1. 1 POPULATION PROJECTIONS Session 2 - Background & first steps Ben Jarabi Population Studies & Research Institute University of Nairobi

2. 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

3. 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

4. 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

5. Demographic Balancing Equation  Pop. change = (Births - Deaths) + (Immigrants -Emigrants)  P t = P 0 + (B -D) + (I-E) where: P 0 = initial population P t = population after time t P t = population after time t  Worldwide, natural increase is the most important component of overall population change over time

6. 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

7. 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”

8. 8 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

9. 9 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 P t = P 0 + bt where P 0 = initial population where P 0 = initial population P t = population t years later P t = population t years later b = annual amount of population change b = annual amount of population change

10. 10 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

11. 11 Projection – Geometric growth  The growth assumes a geometric series  It is expressed as P t = P 0 (1+ r) t P t = P 0 (1+ r) t where P 0 = initial population where P 0 = initial population P t = population t years later P t = population t years later

12. 12 Projection – Linear growth  Assumptions:  Growth rate is constant  Change is only experienced at the end of unit time   Compounding takes place at specified intervals

13. 13 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 P t = P 0 (e rt ) where P 0 = initial population where P 0 = initial population P t = population t years later P t = population t years later r = annual rate of growth r = annual rate of growth e = base of the natural logarithm e = base of the natural logarithm

14. 14 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

15. 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

16. 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

17. 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, n L x 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 x L x+5 / x L x (& T x+5 /T x 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

18. Cohort component method  Population below age 5:  The pop. below age 5 at the end of the 5- year 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

19. 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)  5 P’ o = Births * survival ratio (i.e. 5 L o /5lo)

20. Cohort component method Age nLxnLxnLxnLx nPxnPxnPxnPx n P x+5 0-4 5Lo5Lo5Lo5Lo 5Po5Po5Po5Po B* 5 L o /5l o 5-9 5L55L55L55L5 5P55P55P55P5 5 P o * 5 L 5 / 5 L o 10-14 5 L 10 5 P 10 5 P 5 * 5 L 10 / 5 L 5 15-19 5 L 15 5 P 15 5 P 10 * 5 L 15 / 5 L 10 ……..……..……..…….. ……..……..……..…….. x - x+5 5Lx5Lx5Lx5Lx 5Px5Px5Px5Px 5 P x-5 * 5 L x / 5 L x-5