5. Sources and Methods
5.1 Summary
5.1.1 The household projections are based on population projections produced by National Records of Scotland (NRS). The number of people living in private households is estimated by taking the population projections for each year and subtracting the number of people living in communal establishments, such as student halls of residence, care homes or prisons. To estimate the number of households of each type, information on household formation is projected forward from the 1991 and 2001 censuses, for each household type, age group and local authority. This information is then applied to the private household population to produce the basic household projections.
5.1.2 The overall projections for Scotland are believed to be more accurate than those for individual local authorities, therefore the local authority projections are constrained to the Scottish total. Each year NRS produces estimates of the total number of households in each local authority, based on Council Tax data. These estimates are based on more recent data than the household projections therefore the household projections for 2010 and 2011 are adjusted to match the household estimates for these years, and the household projections for 2012 onwards adjusted by the same proportions as 2011.
5.2 Household types and age groups used in the household projections
5.2.1 Household projections are produced for each local authority, broken down into seven household types, based on the number of adults and children living in the household, and sixteen age groups, as follows:
Table A: Household types and age groups used in the household projections
| Household types |
|---|
| 1 person households: |
| 1 adult: male |
| 1 adult: female |
| 2 person households: |
| 2 adults |
| 1 adult, 1 child |
| 3+ person households: |
| 1 adult, 2+ children |
| 2+ adults, 1+ children |
| 3+ adults |
| Age group |
|---|
| 16-19 |
| 20-24 |
| 25-29 |
| 30-34 |
| 35-39 |
| 40-44 |
| 45-49 |
| 50-54 |
| 55-59 |
| 60-64 |
| 65-69 |
| 70-74 |
| 75-79 |
| 80-84 |
| 85-89 |
| 90+ |
5.3.1 Four sets of data are used as inputs to the household projections: 2010-based population projections, estimates of the proportions of the population that are resident in communal establishments in 2010, headship rates from the 1991 and 2001 censuses and 2010 and 2011 household estimates.
Population projections
5.3.2 The first input into the household projections is the 2010-based population projections for Scotland. These are produced for Scotland by local authority, sex and single year of age, using assumptions about births, deaths and migration. More information about the population projections, and the assumptions used to produce them, can be found in '2010-based Population Projections for Scottish Areas'. The relevant population for household formation is taken to be the adult population, aged 16 or over. The low and high migration variant population projections used in the variant household projections are taken from the same publication.
Communal Establishment Estimates
5.3.3 Estimates of the proportion of the population living in communal establishments, such as care homes or prisons, are used to derive the number of people living in private households from the total population given in the population projections. These proportions are calculated, by age group and sex, from the mid-2010 population estimates published by NRS and numbers of residents in communal establishments collated by NRS.
5.3.4 Numbers of residents in communal establishments are collected from a range of data sources, depending on the establishment type. The data is chosen to represent, as closely as possible, the census definition of residence, that is those individuals "staying, or expecting to stay, in a residential establishment for six months or more". Individuals resident for shorter stays would be considered visitors and are not included, as they should be accounted for in their usual place of residence.
5.3.5 Data is collected from a range of administrative data sources and surveys and refers to 2010, where possible. For some establishment types, however, no such source is available, and in these cases 2001 census data is used. Table B details the sources of communal establishment data and the year to which the data refers. In many cases more than one data source was combined and estimation was required to obtain a full age/gender breakdown for all establishments.
Table B: Communal establishment data sources
| Establishment type | Data source | Year of data |
|---|---|---|
| Adult care1 | Care Inspectorate (List of registered establishments) | 2010 |
| ISD2 Care Home Census | 2010 | |
| Children's care1 | Care Inspectorate (List of registered establishments) | 2010 |
| SG Looked After Children Statistics | 2010 | |
| Defence1 | NRS Armed Forces Data Collection | 2010 |
| DASA3 Regular Forces by Age and Sex | 2010 | |
| Hospitals | ISD2 SMR01 (General/Acute) | 2010 |
| ISD2 SMR04 (Mental Health) | 2010 | |
| ISD2 Continuing Care Census (Other NHS) | 2010 | |
| Hostels | Census | 2001 |
| Hotels and boarding houses | Census | 2001 |
| Prisons | SG Prison Statistics | 2010 |
| Residential Schools | SG Education Analytical Services | 2010 |
| Student Halls of Residence1 | NRS Communal establishment address list | 2011 |
| NRS Further education data collection | 2006 | |
| HESA4 | 2009/10 | |
| Other | Census | 2001 |
Footnotes
1) For this establishment type data from two of more sources are combined to estimate the age/gender breakdown of residents in each local authority, as no comprehensive source was available.
2) ISD - Information Services Division of NHS Scotland
3) DASA - Defence Analytical Services and Advice
4) HESA - Higher Education Statistics Agency
5.3.6 The communal establishment rates used for the 2010-based household projections can be found on the NRS website, in the 'Source Data Tables'. Additional information on the communal establishment data collection for individual establishment types, including information on the quality and limitations of the data, can be found in the Household Analysis Review Group (HARG) paper HARG 2012 (2).
Headship rates
5.3.7 The household formation information used in the household projections is in the form of headship rates, derived from the 1991 and 2001 censuses. These rates are used to convert the private household population into household numbers.
5.3.8 In the census, one member of each household is designated the 'head of household' (the first adult recorded on the household form). The headship rate describes, for each age group, the proportion of the population that is designated the head of household of each household type. The proportion of the population, for each age group, who are not a head of any type of household (non-heads) is also available from the census. The proportions for each household type, including non-heads, sum to one, within each age group and local authority. The number of people who head particular household types is the same as the number of households of this type.
5.3.9 In 2008 the 1991 headship rates changed, due to a small revision to the 1991 census data. This made no difference to the household projections at Scotland level. For the local authorities affected the differences were less than 20 households by the end of the projection period.
Household estimates
5.3.10 Household estimates are published annually by NRS and the household projections use the estimates from the latest two years (2010 and 2011). The estimates are based on Council Tax data, and provide the total number of households for each local authority in Scotland. The latest household estimates can be found in the 'Estimates of Households and Dwellings in Scotland' publication.
5.4.1 There are several stages to the calculation of the household projections. The first stage calculates the private household population. This is done by first estimating the number of communal establishment residents in each year of the projection, by applying the communal establishment rates described above to the population projections. The communal establishment residents are then subtracted from the population projections to give the private household population for each projection year. The projected private household population for 2010, for Scotland and each local authority, can be found on the NRS website, in the 'Source Data Tables'. Variant private household populations are also available in the same dataset, based on the high and low population projections.
5.4.2 The second stage to calculating the household projections is to estimate the number of households from the private household population, using the headship rates described above. The headship (and non-headship) rates for 1991 and 2001 are projected forward using the modified two-point exponential model, the formula for which is as follows:
where i = the year, from 2010 to 2035
yi = the headship rate in year i
k = 1 if y2001 ≥ y1991
0 if y2001 < y1991
a = y1991 - k
b = (y2001 - k)/(y1991 - k)
xi = (i - 1991)/(2001 - 1991)
The projected headship (and non-headship) rates are constrained so that:
The projected headship and non-headship rates from the 2010-based household projections can be found in the 'Source Data Tables'.
5.4.3 The household projections are calculated by applying the projected headship rates to the private household population projections to give an estimate of the number of heads of household in each of the projection years for each household type, age group of the head of household and area.
5.4.4 The final stages of the household projection methodology apply a series of adjustments to the household projections. The first adjustment is to control the local authority projections to the all-Scotland projection, as the latter is thought to be more accurate. This ensures that the local authority projections together sum to the total for Scotland.
5.4.5 The next adjustment is for the total number of households within each local authority in 2010 and 2011 to be controlled so that it is equal to the household estimates for these years. The household projections for 2012 onwards are then adjusted by the same proportions as the 2011 year, to preserve the trend in the household projections. This adjustment allows us to incorporate more recent information on household numbers than the 2001 census into the household projections.
5.4.6 The final adjustment ensures that the minimum number of adults required to fill the projected households is not greater than the projected adult private household population (e.g. a minimum of two adults would live in a 'two or more adult' household). The same check is carried out for children. Where an adjustment is required, the number of households is kept constant, but the balance of household types is adjusted, to reduce the number of large households and increase the number of smaller households. For the 2010-based household projections, the minimum adult adjustments were required for Dundee City and Eilean Siar in the principal and high migration variants. Dundee City and Eilean Siar were also affected in the low migration variant, with the addition of Orkney in the standard headship variant or Aberdeen City in the low migration variant with the alternative headship rate. Only Eilean Siar needed a minimum adult adjustment in the constrained housing variant. No minimum child adjustments were required in any projection.
5.4.7 For the first time this publication also presents variant household projections where the assumptions used to project headship rates are different, as surveys such as the Scottish Household Survey have suggested that people in Scotland are not tending to live in smaller and smaller households to the extent that is projected from the 1991 and 2001 census data. Further detail can be found in HARG 2011(4) and HARG 2012(5). The variant we have chosen is for the headship rates to change at half the rate given by the projection above, from 2002 onwards. This is calculated by the headship rate for each year, age group and household type being the average of the rate from the headship rate projection described above and the rate from the 2001 census. The projected headship and non-headship rates used for the alternative headship rate variants of the 2010-based household projections can also be found in the 'Source Data Tables'.
5.4.7 For the first time this publication also presents variant household projections where the assumptions used to project headship rates are different, as surveys such as the Scottish Household Survey have suggested that people in Scotland are not tending to live in smaller and smaller households to the extent that is projected from the 1991 and 2001 census data. Further detail can be found in HARG 2011(4) and HARG 2012(5). The variant we have chosen is for the headship rates to change at half the rate given by the projection above, from 2002 onwards. This is calculated by the headship rate for each year, age group and household type being the average of the rate from the headship rate projection described above and the rate from the 2001 census. The projected headship and non-headship rates used for the alternative headship rate variants of the 2010-based household projections can also be found in the 'Source Data Tables'.