Chapter 6: Variants, 2010-based NPP Reference Volume

Introduction

Population projections provide a consistent starting point for all government planning which is affected by the numbers in the population. The projections are based on assumptions considered to best reflect demographic patterns at the time they are adopted. However, due to the inherent uncertainty of demographic behaviour, any set of projections will inevitably be proved wrong, to a greater or lesser extent, as a forecast of future demographic events or population structure. Many users will need to take into account the consequences of future experience differing from the assumptions made and, to this end, variant projections based on alternative assumptions of future levels of fertility, mortality and migration are produced.

Aside from the principal projection, nine standard variant projections were published on 26 October 2011. A second release on 23 November included 11 further standard ‘combination’ and special case scenario variants. This chapter summarises the results of official high and low variant projections for the UK. These alternative assumptions have been prepared for each of the three components of population change (fertility, life expectancy and migration). They are intended as plausible alternative scenarios and not to represent upper or lower limits for future demographic behaviour. Probabilistic interpretations of population projections are also discussed later in this chapter.

Assumptions for fertility variants

In the long-term, changes in the level of fertility are critical in determining the size of the population. For example, a sustained increase in the level of fertility would clearly increase the number of births. But, in a generation’s time, it would also increase the number of women of childbearing age, compounding the effect on births.

Cohorts of women who have already completed their childbearing have shown a wide range of completed family sizes. Therefore, assumptions for generations who have not yet entered the childbearing ages, or who have done so only recently, are necessarily highly speculative.

The assumptions made for the fertility variants for the UK are summarised in Table 6.1 and illustrated in Figure 6.1. Under all scenarios, completed family size is seen to rise for successive cohorts between 1970 and 1980, reflecting the achieved fertility to date of these cohorts. The low fertility variant assumes that the average family size will initially rise, and then fall sharply to an ultimate level of 1.64 for women born from 2010 onwards. Although period fertility fell to around this level in 2001, completed family sizes in the UK have not fallen below 1.9 children in recent decades.

The high fertility variant would imply a reversal of the downward trend in average completed family size seen amongst women completing their childbearing over the last two decades. Under this assumption, family size would continue to decline to 1.88 children for the 1972 cohort before rising to a level of 2.12 for those born in the late 1980s, and then reaching an ultimate level of 2.04 for women born 2010 onwards. This is around the level of fertility actually achieved by women born in the mid 1950s, but less than that experienced by women born in the 1940s. The high fertility variant assumes continued increases in fertility rates at ages 25 and over. In the low fertility variant, it is assumed that fertility rates will fall at all ages from 2010 onwards.

Figure 6.1: Actual and assumed completed family size, women born 1950-2010, United Kingdom

Source: Office for National Statistics

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Table 6.1: Actual and assumed average number of children by age and year of birth of women, United Kingdom, women born 1950–2010

Table source: Office for National Statistics

Table notes:

1. figures in bold are partly or wholly assumed

Total fertility rates and numbers of births

The assumed total fertility rates and projected numbers of births resulting from these alternative assumptions of future fertility levels are shown in Figures 6.2 and 6.3. History shows that there can be quite sudden changes in period fertility. It is therefore, important to demonstrate the effect of significant short-term changes, as well as the long-term effects that would result from sustained levels of fertility significantly above or below that assumed in the principal projection. Consequently, the variants diverge quickly from the principal projection. Figure 6.2 shows the total fertility rate in the high fertility variant rises rapidly from the 2010 level of 1.98, reaching 2.14 by 2015 and then reducing to 2.04 in 2025. While the total fertility rate in the low fertility variant falls sharply to 1.64 by 2019.

Figure 6.2: Actual and assumed total fertility rates, 1961-2035, United Kingdom

Source: Office for National Statistics

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Figure 6.3 shows that under the high fertility variant, the number of births is projected to rise from around 807,000 in 2010, to 913,000 around 2017, dropping slightly to 882,000 in 2029 before rising steeply to around 1,020,000 in 2045 and then levelling out. However, under the low fertility variant, the number of births would fall quickly to approximately 716,000 a year and then continue to fluctuate around this level. Under the principal projection, the number of births is projected to rise steeply to 845,000 in 2014, then falling to 796,000 in 2029 rising again to 879,000 in 2048 and then levelling out.

In practice, variations in the timing of childbearing within women’s lives are likely, as in the past, to produce considerable fluctuations in the total fertility rate and the annual numbers of births. Therefore, even if trends in completed family size do tend in the long-term toward the assumptions underlying the principal projection or either of these variants, for any individual year the number of births could differ considerably from those shown here. 

Figure 6.3: Actual and projected number of births, 1961-2060, United Kingdom

Source: Office for National Statistics

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Effect of fertility variants on total population size

The differences between the projected population according to the high and low fertility variant projections and the principal projection are summarised in Table 6.2. Under the alternative fertility assumptions, the population would be 1.8 million higher or 2.4 million lower than the principal projection by 2035.  In the high fertility variant, the projected population at 2035 would be 75.0 million compared with 73.2 million in the principal projection, while in the low fertility variant it would be 70.8 million. Figure 6.8 later in this chapter, demonstrates how long-term total population size is sensitive to changes in the fertility assumption. By 2085, there is a difference of over 22 million between the total population projected by the high and low fertility variants.

Table 6.2: Population differences between fertility variant projections and prinicipal projection by age, 2016-2035, United Kingdom

Table source: Office for National Statistics

Assumptions for mortality variants

The mortality chapter discusses the current wide range of views about prospects for future longevity. To give some indication of these uncertainties, variant projections have been produced based on assumptions of higher and lower life expectancies at birth. The low life expectancy variant assumes slower improvements in mortality rates than in the principal projection and the high life expectancy variant assumes faster improvements. In addition a no mortality improvement variant projection has also been produced.

Current annual improvements in mortality rates vary considerably by age and sex. In each of these variants it is assumed that, for most ages, the improvements will gradually converge to common 'target rates' of improvement at each age and by both sexes by the year 2035, and continue to improve at that constant rate thereafter. However, as with the principal projection, these variant mortality projections also assume that those born after 1924 and before 1939 (cohorts which have consistently experienced relatively high rates of mortality improvement over the last 25 years than those born either side) will continue to experience higher rates of mortality improvement than the rest of the population.

The target rate assumptions (for most ages) are as follows:

·  High life expectancy variant: 2.4 per cent annual improvement at 2035, thereafter annual improvement remaining at 2.4 per cent. For those born between 1925 and 1938 rates of annual improvement in and after 2035 will rise to a peak of 3.7 per cent a year for those born in 1931 and 1932 and then decline back to 2.4 per cent a year for those born in 1939 or later.

·  Principal projection: 1.2 per cent annual improvement at 2035, thereafter annual improvement remaining at 1.2 per cent. For those born between 1925 and 1938 rates of annual improvement in and after 2035 will rise to a peak of 2.5 per cent a year for those born in 1931 and 1932 and then decline back to 1.2 per cent a year for those born in 1939 or later.

·  Low life expectancy variant: 0 per cent annual improvement at 2035, thereafter mortality rates remaining constant. For those born between 1925 and 1938 rates of annual improvement in and after 2035 will rise to a peak of 1.3 per cent a year for those born in 1931 and 1932 and then decline back to 0 per cent a year for those born in 1939 or later.

·  No mortality improvement: 0 per cent annual improvement, so mortality rates remain constant throughout the projection period at the levels assumed for 2010–11.

Because of fluctuations in annual mortality rates, there is always some uncertainty about establishing the ‘real’ current rate of mortality improvement. Further, epidemics (there have been no major ones in recent years), or hard winters, can have a considerable effect on the number of deaths, although this may be partially offset by fewer deaths than normal in the following year. In recent years, however, excess winter mortality has been relatively low, except for the winter of 2010/11.¹

As such uncertainties could have an immediate effect on the number of deaths recorded, the rates of improvement used for 2010 to 2011 in the principal projection were decreased by two percentage points for the low life expectancy and the medium low life expectancy variants, and increased by two percentage points for the high life expectancy and the medium high life expectancy variants.

Expectations of life at birth and numbers of deaths 

The different expectations of life at birth in the variant mortality projections are summarised in Table 6.3 and shown in Figure 6.4. These are period expectations of life, calculated on the basis of the mortality rates for a given calendar year. The projected numbers of deaths resulting from these different expectations of life at birth are shown in Figure 6.5.

Table 6.3: Period expectation of life at birth according to mortality rates assumed for selected years. Variant mortality projections, 2010-2035, United Kingdom

Table source: Office for National Statistics

Figure 6.4: Actual and projected period expectation of life at birth according to mortality rates for given years 1961-2085, United Kingdom

Source: Office for National Statistics

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Figure 6.5: Actual and projected number of deaths, 1961-2085, United Kingdom

Source: Office for National Statistics

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In the high life expectancy variant, period expectation of life at birth for males is projected to increase by 7.2 years from 78.5 in 2010 to 85.7 in 2035, while the corresponding increase for females is 6.1 years (from 82.4 to 88.5 years). In the low life expectancy variant, period expectation of life at birth is projected to increase by 2.5 years for males and 3.1 years for females reaching 81.0 and 85.5 years respectively by 2035. Figure 6.4 illustrates the further improvements assumed in the longer term with life expectancy at birth reaching 99.2 years for males and 100.8 years for females by 2085 for the high life expectancy variant. In the low life expectancy variant, there are only very marginal increases beyond 2035, as mortality rates are assumed to remain constant beyond 2035 at most ages.

Effect of mortality variants on total population size

The differences between the projected populations according to the high and low life expectancy variant projections and the principal projection are summarised in Table 6.4. The population at 2035 would be 73.9 million in the high life expectancy variant compared with 73.2 million in the principal projection (713,000 higher), but 72.5 million (741,000 lower) given the low life expectancy assumptions. Figure 6.8, later in this chapter, shows that by 2085, there is a difference of nearly 13 million between the total population in the high and low life expectancy variant projections. 

Table 6.4: Population differences between variant mortality projections and principal projection by age, 2016-2035, United Kingdom

Table source: Office for National Statistics

Assumptions for migration variants

The number of persons entering or leaving the UK has shown considerable year-to-year fluctuation in the recent past. In 1992–93, there was net outward migration. This was followed by a rapid rise in net inward migration to 267,000 by 2004-05. Between 2005–06 and 2009–10, it has averaged +200,000 per year.

For the principal projection, it is assumed that there will be a long-term net inflow of 200,000 persons a year to the UK. For the variant projections, annual net migration has been assumed to be 60,000 higher or lower than in the principal projection. So the high and low variants assume annual long-term net migration to the UK of 260,000 and 140,000 persons respectively. The variant assumptions are shown in Figure 6.6. Since the assumptions for 2010-11 take account of provisional estimates of long-term international (LTIM) for 2010 (calendar year) and additional provisional cross border migration data, from the NHSCR, for the second half of 2010; the allowance for uncertainty in the first year of the projection is only half that for later years. From 2011-12, the high migration variant is calculated by assuming 30,000 more immigrants and 30,000 fewer emigrants each year than in the principal projection and vice versa for the low migration variant. 

Figure 6.6: Actual and assumed total net migration, United Kingdom, 1991-92 to 2020-21

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The equivalent figure for the constituent countries of the UK can be found in the migration assumptions report published on 26th October 2011, under appendices A-D.

Variants are not intended to represent limits for future demographic behaviour. Indeed, in the case of migration, whatever average level occurs in the future, it is possible that there will be some years when net migration exceeds the level of the high variant and others where it will be below the level of the low variant. Therefore, these migration variants should be regarded as giving an indication of the implications for the future if average migration levels were to differ significantly from those assumed in the principal projection.

Effect of migration variants on total population size

The differences between the population according to the high and low migration variant projections and the principal projection are summarised in Table 6.5. Unlike the fertility and mortality variants, the migration variants are exactly symmetrical with respect to the principal projection, so only one set of figures is shown in the table.

Clearly if, after the first year, annual net migration was 60,000 a year more (or less) than assumed in the principal projection, this would lead to just under 1.5 million more (or less) migrants over the next 25 years. However, because migration is concentrated at young adult ages, there is also a significant second generation effect with the different number of migrants changing the number of women of childbearing age and hence the future number of births. Because migrants are predominantly young, the effect on the number of deaths over this period is considerably smaller. 

Table 6.5: Population differences between variant migration projections and principal projection by age, 2016-2035, United Kingdom

Table source: Office for National Statistics

In fact, Table 6.5 shows that the alternative migration assumptions would lead to 1.9 million more (or less) people in the population at 2035 as compared with the principal projection. But even 25 years ahead, these alternative assumptions would have little effect on the number of people aged over 60. By the year 2035, the population would be 75.1 million in the high migration variant compared with 73.2 million in the principal projection, but only 71.3 million under the low variant assumptions. Figure 6.8, later in this chapter, shows that by 2085, there is a difference of 13.6 million between the total population in the high and low migration variants.

An interesting feature of these migration variants is that, although it is assumed that migration will continue to be concentrated at working ages, there is comparatively little effect on long-term dependency ratios. In the principal projection, the ‘pensionable age dependency ratio’ (defined as the number of persons of pensionable age per 1,000 persons of working age²), would be 349 per 1,000 at 2035. But this ratio is not greatly different under the alternative migration assumptions; in the high and low migration variants, the ratios at 2035 are 340 and 359 per 1,000 persons of working age respectively.

Previous work has shown that any realistic assumption of future migration could only have a very limited effect on population ageing.³  In contrast, the raising of State Pension age has a much greater effect. If State Pension age remained at 65 for men and 60 for women, the pensionable age dependency ratio at 2035 would have been 460 per 1,000 persons of working age rather than 349.

Combination variants

For particular applications, users may also be interested in projections combining two or more of these alternative scenarios, for example, high fertility and low migration. Some key summary statistics from selected combination variants are given in Table 6.6. For example, the largest total population size would result from combining the high variant assumptions for fertility, life expectancy and migration. With this combination of assumptions, the population would be over 77 million by 2035 and nearly 95 million by 2060. However, for the lowest population size which results from combining the low variant assumptions for the three components, the population in 2060 would be 68 million, although this would still be higher than the population in 2010.

Over the 50 year period to 2060, the highest dependency ratios (amongst the combination variants) occur given high fertility, high life expectancy and low migration. However, in the very long-term, the ‘old age structure’ and ‘young age structure’ variants generally produce respectively the highest and lowest overall dependency ratios of all the possible combination variants. 

Table 6.6: Measures of population structure under the principal and variant projections, 2035 and 2060, United Kingdom

Table source: Office for National Statistics

Total population size

Figure 6.7 shows the implications for future population growth under each of the ‘single component’ variant projections. It also shows the results of the high and low population combination variants described above which, for practical purposes, can be regarded as giving plausible upper and lower bounds for future total population size. The chart shows that there is considerable uncertainty about the future size of the population and that uncertainty widens appreciably over time.

In the principal projection, the high population combination variant and all the single component variants, the total population of the UK is projected to continue growing throughout the projection period. But, the low population variant shows that continuing population growth is not inevitable. Under this combination of assumptions, the UK population would peak in size by the late 2040s. 

Figure 6.7: Actual and projected total population, United Kingdom, 1981-2085

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The equivalent figure for the constituent countries of the UK can be found in the results report published on 26th October 2011, under appendices A-D.

Population aged 65 and over

Figure 6.8 shows the projected proportion of the population aged 65 and over under various alternative assumptions. In this case, as well as the single component variants, the chart also shows the results of the ‘old age structure’ and ‘young age structure’ combination variants. Again, these can effectively be regarded as giving upper and lower bounds for the proportion of older people in the population.

The chart shows that population ageing will occur under any plausible set of future assumptions. In 2010, some 17 per cent of the population were aged 65 and over. This is projected to rise sharply at first then more steadily to reach 31 or 32 per cent by 2085 in either the low fertility or high life expectancy variants. Under the low life expectancy or high fertility variants, ageing would be significantly reduced but the proportion over 65 would still increase to 23 or 26 per cent. Even in the ‘young age structure’ variant projection, the proportion would increase to 20 per cent by 2028.

Figure 6.8: Actual and projected percentage of the population aged 65 and over, United Kingdom, 1981-2085

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The equivalent figure for the constituent countries of the UK can be found in the extra variants report published on the 23rd November 2011.

Probabilistic interpretation of population projections

One of the limitations of the traditional deterministic approach – used in the UK to produce the official population projections – is that no probabilities are attached to the principal projections, so users are given no information about the uncertainty associated with them or, with respect to the variants, are given no indication of how these compare to the principal projections in terms of certainty. In response to these concerns, increasing attention is now being given to stochastic forecasting methods. Typically, stochastic forecasts use probability distributions for the components of demographic change, namely of fertility, mortality and migration. These are derived using some combination of three recognised approaches: analysis of past projection errors, expert opinion and time series analysis. By using these approaches, ONS began developing a stochastic forecasting model for the UK and a progress report ⁴ was published in August 2009. The paper reported the early findings of the research and, any results presented are provisional only.

Relative uncertainties of fertility, mortality and migration

Because precise probability statements cannot be ascribed to the variant assumptions, strictly the indications of uncertainty given above for fertility, mortality and migration are not directly comparable. Nevertheless, it is also possible to make some general comments about the relative importance of fluctuations in fertility, mortality and migration for particular users of the projections.

The majority of users are interested principally in the first twenty years of the projection,⁵  over which period possible variations in migration numbers or fertility patterns are likely to have a greater impact on the projected size and age structure of the population than variations in mortality rates. However, for applications concerned primarily with the elderly such as planning health and social care services, interest will centre on variations in mortality. In areas such as long term social security benefit planning, the effect of both mortality and fertility variants has to be considered, whilst for other applications, such as those concerned with the size of the work force and the numbers of households, future migration levels are of particular importance.

Another way of indicating uncertainty is to consider the accuracy of previous sets of projections. A detailed study of the accuracy of past UK national population projections has been published.⁶  The analysis was based on the extensive database of past national projections available on the GAD website.⁷  This UK study was followed by an analysis of how UK projections compared with those for other European countries.⁸   These articles concluded that in the UK, as in most other countries, fertility had tended to be overprojected while life expectancy and net inward migration had generally been underprojected. Compared with other countries, fertility errors were somewhat larger in UK projections, but mortality errors were smaller. Migration errors in UK projections were around the European average.

Figure 6.9 gives an indication of the relative importance of the assumptions regarding fertility, mortality and migration for the population at each age in 2035. It shows (for each component) the difference between the populations in the high and low variant projections at each age, expressed as a percentage of the population in the principal projection. The greatest cause of uncertainty at younger ages is fertility. Migration is the most important variable in determining the size of the working age population in 25 years time, while mortality only begins to become the dominant factor after age 66.

Figure 6.9: Population differences between high and low variants as a percentage of the population in the principal projection by age, 2035, United Kingdom

Source: Office for National Statistics

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Further information

Special case scenarios

It is also sometimes useful to prepare special case scenarios or ‘what if’ projections, to illustrate the consequences of a particular, but not necessarily realistic, set of assumptions. Eight additional projections have been produced based on the following special case assumptions:

• Replacement fertility  
• Constant fertility
• No mortality improvement
• Zero net migration (natural change only)
• Zero net migration and no mortality improvement
• No change
• Stationary
• Long-term balanced net migration ( UK only)

More information on the eight additional variant projections can be found in releases published on 26th October and 23rd November 2011.

References

1.  Excess winter mortality in England and Wales. ONS News Release (November 2009). Available at  www.ons.gov.uk/ons/publications/all-releases.html?definition=tcm%3A77-210640

2.  Working age and pensionable age populations based on the changed definitions of State Pension age under the 1995 and 2007 Pensions Acts: Between 2010 and 2020, State Pension age will change from 65 years for men and 60 years for women, to 65 years for both sexes. Between 2024 and 2046, State Pension age will increase in three stages from 65 years to 68 years for both sexes. These data do not take into account changes due to the Pensions Act 2011, see Chapter 2 figures 2.8 and 2.9 for further information on the effect of these changes.

3.  Shaw C (2001) United Kingdom population trends in the 21st century. Population Trends 103, pp 37-46. Available at:   www.ons.gov.uk/ons/rel/population-trends-rd/population-trends/no--103--spring-2001/population-trends.pdf 

4.  ONS (Q3 2009) Progress report on developing stochastic population forecasts for the United Kingdom. Available at: www.ons.gov.uk/ons/guide-method/method-quality/imps/updates-and-reports/historical/2009/progress-report-on-developing-stochastic-population-forecasts-for-the-uk---august-2009.pdf

5.  Joshi H and Diamond I. Demographic projections: who needs to know? From Population projections: trends, methods and uses. OPCS Occasional Paper 38. Papers of the Annual Conference of the British Society for Population Studies. OPCS (1990). 

6.  Shaw C (2007). Fifty years of United Kingdom national population projections: how accurate have they been? Population Trends 128. pp 8-23: www.ons.gov.uk/ons/rel/population-trends-rd/population-trends/no--128--summer-2007/fifty-years-of-united-kingdom-national-population-projections--how-accurate-have-they-been-.pdf

7.  Government Actuary Department: www.gad.gov.uk/Demography%20Data/Population/index.aspx

8.  Keilman N (2007). UK national population projections in perspective: How successful compared to those in other European countries? Population Trends 129. pp 20-30: www.ons.gov.uk/ons/rel/population-trends-rd/population-trends/no--129--autumn-2007/index.html

Background notes

1. Details of the policy governing the release of new data are available by visiting www.statisticsauthority.gov.uk/assessment/code-of-practice/index.html or from the Media Relations Office email: media.relations@ons.gsi.gov.uk

   These National Statistics are produced to high professional standards and released according to the arrangements approved by the UK Statistics Authority.