +NI} –

so net international migration is apportioned to these for their separate projections.

UK also has estimated figures for net internal migration between constituent countries.


Age- & sex-wise disaggregation

Age gp Persons Males Females 40 - 44 3.6 2.0 1.5

0 - 4 3.0 0.3 2.7 45 - 49 -2.2 -0.9 -1.3

5 - 9 4.2 1.8 2.4 50 - 54 -1.8 -1.2 -0.6

10 - 14 2.5 2.4 0.1 55 - 59 -2.9 -1.9 -1.0

15 - 19 37.9 21.3 16.7 60 - 64 -3.5 -2.5 -1.0

20 - 24 50.7 20.2 30.5 65 - 69 0.0 0.3 -0.3

25 - 29 34.5 18.1 16.4 70 - 74 -0.4 -0.4 0.0

30 - 34 12.2 4.6 7.6 75 + 1.5 0.7 0.8

35 - 39 5.7 3.1 2.6 All ages 145.0 68.0 77.0

Note: net migration so (-) figures make sense.


Fertility and births

The effects of deaths and migration are what change almost all the numbers in a population schedule of numbers by age and sex, when it is projected forward e.g. by one year.

The new arrivals in the first age category are of course the births. These derive from the age-specific fertility rates of the existing female population in the age range 15 – 49.


Projected population aged zero

Births make up the one-year projected population aged zero (with tiny number of net migrants who are babies, migrating with parent + few international adoptions).

nB = total number of live births in the period from mid-year (n-1) to mid-year n.

We also need to think about the mothers’ ages and age-specific fertility rates, and about infant mortality, before we can generate the population projection - nP0


Women at fertile ages

Age-specific fertility rates are usually very low outside the women’s ages 15 - <50.

Take “” (Greek sigma) to mean

“the sum from ages 15 to 49 inclusive”.nBx = number of births to mothers aged x

= (no. of women aged x at the relevant time*) x (age-specific fertility rate for women aged x§)

* Note that this number needs care to define exactly because of mid-year conventions for projections ~ and because this relates to woman’s age when she gave birth

§ .. in the year in question: may change over yrs of projection


The stock of babies

We need to look at the parental stock, specifically at mothers’ ages and fertility rates, to figure out numbers of babies that will be born.

Once born, projections at the level of national populations, treat a baby as a baby, regardless of parental ages or other family characteristics: our concern becomesnB = nBx


Infant deathsnB represents the projected births between

mid-year (n-1) and mid-year n. At mid-year n they vary in age from 0 to just under 1. To survive into the population of mid-year n, they have to survive after birth for an average of ½ a year each, so ignoring migration:

nP0 = nB (1 - ½q0)

The q-term corresponding to the probability of a baby dying within half a year of birth in year (n-1).

n-1


Summing-Up

This session has described the “mechanics” of pop.n projection by the component method.

Existing pop.ns by age/sex are pushed up by a year of age, numbers dying are subtracted, in- and out-migrants are attributed to age bands and added/subtracted respectively, then survivors of births are pushed into the age 0 slots.

Need to look at examples of this process, and some subtleties of its management.


Some practical work follows …

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SADC Course in Statistics Population Projections - I (Session 19)

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