Annex A: Household projections and methodology
Annex A: Household projections and methodology
1. Brief summary of the methodology
Household projections are based on the population projections produced by the General Register Office for Scotland (GROS). 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 type and age group is projected forward from the 1991 and 2001 Censuses, for each household type, age group and local authority area. This information is applied to the private household population to produce the basic household projections.
Because the overall projections for Scotland are believed to be more accurate than those for individual local authorities, the local authority figures are constrained to the Scottish total. Each year, GROS produces household estimates based on Council Tax data. These estimates do not include information on household type or age group, but they provide an overall estimate of the number of households in each local authority area, which is based on more uptodate data than the household projections. Therefore, the household projections for 2004 and 2005 are adjusted to match the household estimates for these years, and the household projections for 2006 onwards are adjusted by the same proportion as the 2005 figures, to preserve the trends.
2. Household types and age groups used in the household projections
Household projections are produced for each local authority area, broken down into seven household types (based on the number of adults and children living in the household) and ten age groups, as follows:
Annex Table A: Household types and age groups used in the household projections
Household types 
Age of head of household 
1 person households: 
1624 
3. Household projections methodology part 1: Population projections
The first main input into the household projections is the 2004based population projections for Scotland produced by GROS. 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 ‘2004based Population Projections for Scottish Areas’. The relevant population for household formation is taken to be the adult population, aged 16 or over.
The projected number of households is derived from projections of the numbers of people living in private households. To obtain this from the population data, estimates of the numbers living in communal establishments are subtracted from the total adult population for each projection year. The 2001 Census was used to calculate the proportion of the population living in communal establishments in 2004, by gender and age group. Local authorities were then consulted on these figures, and the figures were amended as appropriate, based on local authorities’ more detailed local knowledge. The final communal establishment proportions were then applied to the GROS population projections for each year. This methodology assumes constant proportions of people living in communal establishments for each of the 20 projection years.
4. Household projections methodology part 2: Household composition
The second main input to the household projections is the information on the number of households from the 1991 and 2001 population Censuses. The proportions of households by local authority area, household type, and age group of the head of household are known for 1991 and 2001. The proportions of each household type sum to one within each age group within each local authority area.
An example of the Dumfries and Galloway 2001 Census data for persons aged 35 to 44 years old is given below.
Annex Table B: Number and proportion of heads of households aged 3544 by household type: Dumfries and Galloway 2001
Type of household 
Number 
Proportion 
1 adult: male 
1,279 
0.059 
The number of people who head particular household types will be the same as the number of households of this type. The proportion of these within any particular age group and local authority area is known as the ‘headship’ rate and it is this that is projected forwards then applied to the population projections (by age group and local authority area) to give the household projections. We also know the number of people in each area and age group who are not the head of household, for which ‘nonheadship’ rates are calculated.
The headship (and nonheadship) rates are projected forward using the modified twopoint exponential model, the formula for which is as follows.
y_{i} = k + ab^{x}^{i}
i 
= the year, from 2004 to 2024 
y_{i} 
= headship rate in year i 
k 
= 1 if y_{2001 }≥y_{1991 }0 if y_{2001 }<y_{1991} 
a 
= y_{1991 }– k 
b 
= (y_{2001} – k)/(y_{1991 }– k) 
x_{i} 
= (i 1991)/(20011991) 
The projected headship (and nonheadship) rates are constrained in two ways:

they cannot individually go above 1 or below 0;
 they sum to 1 within an area and age group.
The household projections are then calculated by applying these projected headship rates to the 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.
These figures are then controlled, so that figures for local authorities sum to the total for Scotland.
The total number of households within each local authority in 2004 and 2005 is then adjusted to equal the annual household estimates. The household projections for 2006 onwards are adjusted by the same proportion as the 2005 figures, to preserve the trends.
Finally, the figures are adjusted to ensure 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 the household type ‘two or more adults’), and the same check is carried out for children. Where this 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 revised 2004based household projections, this adjustment was required for Aberdeen City.