User Guide to the
2011/12 Small Area
Model-Based
Income Estimates
October 2015
Office for National Statistics
© Crown Copyright 2015
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Pen Portraits for the 2011 Area Classification for Output
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User Guide
Contents
Table of Contents
Summary ..................................................................................................................................... 4
1
Background and Guidance on Use ..................................................................................... 5
1.1
Introduction ........................................................................................................................................ 5
1.2
Model-based approach....................................................................................................................... 5
1.3
Guidance on use and limitations of the estimates............................................................................... 5
1.3.1 Consistency and accuracy of estimates for other geographical areas ..............................................................6
1.3.2 Distribution and ranking of income levels.........................................................................................................6
1.3.3 Consistency between the four different types of income.................................................................................6
1.3.4 Comparability with previous estimates and measurement of change .............................................................7
1.3.5 Examples of data use.........................................................................................................................................7
1.4
Results............................................................................................................................................... 8
2 Guide to the Methodology......................................................................................................... 8
2.1
How do model-based estimates differ from standard survey estimates? ............................................ 8
2.2
Description of the data ....................................................................................................................... 9
2.3
Deriving the estimates........................................................................................................................ 9
2.4
The model for income ...................................................................................................................... 10
2.5
Validation of the model..................................................................................................................... 10
2.6
How precise are the estimates? ....................................................................................................... 10
3 Maps.......................................................................................................................................... 11
3.1
Introduction ...................................................................................................................................... 11
3.2
England and Wales .......................................................................................................................... 11
Appendix ..................................................................................................................................... 15
A Survey data - income definitions ............................................................................................................ 15
Total household weekly income (unequivalised) .................................................................................................... 15
Net household weekly income (unequivalised) ...................................................................................................... 15
Net household weekly income before housing costs (equivalised) ........................................................................ 15
Net household weekly income after housing costs (equivalised) ........................................................................... 16
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Summary
The small area model-based income estimates are the official estimates of weekly household income at the
middle layer super output area (MSOA) level in England and Wales for 2011/12. They are calculated using a
model based method to produce the following four estimates of income using a combination of survey data
from the Family Resources Survey, and data from the 2011 Census and a number of administrative data
sources:
1. Total weekly household income
2. Net weekly household income
3. Net weekly household income (equivalised) 1 before housing costs
4. Net weekly household income (equivalised)1 after housing costs
These four different estimates provide an indication of the average (mean) overall household income along
with the average household income after taking into account tax payments and housing costs. In addition,
the equivalised1 estimates of household income take into account household composition so that more
meaningful comparisons can be made between households with different numbers of occupants. The full
definitions of the four types of income are described at the beginning of each of the next four sections in the
statistical bulletin.
If you are new to small area income estimates, this guide will help you understand the main data sources,
methods, uses and limitations of these statistics. If you are already familiar with the small area income
estimates, you might find it helpful to read our detailed information about the methods and data sources
used to produce the estimates, which is available in the technical report released alongside the data and this
statistical bulletin.
The first section of this user guide provides some background to the statistics and some guidance on the use
of the estimates. The second section provides a brief technical description of the method used to produce
the model-based estimates. Maps of the MSOA level estimates for England and Wales are presented in
Section 3.
1
Equivalised income means that the household income values have been adjusted to take into consideration household
size and composition.
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1
Background and Guidance on Use
1.1 Introduction
There is a specific and increasing interest in obtaining income data at the smallest possible geographical
level. Interest stems from a variety of sources: central government departments, local authorities,
academics, commercial organisations and independent researchers. These data are essential for the
identification of deprived and disadvantaged communities, evaluation research, provision of information for
practitioners, and for the profiling of geographical areas.
The technique of synthetic estimation produces estimates for domains for which survey data are insufficient
by borrowing strength from other data sources. The other data sources (known as auxiliary data or
covariates) are available on an area basis and for all areas in the target population. At the level of these small
areas, sample survey sources are not generally available so the covariate data are usually from some
administrative system or from a previous census.
1.2 Model-based approach
The model-based approach is based on determining 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 MSOAs that are represented in the Survey. This relationship is then used to
provide estimates of average weekly household income for all MSOAs.
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 at the regional level
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, whether 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 MSOA in order to make the precision of the estimates
clear (see Section 2.6 for further information).
Five further limitations of the estimates must be considered:
• The consistency and accuracy of income estimates in relation to those 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 between different time periods
• Comparability with previous estimates
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1.3.1 Consistency and accuracy of estimates for other geographical areas
The model-based methodology produces MSOA level estimates of average weekly household income. These
MSOA level estimates can be aggregated to provide income estimates for larger geographical areas such as
local authorities or regions. However, this method is approximate and hence it is not possible to assess the
precision of the aggregated estimates. As such, the descriptions of the results presented in the statistical
bulletin which accompanies the 2011/12 small area income estimates does not attempt to describe
differences between regions and instead describes only the geographical trends of income at the small area
level.
The model-based methodology has been developed to ensure that the MSOA estimates are constrained to
direct survey estimates from the FRS for regions in England and the estimate for the country of Wales
(section 1.2). For example, the model-based estimates for the MSOAs in Wales, when aggregated,
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.
1.3.2 Distribution and ranking of income levels
In common with any ranking based on estimates, when ranking MSOAs by income, care must be exercised in
interpreting the ranks. One needs to take into account the variability of the estimates when using these
figures. For example, the confidence interval around the highest ranked MSOA suggests that the estimate lies
among the group of MSOAs with the highest income levels rather than being the MSOA with the highest
average MSOA income. Estimates for two particular MSOAs can be described as significantly different if the
confidence intervals for those estimates do not overlap.
The estimation procedure tends to shrink estimates towards the average level of income for the whole
population, and so model-based estimates at each end of the scale tend to be over or under-estimated. The
confidence intervals presented alongside the estimates of average income give an indication of the relative
uncertainty around the estimates. These should be referred to when identifying areas of high and low
average income. Nevertheless, estimates can be used to make certain inferences, e.g. the average weekly
household income for MSOA A is greater than the average for MSOA B (if the appropriate confidence
intervals do not overlap).
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 MSOA, e.g. a MSOA 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
MSOAs. This reinforces the need to look at the confidence intervals and not just the point estimates as the
confidence intervals summarise the variability of the estimates caused by the modelling process (see Section
2).
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1.3.4 Comparability with previous estimates and measurement of change
To enable comparisons between two sets of model-based estimates the methodology employed should be
the same, as should the output geographies for the estimates. The method used to produce the 2007/08 and
2011/12 model-based estimates is the same and both sets of estimates refer to MSOA boundaries.
Therefore, it is possible to draw comparisons between estimates for the same MSOA in the two different
time periods. If the confidence intervals for the estimates do not overlap then there is some evidence of
change over time but, users are warned not to interpret the difference between the point estimates as a
precise measure of change. Statistical comparisons between these estimates should rely on confidence
intervals.
Each estimate has been independently produced as the best estimate of mean household income at the
appropriate point in time but as such they are not optimised to give the best measure of change. The
selection of different covariates for the latest (2001/12) model and previous models may induce changes in
the estimates for particular areas where no underlying change has actually taken place. For this reason,
comparisons over time are not described in the statistical bulletin which accompanies the 2011/12 small area
income estimates.
The separate model selection process and the availability of different data sources for the two sets of
estimates cause different covariates to be included in the models. Users should note that some large changes
in the estimates may be observed for particular MSOAs because of this.
1.3.5 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.
1.3.5.1 MSOA comparisons
When comparing two model-based estimates, one MSOA may be said to have a significantly lower or higher
average income than another if the confidence intervals for the two MSOAs do not overlap. For example,
using Table 1 it may be said that MSOA 3 has a significantly lower model-based income estimate than MSOA
1 since the 95% confidence intervals do not overlap. However, it would be wrong to say that MSOA 2 has a
significantly lower model-based income estimate than MSOA A, since the confidence intervals overlap.
Table 1: Model-based income estimates and confidence intervals for three hypothetical MSOAs
Area
MSOA 1
MSOA 2
MSOA 3
Estimate (£)
Lower Confidence Limit (£)
1,660
1,310
1,110
910
1,080
920
Upper Confidence Limit (£)
2,120
1,360
1,270
MSOA-level estimates can be aggregated to higher geographical levels. Table 2 provides model-based
estimates of the average level of household income for three local authorities. Although the income estimate
for local authority 1 seems to be a great deal lower than that for local authority 3, there are no confidence
intervals available for geographies other than MSOAs. 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. The same limitation applies to aggregating the averages to the region or country level
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and as such, the statistical bulletin which accompanies the 2011/12 small area income estimates doesn’t
describe local authority or regional patterns of average weekly household income.
Table 2: Aggregated model-based income estimates for three hypothetical local authorities
Area
Local authority 1
Local authority 2
Local authority 3
Estimate (£)
420
560
770
1.3.5.2 MSOA profiles
The model-based MSOA estimates of income can be used in conjunction with other data sources to build up
a profile of a particular MSOA. For example, combining the income estimates data with MSOA level house
prices data can be used to provide indications of housing affordability at the small area level. This is
described as a case study in the statistical bulletin which accompanies the 2011/12 small area income
estimates.
1.4 Results
Model-based estimates and their 95% confidence intervals have been produced for MSOAs in England and
Wales for the following income types:
1.
2.
3.
4.
Total household weekly income (unequivalised)
Net household weekly income (unequivalised)
Net household weekly income before housing costs (equivalised)
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 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.
2 Guide to the Methodology
This section provides a brief description of the methodology for producing model- based estimates of
average weekly household income at MSOA level. A full description of the methodology is available in the
technical report which accompanies the 2011/12 small area income estimates.
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 MSOAs is that the vast
majority will contain no sample respondents at all and hence no direct survey estimates will be possible. In
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order to provide MSOA 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 MSOAs. The administrative data used are all previously
published National Statistics, and so meet the quality requirements for modeling income. We can then
‘borrow strength’ from this relationship to generalise and produce reliable estimates of average household
weekly income for all MSOAs.
During our research a number of different relationships and sources of information were investigated. The
best sources of information available were selected for modelling. 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.
2.2 Description of the data
The survey data:
The survey data were obtained from the 2011/12 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:
•
•
•
•
•
•
Census, 2011
DWP benefit claimant counts, August 2011
VOA Council Tax Bandings, 27 March 2011
Her Majesty’s Revenue and Customs, Child Tax Credit and Working Tax Credit, 2011
Communities and Local Government, Change of ownership by dwelling price, 2009
Regional/country indicators which denote whether a given MSOA lies within a particular region or
country
2.3 Deriving the estimates
To derive the required estimates of average weekly household income for MSOAs we:
• Built a model relating the survey variable to the covariate information for MSOAs covered by the
survey
• Used the model and covariate data (which are available for all MSOAs) to estimate the average
weekly household income for all MSOAs
• Ensured the model-based estimates were constrained to the FRS income estimates at the region/country level.
The model-based MSOA estimates of income were aggregated to region/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 region/country level were then used to scale
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the model-based MSOA-level estimates.
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 2:
•
•
•
•
•
•
•
•
•
•
Region or country of MSOA
Average number of people per household
Proportion of people aged 16-74 whose NS-SEC is managerial and professional
Proportion of people aged 16 to 59
Proportion of people in households with a long-term limiting illness
Proportion of people claiming Disability Living Allowance: Mobility Award Higher
Proportion of people aged 16 and over claiming Incapacity Benefit/Severe Disablement Allowance
Number of transactions by dwelling type: total sales
Proportion of people aged 60 and over claiming Pension Credit
Proportion of households that are overcrowded
The result of the models is average weekly household income by MSOA (for four different types of income).
2.5 Validation of the model
A number of diagnostic checks have been used to assess the appropriateness of the models developed for
producing MSOA-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. 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 model-based
estimates are plausible.
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. For each MSOA, assuming the model holds, we are 95% confident the confidence
interval will contain the true value.
2
The predictors used varied depending on the variable being estimated.
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3 Maps
3.1 Introduction
The model-based MSOA level estimates of average weekly household income can be displayed on maps to
show spatial patterns. The interval ranges in each map have been calculated based on clusters of MSOAs
which occur in the data, and the highest and lowest ranges are defined by the clusters and the highest and
lowest values in the range respectively. The number of MSOAs 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 MSOA estimates of average total weekly household income
(unequivalised) in England and Wales. Map 2, Map 3 and Map 4 display the geographical variation of MSOA
income in England and Wales for the three other income types.
Map 1: Mean total weekly household income by MSOA, England and Wales, 2011/12
Notes for Map 1:
1. Source: Office for National Statistics
2. Contains Ordnance Survey data © Crown copyright and database right 2015
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Map 2: Mean net weekly household income (unequivilised) by MSOA, England and Wales, 2011/12
Notes for Map 2:
1. Source: Office for National Statistics
2. Contains Ordnance Survey data © Crown copyright and database right 2015
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Map 3: Mean net weekly household income (equivalised) before housing costs by MSOA, England and
Wales, 2011/12
Notes for Map 3:
1. Source: Office for National Statistics
2. Contains Ordnance Survey data © Crown copyright and database right 2015
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Map 4: Net weekly household income (equivalised) after housing costs by MSOA, England and Wales,
2011/12
Notes for Map 4:
1. Source: Office for National Statistics
2. Contains Ordnance Survey data © Crown copyright and database right 2015
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Appendix
A
Survey data - income definitions
This appendix contains details on the four income types modelled. For more specific information each of the
models see the technical report that accompanies the 2011/12 small area income estimates.
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
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
All maintenance and child support payments, which are deducted from the income of the person
making the payments
• 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 an equivalisation scale. Applying an equivalisation 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.
Equivalisation is needed in order to make sensible income comparisons between households. For example,
one household may have two adults and two children, and have a total weekly household income of £300. If
this is compared with a household containing just one 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 (assuming equal living and housing expenses).
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Although a number of equivalence scales have been developed, the equivalence scale used for the income
estimates is the OECD’s scale. An example of the effect of applying the OECD’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).
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 OECD’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)
Ground rent and service charges
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