# Population Projections Scotland (2008-based)

### 5. Methodology and assumptions

5.1 Methodology

5.1.1 The results are produced by the demographic component method using a single year projection model (see paragraph 5.1.2). That is, a projection is made by sex and single year of age (up to age 90 & over) for each future year. This is done for arithmetical convenience and should not be taken to imply that reliable projections can be made in such detail. However, it provides "building blocks" which users can aggregate into age-groups of their choice for the years in which they are interested. For example, the production of results in standard five-year age groups (0-4, 5-9, 10-14, etc.) does not help the education planner wishing to know the size of the future population of secondary school age. Also, as some planning is done on a "rolling" basis (for example 10 years from a moving base date), it is useful to be able to provide a projection for any future year rather than just selected years.

5.1.2 The projection starts with the population estimates for the base year, disaggregated by single year of age, sex, and area. This base population is then projected one year ahead. First, an estimate of the numbers surviving to be one year older is made by applying a series of mortality rates to give the numbers of deaths, and hence survivors, at each age. The numbers of live births in the year are produced, using fertility rates in combination with the female populations of child bearing age; and an allowance is made for infant mortality. Lastly, the expected number and age/sex structure of people entering and leaving the area is taken into account in order to cover changes in the population due to migration. These three components of population change, together with the starting population, combine to form a projection of the population one year from the base date. The process can be repeated as often as required. For each year of the projection period, it is necessary to make assumptions about the future fertility rates (to give the number of births), mortality rates (for deaths) and migration. The following paragraphs describe the base population, the small changes made to the method compared with previous projections as well as the assumptions made in the new projections.

5.2 Base population

5.2.1 The Registrar General's mid-2008 population estimates were published in April 2009. It is these figures which are used as the base population. These cover all persons usually resident in each area, whatever their nationality. Usual residents temporarily away from home are included, but visitors are excluded. Students are taken to be resident at their term-time address. Members of Her Majesty’s (HM) and non-UK Armed Forces stationed in Scotland are included; HM forces stationed outside Scotland are excluded. Population figures relate to 30 June 2008 and ages relate to age last birthday.

5.3 Projections software system and other small method changes

5.3.1 The software used to produce the population projections is an in-house Microsoft (MS) Excel macro system which has been developed over a number of years. The system runs on 36 "building bricks" - areas which aggregate to both council and NHS board areas. In order to get the base populations for the part areas the 2008 Small Area population estimates (published September 2009) are used to get the best fit to these areas. While datazones nest into council areas they do not nest into NHS health board areas. Therefore it is assumed that the difference in the base year population estimates and the "best fit" estimates for NHS board areas remains constant for all 25 years of the projection period. All the projection outputs are adjusted accordingly with these small changes.

5.4 Fertility

5.4.1 The projected number of births was obtained by applying age specific fertility5 rates to the numbers of women at each childbearing age, for each year of the projection period. In determining the fertility rates used in the national projections for Scotland, assumptions were made about the average completed family size for successive generations of women. This measure tends to be more stable over time than fertility rates for specific years (so-called period fertility rates), because of generational differences in the timing of having families. It was assumed that the average completed family size will continue to decline from around 1.85 children per woman for those born in the early 1960s and now reaching the end of their childbearing lives, before levelling off at 1.70 for those born in the 1990s and later. The number of births is expected to fall from around 60,000 in 2008 to around 53,600 in 2033. The resultant age specific fertility rates assumed for Scotland as a whole are given in Annex A. More information on the fertility assumptions for Scotland can be found in Annex A to the publication "Projected Population of Scotland (2008-based)" on the General Register Office for Scotland’s website.

5.4.2 The projected number of births by administrative area is shown in Table 4. The percentage change in the number of projected births between 2008 and 2033 by council area is also shown in Figure 11.

Figure 11 Projected percentage change in births (2008-based), by council area, 2008-2033

5.4.3 For local areas, the assumed national fertility rates have been adjusted to take account of local variations observed in the five year period preceding the projection. The local scaling factors used to adjust the national rates are given in Annex C.

5.5 Mortality

5.5.1 The projected number of deaths each year was calculated by applying mortality rates by age and sex to the appropriate sub-populations. The national rates for the first year of the projections, 2008-09, were based on autumn 2009 estimates of the numbers of deaths at each age in that period. The mortality rates for later years were based on long-term trends before 2008. Future improvements in mortality rates are based on the trend observed in the period 1961 to 2007. It is assumed that annual rates of reduction in mortality rates will tend toward a common reduction at each age of 1 percent a year by 2033. Thereafter, the mortality improvement is assumed to continue at this rate. However, it is assumed that those born in the years 1923 to 1940 (cohorts which have consistently experienced relatively high rates of mortality improvement over the last 25 years) will continue to experience higher rates of mortality improvement until they die, with assumed rates of improvement in and after 2033 rising from 1.0 per cent a year for those born before 1923 to a peak of 2.5 per cent a year for those born in 1931 and then declining back to 1.0 per cent a year for those born in 1941 or later. The difference between the expectations of life for Scotland compared to the rest of the UK has been gradually widening for males under the age of 80, since the early 1980s. There have also been increases in divergence for females at the younger age groups over the last four of five years. Further analysis indicated that lower rates of improvement should be adopted in Scotland for males aged 31 to 56 and 67 to 90 and for females aged 32 to 38 and 65 to 90, than for the UK as a whole. Therefore it has been assumed that the mortality rates for Scotland will continue to be higher at most ages than those for the rest of the UK.

5.5.2 Based on these rates, expectation of life at birth is projected to increase from 74.8 years in 2007 to 80.7 in 2033 for men; and from 79.8 in 2007 to 85.3 in 2033 for women. The national mortality rates are shown, for selected ages and for selected years of the projection, in Annex B. Compared to the assumptions used in the 2006-based projections for Scotland, these lead to very small increases in the expectations of life at birth for men of around 0.1 years in 2033, and for women of 0.2 years.

5.5.3 Similar to the fertility assumptions for local areas, the assumed national mortality rates have been adjusted to take account of local variations observed in the five year period preceding the projections. As recommended by the Population Projections Working Group (PPWG) different scaling factors were used for different age groups to reflect the fact that the variation in mortality rates between areas will itself vary between age groups. Rather than using a single scaling factor for men and another for women different scaling factors were used for age groups 0-59, 60-79 and 80+ and for men and women meaning that up to 6 scaling factors were used for each area. In some smaller areas, fewer scaling factors were used as the small numbers of deaths were subject to large fluctuations. The local scaling factors used to adjust the national rates are shown in Annex C. More information on the mortality assumptions for Scotland can be found in Annex B to the publication "Projected Population of Scotland (2008-based)" on the General Register Office for Scotland’s website.

5.6 Migration

5.6.1 Assumptions about future levels of migration to and from Scotland were based on analysis of trends in civilian migration to and from the UK and between the four constituent countries of the UK. The principal projection assumes net in-migration of 12,000 from 2014-15 onwards; the previous 2006-based principal projection, assumed net in-migration of 8,500 per year for the long-term. In the first six years of the new projection higher net inflows are assumed, reflecting these recent trends. It is assumed that in the short-term there will be a net inflow of 16,000 migrants to Scotland in 2008-2009, 17,400 in 2009-2010, 16,200 in 2010-2011, 15,100 in 2011-12, 12,900 in 2012-2013 and 12,400 in 2013-2014 before the level drops to an assumed net inflow of 12,000 for the rest of the projection period. This reflects recent increases in the number of people migrating to Scotland, after many years when net out-migration was the norm. It also includes an allowance for migrants from the A8 countries in Eastern Europe which joined the European Union in 2004.

5.6.2 For the high migration variant projection net in-migration of 20,250 is assumed for 2008-09. Migration is assumed to peak in 2009-10 at 25,900 before declining over the next 5 years to 20,500 from 2014 onwards.

5.6.3 For the low migration variant projection net in-migration of 3,500 is assumed from 2014-15 onward with higher levels (starting at 11,750 in 2008-09) assumed for the first six years.

5.6.4 More information on the migration assumptions for Scotland can be found in Annex C to the publication "Projected Population of Scotland (2008-based)" on the General Register Office for Scotland’s website.

5.6.5 The net migration assumptions for local areas used in the principal projection were made after consultation with local authorities. The initial long-term assumptions were calculated by taking 5 year averages of in and out migration between councils within Scotland and between councils and other countries. These averages were scaled to match the migration assumptions used in the national projections. In the 2006-based projection the short-term assumptions were calculated by moving between the 2006-07 migration estimate and the long-term assumption at the same rate as the national figures changed. However this method did not produce credible figures for some councils areas for these projections, particularly for the high migration variant, due to the non-linear nature of the projected national migration assumptions. Therefore a slight change to the methodology for the short-term assumptions was needed. After the long-term assumption had been calculated for each council area (using the same method as for previous projections), the percentage of migrants located in each council area is calculated for the long-term assumption and also in the base year using the 2007-08 migration figures. The change in the percentage of migration in each council area from the base year to the long-term projection is then calculated and divided across the run-in years. The national assumption for the run-in years can then be divided up for each council area. The assumptions for each area are shown in Annex D. It is important to remember that the sum of the local assumptions have to match the totals used in the national projections. It is also important to note that long term migration assumptions are highly speculative.

5.6.6 For the high and low migration variant projections a similar method is used but this time the local assumptions have to match with the higher and lower totals used in the national variant projections. The higher and lower net inflows only affect moves to and from outwith Scotland and has no impact on moves within Scotland. Migration to and from an area is made up of a mixture of within Scotland and outwith Scotland migration and the extent to which a particular area experiences more of one or the other type of migration will determine the impact of the variant projection. Figure 12 shows the council areas which have gained large number of migrants from other countries over the past 5 years and which are therefore most likely to be affected by the high and low migration variants. These include Edinburgh, Perth & Kinross, Highland, Aberdeen, and Orkney. The trends in net migration for the previous five years are shown in Annex G. The high migration variant assumptions for each area are shown in Annex E and the low migration assumptions are shown in Annex F.

Figure 12 Migration to and from outwith Scotland and to and from other council areas within Scotland

5.6.7 Council and NHS board area specific age/sex distributions have been assumed for the in- and out- migrant flows using information on movement of patients from the National Health Service Central Register (NHSCR) observed in the previous three years and the Community Health Index (CHI), again over the previous 3 years. These distributions have been made consistent with the age/sex distribution used for Scotland in the national projection.