Household ProjectionsDorothy Watson

General Register Office for ScotlandHousehold Estimates and Projections Branch

Four sets of information are used to produce household projections:

Population Projections

Communal Establishment Rates

Headship Rates

Household Estimates

Overview of Household Projection Process

Population Projections

Communal Establishments

Private Population

Projected Headship

Rates

Projected Households

Household Estimates

1991 and 2001 Head of House Census data

Household types and age groups

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 sixteen age groups.

Household types1 person households: 1 adult: male 1 adult: female2 person households: 2 adults 1 adult, 1 child3+ person households: 1 adult, 2+ children 2+ adults, 1+ children 3+ adults

Age groups16-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-7475-7980-8485-8990+

Population Projections

There are three components of population change

Mortality

Fertility

Migration

These three components together with the base population estimate for the starting year (2008) combine to form a projection of the population from one year to the next.

Population projections by age group, by gender and by council area are needed for household projections.

Example:40 to 44 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018female 7,572 7,486 7,341 7,283 7,268 7,182 7,021 6,816 6,623 6,396 6,323male 7,615 7,600 7,540 7,594 7,439 7,455 7,372 7,351 7,302 7,431 7,606

Communal Establishments (CEs)

CEs include residential schools, student halls, adult and children’s care homes, prisons etc.

The Communal Establishment Rate is the proportion of the population of a particular age group and gender who are resident in a CE.

005716.0

572,7

278.43

Population Total

CEsin Residents Rate CE

The calculated CE rate for each age group and gender is kept constant for the entire projection period.

40 to 44 2008 2009 2010 … 2016 2017 2018female 0.005716 0.005716 0.005716 … 0.005716 0.005716 0.005716male 0.011199 0.011199 0.011199 … 0.011199 0.011199 0.011199

40 to 44 Total

PopulationResidents in

CEs CE Ratefemale 7,572 43.278 0.005716male 7615 85.28 0.011199

Private Population

The private population is calculated by subtracting those who live in CEs from the projected population.

Private Population = Projected Population x (1 – CE rate)

= 7,572 x (1 – 0.005716)

= 7,529

40 to 44 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018female 7,572 7,486 7,341 7,283 7,268 7,182 7,021 6,816 6,623 6,396 6,323male 7,615 7,600 7,540 7,594 7,439 7,455 7,372 7,351 7,302 7,431 7,606

Population Projections

40 to 44 2008 2009 2010 … 2016 2017 2018female 0.005716 0.005716 0.005716 … 0.005716 0.005716 0.005716male 0.011199 0.011199 0.011199 … 0.011199 0.011199 0.011199

Communal Establishment Rates

40 to 44 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018female 7,529 7,443 7,299 7,241 7,226 7,141 6,981 6,777 6,585 6,359 6,287male 7,530 7,515 7,456 7,509 7,356 7,372 7,289 7,269 7,220 7,348 7,521

Private Population

Headship Rates

The proportions of households by council area, household type and age group of the head of household are known for each of the 1991 and 2001 Census years.

Example

Number Proportion1 adult, male 1565 0.102041 adult, female 847 0.055232 adults 1180 0.076941 adult, 1 child 390 0.025433+ adults 623 0.040621 adult, 2+ children 376 0.024522+ adults, 1+ children 4189 0.27313People not head of household 6167 0.40210Total people in group 15337 1.00000

Number and proportion of heads of household aged 40-44 by household type: Aberdeen City, 2001

Projected Headship Rates

The headship (and non-headship rates) are projected forward using the modified two-point exponential model.

19912001if

19912001if

yearin rate headship

0

1

yyk

yyk

iiy

ii

xabky

where:

19912001

1991

1991

2001

1991

i

x

ky

kyb

kya

i

Projected Headship Rates

Example:The headship rate for 2008 is calculated from the known headship rates for 1991 and 2001.

2+ adults, 1+ children 0.28227 0.27313

Household type 1991y 2001y

Since 0.27313 < 0.28227 then k = 0 and the equation becomes

26691.0

28227.0

27313.028227.0

7.1

19912001

19912008

1991

20011991 2008

y

yyy

Headship rates for other years are calculated in a similar way.

Projected Headship Rates

0

0.1

0.2

0.3

0.4

0.5

1991 1996 2001 2006 2011 2016 2021 2026 2031

Age group of head of household = 40 to 44

Household type = 2+ adults, 1+ children

Projected headship rates

1991 and 2001 Census headship rates

Constrained Headship Rates

The projected headship (and non-headship) rates are constrained in two ways they cannot individually go above1 or below 0 they sum to 1 within an area and age group

householdtype projected headship constrained headship1 adult 2+ children 0.03382 0.033431 adult, 1 child 0.03364 0.033251 person female 0.06984 0.069031 person male 0.12781 0.126342 person all adult 0.07492 0.074052+ adult 1+ children 0.26691 0.263823+ person all adult 0.02580 0.02550Non-heads 0.37896 0.37458Total 1.01170 1.00000

0.03382 1.01170 = 0.03343

Projected Households

The household projections are calculated by applying the constrained projected headship rates to the total private population projections.

Constrained projected headship rates40 to 44 2008 2009 2010 … 2016 2017 20181 person female 0.06903 0.07092 0.07279 … 0.08358 0.08531 0.087022+ adult 1+ children 0.26382 0.26238 0.26093 … 0.25190 0.25036 0.24882

Total Private Population40 to 44 2008 2009 2010 … 2016 2017 2018TOTAL 15,058 14,958 14,755 … 13,805 13,707 13,808

15,058 x 0.06903 = 1,040

Projected households40 to 44 2008 2009 2010 … 2016 2017 20181 person female 1,040 1,061 1,074 … 1,154 1,169 1,2022+ adult 1+ children 3,973 3,925 3,850 … 3,478 3,432 3,436

Final Adjustments

The projected numbers of households are controlled so that figures for local authorities sum to the total for Scotland.

The total numbers of households within each local authority are adjusted to equal the latest annual household estimates. To preserve trends, projections are also adjusted by the same proportion.

Finally figures are adjusted to ensure that the minimum number of adults required to fill the projected households is not greater than the projected private adult population and a similar check is carried out for children.

The most recent 2008- based household projections for Scotland can be found on the GROS website

http://www.gro-scotland.gov.uk/