National Records of Scotland

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Annex B - Method of Projection, Accuracy of Projections and Base Population

Annex B - Method of Projection, Accuracy of Projections and Base Population

Method of Projection

The projections are made for successive years running from one mid-year to the next. For each age, the starting population plus net inward migrants less the number of deaths produces the number in the population, one year older, at the end of the year. To this has to be added survivors of those born during the year. Age is defined as completed years at last birthday.

Migration is assumed to occur evenly throughout the year. For computing purposes, this is equivalent to assuming that half the migrants in a given year at a given age migrate at the beginning of the year and half at the end of the year. The number of net migration to be added to obtain the population aged x+1 at the end of the projection year therefore consists of half those migrating during the year at age x and half of those migrating during the year at age x+1.

The number of deaths in a year is obtained by adding half of the net inward migrants at each age to the number in the population at the beginning of the year and applying the mortality rate qx. The mortality rates used in the projections represent the probabilities of death between one mid-year and the next, according to a person’s age last birthday at the beginning of the period. Infant mortality, i.e. the probability of a new-born child not surviving until the following mid-year, is about 85 per cent of the full, first year of life infant mortality rate.

The number of births in the year are calculated by multiplying the average number of women at each single year of age during the year (taken as the mean of the populations at that age at the beginning and end of the year) by the fertility rate applicable to then during that year. The total number of births in a year is assumed to be divided between the sexes in the ratio of 105 males to 100 females, in line with recent experience.

The number of infants aged 0 at the end of the year is calculated by taking the projected number of births, deducting the number of deaths found by applying the special infant mortality rate (see above) and adding half the number of net migrants aged 0 last birthday.

Accuracy of Projections

Although many projection makers might prefer a projection to be regarded simply as a "scenario" (the certain outcome of a given set of assumptions), it is inevitable that users of projections will treat them as if they were forecasts of the most likely course of future events. It is important, therefore, that users know the inherent uncertainty of predicting demographic variables.  The point that successive sets of projections for a particular year are likely to improve in accuracy is an obvious but important one. This effect has sometimes been described as a "narrowing funnel of uncertainty" and users must be prepared to revise their plans in the light of updated projections.[Footnote 1]

The size of a population changes because of births, deaths and net migration. Errors in population projections are therefore mainly a consequence of the errors in the projections of each of these three components. However, errors in the population estimates upon which the projections are based also contribute to projection error. Projections are based on the latest estimate of the size and age structure of the population. However, these estimates are subject to later revision. Each Census provides a new starting point for the annual population estimates, removing errors which have accumulated because of imperfections in the data available, particularly regarding migration, for annual updating. These revisions are usually small compared with the other sources of error in population projections. However, base population errors are likely to grow in significance during an inter-censal period and be at their greatest immediately prior to the carrying out of a new Census.  GROS revised Scotland’s population estimates for 1981 to 2000 after the 2001 Census, reducing by about 23,000 the 1991 mid-year estimate.

Base Population

The Registrar General's 'Mid-2004 Population Estimates, Council and Health Board areas', published in June 2005 on this website, were 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 HM and non-UK Armed Forces stationed in Scotland are included; HM forces stationed outside Scotland are excluded.


1. Shaw C. GAD, Accuracy and uncertainty of the national population projections for the United Kingdom, Population Trends 77, Published 1994.

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