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What are Variant Projections and Why are They Needed?

What are Variant Projections and Why are They Needed?

1.  Every two years the Government Actuary's Department (GAD) has, in consultation with the Registrar Generals produced a "principal" population projection and a number of "variant" projections, based on alternative assumptions of future fertility, mortality and migration, for the UK and its constituent countries. The variants are produced to give users an indication of the inherent uncertainty of demographic behaviour. The purpose is to illustrate possible alternative scenarios and not to represent upper or lower limits on future demographic behaviour. There are two distinct types of variant produced: "standard" variants and "special case scenarios".

2.  As well as producing the "principal" assumptions, high and low assumptions are prepared for each of the components of population change (fertility, life expectancy and net migration). These are usually referred to as "standard variants". There are 27 possible combinations of these sets of assumptions, although aside from the principal projection only 12 are published by GAD. These are the six possible "single component" variants (i.e. varying only one component at a time from the principal assumptions) and six selected "combination" variants (those which produce the largest/smallest total population size (the "high" and "low" population projections), the oldest/youngest age structure (the "old" and "young" projections) and the highest/lowest dependency ratios ("high dependency" and "low dependency" projections)). Dependency ratios show the relationship between the working age population and the two main dependent groups – children under 16 and people of state pensionable age.

3.  As well as producing the "standard variants", GAD produce "special case scenarios", or "what if" projections, to illustrate the consequences of a particular, but not necessarily realistic, set of assumptions. Four sets of special case scenarios were prepared:

  • Replacement fertility represents the level of fertility required for the population to replace itself in size the long-term given constant mortality rates and in the absence of migration.  Around 2.075 children per woman are needed to ensure the long-term “natural” replacement of the population. The replacement fertility projection combines that level of fertility with the principal projection assumptions of mortality and migration;
  • Constant fertility assumes that age specific fertility rates [Footnote 1] will remain constant at the values assumed for the first year (2004-05) of the principal projection. Fertility rates have risen over the last two or three years and a continuation of these 2004-05 fertility rates produces long-term total fertility rates which are marginally above those assumed for the principal projection. The constant fertility projection combines constant level fertility with the principal projections of mortality and migration;
  • No mortality improvement assumes that age/sex specific mortality rates will remain constant at the values assumed for the first year of the principal projections. This projection combines no mortality improvement with the principal projections of fertility and migration;
  • Zero migration uses the principal assumptions of fertility and mortality and assumes that there will be zero net migration (at every age). It therefore shows the projected natural change in the population based on the principal assumptions of fertility and mortality in the absence of migration, or where migration inflows and outflows are exactly equal at every age.

4.  Two further special case projections, based on combinations of these assumptions, were also prepared:

  • No change projection shows what would happen if fertility, mortality and net migration were to remain constant at current levels. It therefore assumes the fertility rates from the constant fertility projections and the mortality rates from the no mortality improvement projection. Given recent fluctuations in net migration, it is much more difficult to define what is meant by the current level of migration. However the principal projections assume constant annual net migration from 2007-08 onwards at levels based on analysis of recent trends.  Therefore the principal migration assumptions have been used for the no change projection.
  • Stationary projection shows a population with an unchanging size and age structure which would arise, eventually, given replacement level fertility, constant mortality rates at all ages and zero net migration at all ages. The projection therefore assumes the fertility rates from the replacement fertility projection, the mortality rates from the no mortality improvement projection and zero net migration at each age as in the zero migration projection. In practice, it takes time for the population to reach stationary conditions because of the momentum resulting from the existing population age structure.

5.  These alternative variant projections and scenarios are needed because it is impossible to project future population levels with complete accuracy. The principal projection is based on recent trends in births, deaths and migration. But it is not a firm forecast of what will happen and, in particular, it takes no account of future policy changes. It simply shows what might happen if the recent trends were to continue. The variant projections and scenarios show a range of possibilities and also show the effects of changing the underlying assumptions. These alternatives are especially useful for planning purposes.

6.  Table 1 shows the assumptions used in the principal projection and also the alternative assumptions used in the variant projections. For example, a net inflow of +12,500 is assumed for the long-term under the high migration variant and a net outflow of -4,500 under the low migration variant, compared with the assumed net inflow of +4,000 used in the principal projection. So the high migration variant assumes +12,500 people per annum due to migration over the long-term with the fertility and mortality assumptions used in the principal projection (i.e. TFR [Footnote 2] of 1.6 and projected life expectancy at birth of 79.1 for males and 83.6 for females by 2030-31).

7.  Variant projections were first produced for Scotland (and the other individual countries of the UK) for the 2000-based round. The aim was that the standard variants should represent broadly comparable margins of uncertainty to the established series produced for many years at UK level. The separate fertility, mortality and migration variants are also intended to cover approximately similar margins of uncertainty. However, the cohort component method used to produce these projections does not enable statements of probability to be attached to them, or for confidence intervals to be ascribed to variants. Necessarily, therefore, the choice of assumptions is inevitably somewhat subjective.

8.  For fertility and mortality, uncertainty at individual country level is unlikely to differ significantly from that at UK level. So, for fertility, for example, the high and low variants for Scotland assume long-term TFRs which differ from the principal by ± 0.2 children per woman as has been the convention for UK level variants. For migration, however, relative uncertainty tends to increase for smaller areas. The choice of variant migration assumptions for the individual countries has been informed by an analysis of relative standard deviations in the annual historical migration time-series.

9.  ONS are currently conducting research into probabilistic projection methods with a view to improving the quantification of uncertainty in national population projections. 

10.  This paper presents the results for the variant projections by looking first at the standard "single component" variants and the standard "combination" variants together (as these are based on alternative plausible assumptions) before looking at the "special case scenarios" (as these are based on less realistic assumptions). The paper concludes by looking at projected population growth due to migration and the effect of natural change. Annex A provides information on how to obtain the detailed results of the variant projections and contains two tables which summarise the assumptions which are used in each type of projection. Annex B gives information on the method of projection, the accuracy of projections and the base population used. Some of the figures in this paper show results up to 2074. But projections so far ahead should be treated with great caution: the further in the future they go, the more uncertain they become.


1.  Age Specific Fertility Rate (ASFR) – the number of births per individual for a specific age during a specified time.

2.  The total fertility rate (TFR) is a commonly used summary measure of fertility levels calculated by summing the age specific rates (ASFR) for a particular year.  It gives the average number of children that a group of women would expect to have if they experienced the observed ASFR in each of their childbearing years (assumed to be from age 15 to 45 for projection purposes).

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