Model-Based Estimates of Income for Wards in
England and Wales, 2001/02
User Guide
Summary
Consultation with users has indicated that there is a widespread requirement to have
better information on income at the small area level. Following the Government's
decision not to include an income question in the 2001 Census, the Office for
National Statistics (ONS) took the lead in exploring alternative measures for the
provision of income data for small areas.
The Small Area Income Estimates Project was established with the aim of producing
sets of ward-level estimates of average household income using the modelling
techniques developed by the ONS Methodology Directorate.
Estimates and confidence intervals for the values of average ward income (1998/99)
for all wards in England and Wales have been produced based on 1998 ward
boundaries. These were released as experimental1 statistics on the ONS website in
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February 2004 (Longhurst et al (2004)).
One of the main limitations of the estimates highlighted by users concerned the
relevance of the estimates in terms of making comparisons with the 2001 Census data
– as they relate to 1998/99 and are based on 1998 ward boundaries. A Neighbourhood
Statistics (NeSS) funded project was established to improve the model and make it
comparable with the 2001 Census by using more recent sources of covariate2 and
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survey data. Estimates of average weekly household income have been produced for
2001/02 based on Census Area Statistics (CAS) wards for 2003. These have been
rounded to the nearest £10. Estimates are produced for the following four income
types:
•
total3 household weekly income (unequivalised);
•
net household weekly income (unequivalised);
•
net household weekly income before housing costs (equivalised); and
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1
The term ‘experimental’ is applied to any set of ONS statistics that do not yet meet the rigorous
quality standards of National Statistics and/or maybe subject to change due to methodological
development.
2
A variable (or variables) that is either known or can be estimated relatively accurately and is then
used in the estimation of other variables.
3
Total income is consistent with the gross income measure used in the 1998/99 model-based estimates.
For more information on definitions see appendix A.
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1
•
net household weekly income after housing costs (equivalised).
Note equivalised income means that the household income values have been adjusted
to take into consideration household size and composition.
The release of a second more up-to-date series of model-based average weekly
household income estimates for wards raises the issue of comparability with the
1998/99 estimates. The 2001/02 estimates are not comparable with the 1998/99
estimates. This document summarises the reasons why the 2001/02 estimates are not
comparable with the 1998/99 estimates. The 1998/99 estimates have been removed
from the public domain and replaced with the 2001/02 estimates to prevent erroneous
comparisons. Details of how the estimates have been developed and guidance on the
appropriate use of the estimates are also given.
The first section of the report provides some background to the project and some
guidance on the use of the estimates. The second section provides a brief technical
description of the methodology used to produce the model-based estimates. Maps of
the ward level estimates for England and Wales are presented in Section 3.
It must be noted that these experimental estimates are not calculated in the same way
as the national and regional household income data published in June 2004 and April
2005 (ONS (2005)). The output geography and definition of income are different as
are the statistical data sources employed. Therefore these two data sets cannot be
quantitatively reconciled.
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1
1.1
Background and Guidance on Use
Introduction
Consultation with users, including representatives from central and local government,
the academic and business sectors, about requirements for information from the 2001
Census underlined the need for a question on income. In particular, the work
substantiated the widespread and increasing demand for detailed information at a
range of geographical levels.
Although the Government recognised the need for information on income, concern
about the risks to the conduct of the Census meant that the preferred approach was to
assess whether or not requirements could be met by using alternative sources of data.
In accordance with proposals set out in the Census White Paper, the Government
Statistical Service (GSS) set up a working group to investigate the feasibility of
various options including:
•
using data on the receipt of benefits from the Department of Work and Pensions;
and
•
producing modelled income data.
The results of this work were set out alongside findings from the detailed Census
programme of research and question testing in a paper circulated to users so they
could identify the preferred approach for meeting their requirements. The Government
considered this information before they made the decision not to include an income
question in the 2001 Census.
Following the initial work into the feasibility of producing model-based estimates of
income the ONS established a project to implement this approach. Estimates and
confidence intervals for average weekly household income for wards in England and
Wales, for 1998/99 were released in February 2004.
One of the main limitations of the estimates highlighted by users concerned the
relevance of the estimates in terms of making comparisons with the 2001 Census data
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– as they relate to 1998/99 and are based on 1998 ward boundaries. A Neighbourhood
Statistics (NeSS) funded project was established to update the model-based estimates
and make them comparable with the 2001 Census. The model-based methodology
used for the 1998/99 estimates has been used for the 2001/02 estimates.
1.2
Model-based approach
The model-based approach is based on finding a relationship between weekly
household income (as measured in the Family Resources Survey (FRS)) and covariate
information (usually from Census or administrative sources) for the wards that are
represented in the Survey. This relationship is then used to provide estimates of
average weekly household income for all wards.
To ensure that the model-based estimates are consistent with the FRS published
estimates at higher geographical levels, the model-based estimates are constrained to
the direct estimates for Government Office Regions (GORs) in England and the
estimate for the country of Wales.
It is important to recognise that the model-based approach gives estimates that are of a
different nature from the standard estimates from the FRS. This is because they are
dependent upon correctly specifying the relationship between weekly household
income and the covariate information. A brief explanation of the methodology is
provided in Section 2.
1.3
Guidance on use and limitations of the estimates
The main limitation of estimates for small areas, either those estimated directly from
responses to surveys or model-based, is that they are subject to variability (see Section
2).
ONS has produced confidence intervals associated with the model-based
estimates for each ward in order to make the accuracy of the estimates clear (see
Section 2.6 for further information).
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Five further limitations of the estimates must be considered:
•
the consistency and accuracy of income estimates for other, often larger
geographical areas;
•
the conclusions that may be drawn from the estimates on the overall
distribution of income and the ranking of specific areas;
•
consistency between the estimates for the four different types of income;
•
consistency with different time periods; and
•
comparability with 1998/99 estimates.
1.3.1
Consistency and accuracy of estimates for other geographical areas
The model-based methodology produces ward-level estimates of average weekly
household income. These ward level estimates can be aggregated to provide income
estimates for larger geographical areas such as Local Authority Districts (LADs) or
regions. However, this method is approximate and hence it is not possible to assess
the precision of the aggregated estimates.
The model-based methodology has been developed to ensure that the ward estimates
are constrained to direct survey estimates from the FRS for GORs in England and the
estimate for the country of Wales. For example, the model-based estimates for the
wards in Wales when added together correspond to the FRS estimate of average
weekly household income for Wales. However, the model-based estimates will not be
consistent with FRS estimates of average weekly household income for other
geographical levels.
The issue of geographic consistency and methods for assessing the accuracy of
estimates for areas other than wards will be explored as part of future research.
1.3.2
Distribution and ranking of income levels
In common with any ranking based on estimates, care must be exercised in
interpreting the ranking of the wards. One needs to take into account the variability of
the estimates when using these figures. For example, the confidence interval around
the highest ranked ward suggests that the estimate lies among the group of wards
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with the highest income levels rather than being the ward with the highest average
ward income.
Estimates for two particular wards can only be described as
significantly different if the confidence intervals for those estimates do not overlap.
Although these model-based estimates can be used to rank wards by income they
cannot be used to make any inferences on the distribution of income levels across the
wards. The estimation procedure will tend to shrink estimates towards the average
level of income for the whole population, so model-based estimates at each end of the
scale tend to be over or under-estimated. Nevertheless estimates can be used to make
certain inferences, e.g. the average weekly household income for ward A is greater
than the average for ward B (if the appropriate confidence intervals do not overlap).
However, making assertions such as x% of wards have an average household income
over £y per week is not valid.
1.3.3
Consistency between the four different types of income
Estimates have been produced for four different types of income. In some cases slight
inconsistencies (when examining the estimates) may occur between the income types
for a particular ward, e.g. a ward may have a larger estimate for net income when
compared with total income. Although there may be some such inconsistencies the
models selected are the best possible to model the general pattern of income over all
wards. This reinforces the need to look at the confidence intervals and not just the
estimates as the confidence intervals summarise the variability of the estimates caused
by the modelling process (see Section 2).
1.3.4
Consistency with different time periods
These estimates have been produced on 2003 CAS ward boundaries and therefore
cannot be translated onto any other boundary system. Users must be aware of this
when using the estimates in any application or drawing conclusions from the data.
The estimates are also based on 2001/02 survey data and so are only valid for this
period.
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1.3.5
Comparability with the 1998/99 estimates
In order for two sets of model-based estimates to be comparable, the survey and
covariate data used in the models should be the same with the exception of the
reference time period. In addition the methodology employed to estimate the two sets
of estimates should be the same as should the output geographies for the estimates. If
these criteria are met, one can say that estimates for the same ward in two different
time periods are significantly different if the confidence intervals do not overlap.
The methodology for estimating ward-level average income for 2001/02 is exactly the
same as that used for the 1998/99 estimates. However, due to the availability of
different covariates and also different output geographies, the 2001/02 estimates are
not comparable with the 1998/99 estimates. As a result, the 1998/99 estimates have
been removed from the public domain and replaced with the 2001/02 estimates to
prevent erroneous comparisons.
1.3.6
Examples of data use
Given that the model-based estimates are subject to limitations some examples of
appropriate and inappropriate uses for the estimates have been produced.
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1.3.6.1 Ward comparisons
When comparing two model-based estimates, one ward may only be said to have a
significantly lower or higher average income than another if the confidence intervals
for the two wards do not overlap. For example, using Table 1 it may be said that ward
C has a significantly lower model-based income estimate than ward A since the 95%
confidence intervals do not overlap. However, it would be wrong to say that ward B
has a significantly lower model-based income estimate than ward A, since the
confidence intervals overlap.
95% confidence intervals for the income estimate
Estimate
Lower Confidence Upper Confidence
Limit
Limit
Ward A
1660
1310
2120
Ward B
1110
910
1360
Ward C
1080
920
1270
Table 1: Model-based income estimates and confidence intervals for three wards
Estimate
LAD A
420
LAD B
560
LAD C
770
Table 2: Aggregated model-based income estimates for three LADs
Ward level estimates can be aggregated to higher geographical levels.
Table 2
provides model-based estimates of the average level of household income for three
LADs. Although the income estimate for LAD A may seem a great deal lower than
that for LAD C, there are no confidence intervals available for geographies other than
wards. This means that we have no measure of the precision of the estimates and
therefore cannot say that one aggregated model-based estimate is significantly
different to another.
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1.3.6.2 Ward profiles
The model-based ward estimates of income can be used in conjunction with other data
sources to build up a profile of a particular ward. Examples are shown below in Table
3.
Ward A
Ward B
Ward C
Model-based estimate of total weekly £230
£710
£1230
household income with 95% confidence [200, 280]
[600, 840]
[950, 1610]
Rank of LAD in which ward lies on the Top 15
Upper
Bottom 15
Index of Multiple Deprivation, income
Quartile
interval
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domain (2004)
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% Adults claiming Income Support 37%
3%
2%
3%
29%
(2001/02)
% Properties in Council Tax band H <1%
(2001)
Table 3: Ward Profiles
1.4
Results
Model-based estimates and their 95% confidence intervals have been produced for
2001/02, for CAS wards (2003) in England and Wales for the following income types:
•
total household weekly income (unequivalised);
•
net household weekly income (unequivalised);
•
net household weekly income before housing costs (equivalised); and
•
net household weekly income after housing costs (equivalised).
Equivalised income means that the household income values have been adjusted to
take into consideration the number and type of people in the household; it represents
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The area with a rank of 1 is the most deprived.
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the income level of every individual in the household. Equivalisation is needed in
order to make sensible income comparisons between households. For more details on
these income definitions see Appendix A.
Reliable estimates cannot be produced for a small number of wards. The wards
affected are those lying in the City of London and the Isles of Scilly. Instead,
estimates have been provided for the LADs in which these wards lie.
1.5
Future plans
This project was established to address users’ requirements for more up-to-date
information on income levels, for areas that are comparable with outputs from the
2001 Census. The 2001/02 model-based average income estimates on 2003 CAS
ward boundaries meet these requirements. However, a limitation is they cannot be
compared with the 1998/99 model-based estimates because they are based upon
different covariate data sources and different output geographies. In order to optimise
the comparability of future series of average income estimates with the 2001/02
estimates a scoping exercise should be carried out to identify and secure the
availability of the same survey and covariate data sources.
As a result of strong user interest for information on the distribution of income within
wards, a separate project has been set up to look at providing estimates of the
proportions of households on low incomes within wards.
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2
Guide to the Methodology
This section provides a brief description of the methodology for producing modelbased estimates of average weekly household income at ward level. A full description
of the methodology can be obtained by request from ‘spatialanalysis@ons.gov.uk’.
For more information on the general small area estimation modelling procedure
developed by the ONS, refer to the Small Area Estimation Project (SAEP) Report
(Heady et al (2003)).
2.1
How do model-based estimates differ from standard survey estimates?
The principal reasoning behind the need for small area estimation is that surveys are
designed to provide reliable estimates at national and sometimes regional levels, they
are not typically designed to provide estimates for smaller geographical areas. The
inevitable result for areas such as wards is that the vast majority will contain no
sample respondents at all and hence no direct survey estimates will be possible. In
order to provide ward estimates of income using survey data (here the Family
Resources Survey (FRS) is used) a model-based approach has been adopted. This
methodology is dependent upon the correct specification of the model, the quality and
relevance of the input data sources and the fit of the model.
The premise behind the model-based methodology is that we can find a relationship
between weekly household income, as measured by the FRS, and other covariate
sources of information (mainly provided from Census and administrative data) in the
sampled wards. We can then ‘borrow strength’ from this relationship to generalise and
produce reliable estimates of average household weekly income for all wards.
During our research a number of different relationships and sources of information
were investigated.
modelling.
The best sources of information available were selected for
We are satisfied that while there are some limitations with our
methodology (see Section 1) the models are well specified and the modelling
assumptions hold.
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2.2
Description of the data
The survey data:
The survey data were obtained from the 2001/02 Family Resources Survey (FRS).
The FRS was chosen as the source for this study since it is the survey with the largest
sample that includes appropriate questions on total (gross income plus tax
credits/benefits) and net income.
The covariate data:
The covariate data came from the following sources:
•
the 2001 Census;
•
2001/02 Department of Work and Pensions (DWP) benefit claimant counts;
•
2001 HM Land Registry dwelling price data;
•
2002 Council Tax data; and
•
Regional/country indicators – GOR indicators (that split England into nine
regions) plus a country indicator for Wales.
2.3
Deriving the estimates
To derive the required estimates of average weekly household income for wards we:
•
built a model relating the survey variable to the covariate information for wards
covered by the survey;
•
used the model and covariate data (which are available for all wards) to estimate
the average weekly household income for all wards; and
•
ensured the model-based estimates were constrained to the FRS income estimates
at the GOR/country level. The model-based ward estimates of income were
aggregated to GOR/country level and comparisons made between these
aggregated estimates and the FRS estimates at these levels. The relevant ratios of
the FRS estimates to the aggregated model-based estimates at the GOR/country
level were then used to scale the model-based ward-level estimates.
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2.4
The model for income
Models have been developed for the purpose of producing small area estimates of
income, for England and Wales for each income type. The models defined relate the
FRS survey estimate of weekly household income to the following predictors. The
covariate data are listed in order of significance:
England and Wales
•
the social class of the ward population;
•
the composition of households in the ward, e.g. number of children in the
household;
•
regional/country indicators;
•
the employment status of the ward population;
•
the proportion of the ward population claiming DWP benefits; and
•
the proportion of dwellings in each of the Council Tax bands in a ward.
The result is average weekly household income by ward.
2.5
Validation of the model
A number of diagnostic checks have been used to assess the appropriateness of the
models developed for producing ward-level estimates of income. The analysis shows
that in general the models are well specified and the assumptions are sound. This
provides confidence in the accuracy of the estimates and the associated confidence
intervals. In addition the methodology used to produce the model-based estimates has
undergone an academic review and been evaluated by the wider academic community.
As well as validating the process of making the estimates it is necessary to validate
the estimates themselves. Analysis to compare the model–based estimates with other
sources of income data was carried out to establish the plausibility of the model-based
estimates. These processes have ensured that the methodology and its application are
valid, the models developed are the best possible for the data available and the modelbased estimates are plausible.
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2.6
How precise are the estimates?
Each of the estimates is accompanied by a 95% confidence interval. This interval
represents ‘uncertainty’ in the modelling process. This means that, assuming the
model holds, on average the confidence interval is expected to contain the true value
around 95% of the time. For example, if a ward estimate of average weekly household
income is £580 and the 95% confidence interval is [£510, £650] we know that 95% of
the time the average weekly household income for that ward will fall within this
range.
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3
Maps
3.1
Introduction
The model-based ward-level estimates of average weekly household income can be
displayed on maps. The interval ranges in each map have been chosen to aid
interpretation. 5% of wards are included in the ranges for the highest and lowest
income levels. 20% of wards are included in the ranges for the second highest and
second lowest income levels. 75% of wards are included in the ranges for income
levels nearest the average value. The number of wards in each interval range is
shown. Section 3.2 shows the maps of the estimates for the four income types for
England and Wales.
3.2
England and Wales
Map 1 shows the geographical variation of ward estimates of average total weekly
household income (unequivalised) in England and Wales. The map shows that the
majority of wards with the highest levels (darkest areas) of total weekly household
income are concentrated in the South of England, in and around London. As we move
out further from this area the average ward income decreases. Areas of lighter colour,
i.e. lower income levels, are common in the South West and North of England. The
majority of wards in Wales have average income levels below the national average.
South Wales and North East England show the lowest income levels.
Maps 2, 3 and 4 display the geographical variation of ward income in England and
Wales for the three other income types. The maps show a similar pattern of income
distribution as Map 1, although Map 3 and Map 4 show a slightly stronger North
South divide.
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Map 1
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Map 2
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Map 3
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Map 4
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Appendix
A Survey data - income definitions
This appendix contains details on the four income types modelled. For more specific
information please refer to the survey reports (Dhaneca et al (2003) and Adihetty et al
(2003)).
Total household weekly income (unequivalised)
Total household weekly income is the sum of the gross income of every member of
the household plus any income from taxes/benefits such as Working Families Tax
Credit. It is calculated as the sum of income from:
•
earnings (gross);
•
self-employment;
•
investments;
•
disability benefits;
•
retirement pensions and income support;
•
other benefits (including tax credits);
•
other pensions; and
•
other/remaining sources.
Net household weekly income (unequivalised)
Net household weekly income (unequivalised) is the sum of the net income of every
member of the household. It is calculated using the same components as total income
but excludes:
•
income tax payments;
•
national insurance contributions;
•
domestic rates/council tax;
•
contributions to occupational pension schemes;
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•
all maintenance and child support payments, which are deducted from the income
of the person making the payments; and
•
parental contribution to students living away from home.
Net household weekly income before housing costs (equivalised)
Net household weekly income before housing costs (equivalised) is composed of the
same elements as net household weekly income but is subject to the McClement’s
equivalence scale (Adihetty et al (2003)).
Applying the equivalence scale adjusts the household income values to take into
consideration the number and composition of people in the household; it represents
the income level of every individual in the household. Equivalence is needed in order
to make sensible income comparisons between households. For example, one
household may have 2 adults and 2 children and have a total weekly household
income of £300. If this is compared with a household containing just 1 adult who has
a total weekly household income of £270, then although the first household has the
higher total weekly income it is the second that has the higher standard of living.
Although a number of equivalence scales have been developed, the equivalence scale
used for the income estimates is the McClement’s scale, which is used across a
number of Government surveys. An example of the effect of applying the
McClement’s scale is as follows:
A single person, a couple and a couple with two children aged four and seven,
all have unequivalised net weekly household incomes of £100 before housing
costs. After equivalisation, these become £164 (single person); £100 (couple);
£72 (couple with children).
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Net household weekly income after housing costs (equivalised)
Net household weekly income after housing costs (equivalised) is composed of the
same elements of net household weekly income but is subject to the following
deductions prior to the McClement’s equivalence scale being applied:
•
rent (including housing benefit);
•
water rates, community water charges and council water charges;
•
mortgage interest payments;
•
structural insurance premiums (for owner occupiers); and
•
ground rent and service charges.
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B Bibliography
Adihetty, S., Lunn, S., Pitt, W., Stanborough, J., Vigurs, C., Wilkie-Jones, C. (2003)
Households Below Average Income: An analysis of the income distribution
from 1994/95 – 2001/02. DWP Publication. The Stationary Office, ISBN 1
84123 557 1.
http://www.dwp.gov.uk/asd/hbai.asp/
Dhaneca, N., Ellerd-Elliott, S., Herring, I., Horsfall, E., Matejic, P., Shome, J.,
Snow,. J. (2003).
Family Resources Survey: Great Britain, 2001/02. DWP Publication. The
Stationary Office, ISBN 1 84388 153 5.
http://www.dwp.gov.uk/asd/frs/2001_02/index.asp/
Heady, P., Clarke, P., Brown, G., Ellis, K., Heasman, D., Hennell, S., Longhurst, J.,
Mitchell, B. (2003).
Small Area Estimation Project Report. Model-Based Small Area Estimation
Series No.2, ONS Publication.
http://www.statistics.gov.uk/
Longhurst, J., Cruddas, M., Goldring, S., Mitchell, B. (2004).
Model-based Estimates of Income for Wards, 1998/99: Technical Report. To
be published in Model-Based Small Area Estimation Series,ONS Publication.
Office for National Statistics (2005).
Regional Household Income.
http://www.statistics.gov.uk/StatBase/Product.asp?vlnk=7359/
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