Department for Work and Pensions
Research Report No 219
Families and Children Strategic
Analysis Programme
The dynamics of
deprivation:
the relationship between
income and material
deprivation over time
Richard Berthoud, Mark Bryan and Elena Bardasi
A report of research carried out by the Institute for Social and Economic
Research at the University of Essex on behalf of the Department for Work
and Pensions
Corporate Document Services
© Crown Copyright 2004. Published for the Department for Work and Pensions
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First Published 2004.
ISBN 1 84123 728 0
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Printed by Corporate Document Services.
Contents
Contents
Acknowledgements ....................................................................................... ix
The Authors ................................................................................................... x
Glossary of terms ........................................................................................... xi
Summary ....................................................................................................... 1
1 Introduction ............................................................................................. 9
1.1 Background and objectives .............................................................. 9
1.2 Outline of the report ..................................................................... 11
1.3 What is ‘material deprivation’? ...................................................... 12
2 Source surveys ........................................................................................ 17
2.1 The Families and Children Survey (FACS) ....................................... 17
2.2 The British Household Panel Survey (BHPS) .................................... 20
3 ‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles ........ 23
3.1 The Policy Studies Institute hardship index ..................................... 23
3.2 Headlines ...................................................................................... 25
3.3 Persistent poverty .......................................................................... 27
3.4 Trends in hardship rates from year to year ..................................... 31
3.5 Discussion ..................................................................................... 32
4 Measuring material deprivation ............................................................... 35
4.1 Approach ...................................................................................... 36
4.2 Components of the new FACS index ............................................. 38
4.3 Components of the BHPS index ..................................................... 41
4.4 Trends in the prevalence of deprivation components ..................... 43
4.5 Formulating the index ................................................................... 47
4.6 Properties of the index .................................................................. 48
4.7 Discussion ..................................................................................... 51
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Contents
5 Measuring income .................................................................................. 53
5.1 Defining income ............................................................................ 53
5.2 Equivalence scales ......................................................................... 54
5.3 Very low incomes .......................................................................... 55
5.4 Discussion ..................................................................................... 59
6 ‘Cross-sectional’ relationships between material deprivation and
other factors, at one point in time .......................................................... 61
6.1 Income .......................................................................................... 63
6.2 Family structure ............................................................................. 67
6.3 Other factors ................................................................................. 68
6.4 Strength of the relationships ......................................................... 71
6.5 BHPS comparison .......................................................................... 73
7 ‘Underlying’ relationships during a period ............................................... 77
7.1 Approach ...................................................................................... 77
7.2 Estimating underlying relationships ................................................ 79
8 ‘Longitudinal’ relationships from year to year .......................................... 83
8.1 Testing alternative longitudinal models .......................................... 83
8.2 Estimating longitudinal relationships .............................................. 86
8.3 An illustration................................................................................ 88
8.4 Stable versus unstable households ................................................. 89
8.5 Components of the deprivation index ............................................ 91
8.6 Households with and without children .......................................... 93
8.7 Lone parents in FACS .................................................................... 95
9 Review and conclusions .......................................................................... 97
9.1 Analytical conclusions.................................................................... 97
9.2 Measurement issues .................................................................... 102
9.3 Considerations for policy ............................................................. 104
References ................................................................................................. 107
Contents
List of tables
Table 2.1
Table 2.2
Table 2.3
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 5.1
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8
Table 7.1
Summary of the coverage of the Families and
Children Survey ...................................................................... 18
Sample of families in FACS Waves 1 to 4 ................................ 19
The BHPS sample of individuals under pension age,
by number of waves of available data (Waves 6 to 12) ............ 22
Nine indicators in the PSI hardship index ................................. 24
Hardship among poor, middle-income and well-off
families at Wave 4 (2002) ....................................................... 25
Hardship at Wave 4: couples and lone parents compared ....... 26
Hardship at Wave 4, by total number of waves in
poverty over four-wave period ................................................ 28
Movements in and out of hardship between Waves 3 and 4,
in relation to movements in and out of poverty ....................... 30
Hardship among poor and non-poor families,
by wave of observation ........................................................... 31
Detailed components of the FACS index of
material deprivation ................................................................ 39
Overview of four FACS deprivation sub-indices ....................... 40
Detailed components of the BHPS index of
material deprivation ................................................................ 42
Overview of four BHPS deprivation sub-indices ....................... 43
Estimated slope of the cross-sectional relationship
between income and FACS deprivation score,
with and without adjustment for very low incomes ................. 59
Cross-sectional regression equations for the FACS deprivation
index using alternative measures of current income ................ 65
Cross-sectional regression equations for the FACS deprivation
index using alternative measures of family composition .......... 68
Cross-sectional regression equation for the FACS deprivation
index: other factors ................................................................ 69
Incomes and deprivation scores by income sources ................. 70
Full cross-sectional regression equation for the FACS
deprivation index .................................................................... 71
Proportion of cross-sectional variance in FACS deprivation
index explained by each group of factors ................................ 72
Full cross-sectional regression equation for the BHPS
deprivation index .................................................................... 73
Proportion of cross-sectional variance in BHPS deprivation
index explained by each group of factors ................................ 75
Between-cases regression equation for the BHPS
deprivation index .................................................................... 80
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Contents
Table 7.2
Table 8.1
Table 8.2
Table 8.3
Table 8.4
Table 8.5
Table 8.6
Table 9.1
Table 9.2
Table 9.3
Proportion of between-cases variance in BHPS deprivation
index explained by each group of factors ................................ 81
Comparison of differences equations and within-cases
equations using various combinations of waves (all confined
to members of the balanced seven-wave panel) ...................... 84
Within-cases regression equation for the BHPS
deprivation index .................................................................... 87
Between- and within-cases regression equations for the
BHPS deprivation index: individuals in stable and
unstable households ............................................................... 91
Effects of income in the between- and within-cases
regression equations, using the components of the
deprivation index as dependent variables ................................ 92
Between- and within-cases regression equations for the
BHPS deprivation index: households with and
without children ..................................................................... 94
Between- and within-cases regression equations for the
FACS deprivation index: families who were lone parents
at Wave 1............................................................................... 96
Proportion of variance in deprivation indices explained
by each group of factors ....................................................... 100
Attribution of variance in the deprivation index to
underlying and longitudinal relationships .............................. 101
Access over time to money for trips and a computer,
among FACS non-working families ....................................... 104
List of figures
Figure 1.1
Figure 3.1
Figure 3.2
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Two interpretations of the essence of poverty ......................... 14
Hardship at Wave 4, across the full distribution of
equivalent income .................................................................. 27
Hardship risk at Wave 4, by whether in or out of
poverty at each wave .............................................................. 30
Trend in lack of consumer durables among non- working
families with children, 1996 to 2002 ...................................... 44
Trends in daily living deprivation and financial hardship
among non-working families with children, 1996 to 2002 ...... 46
Proportion of households scoring one or more on the Irish
basic deprivation index, by economic activity of household
reference person, 1994-2001 ................................................. 47
Distribution of the three-group deprivation indices in 2002 ..... 49
Mean deprivation score in 2002, by quintile groups of
equivalent income .................................................................. 50
Contents
Figure 4.6
Figure 5.1
Figure 5.2
Figure 5.3
Figure 6.1
Figure 6.2
Figure 6.3
Figure 8.1
Figure 9.1
Proportion of poor and non-poor BHPS respondents scoring
more than 30 points on the continuous deprivation index,
by wave.................................................................................. 51
Trends in inequality of equivalent household incomes:
BHPS non-pensioner families with and without children .......... 54
Estimated average deprivation scores for families/households
in each two per cent range of the distribution of income
(up to £500) ........................................................................... 56
Measures of resources among households with very low
incomes based on the Family Resources Survey and the
Family Expenditure Survey....................................................... 57
Stylised relationship between income and deprivation ............. 62
FACS deprivation index by income – three
metrics compared ................................................................... 64
Estimated FACS deprivation scores by income: with and
without controls for family structure and other factors ............ 66
Stylised representation of the underlying and longitudinal
relationships between income and deprivation........................ 89
Reduction in BHPS deprivation score associated with a
£10 increase in income at £200: sequence of
improved estimates ................................................................ 99
vii
Acknowledgements
Acknowledgements
This report is based on research commissioned by the Department for Work and
Pensions (DWP), as part of its Families and Children Strategic Analysis Programme.
Stephen Morris was the main DWP liaison officer, and Elaine Squires, Kirby Swales
and Maxine Willitts contributed to the development of the project. Simon Lunn
provided some special analyses of the Family Resources Survey.
Special thanks to Alan Marsh and Sandra Vegeris at the Policy Studies Institute (PSI)
for providing and explaining the FACS hardship variables which they had developed;
to Stephen McKay, at Bristol University, for advice on the income data; to Alissa
Goodman and Andrew Leicester, at the Institute for Fiscal Studies, for providing an
analysis of Family Expenditure Survey (FES) data; and to Institute for Social and
Economic Research (ISER) colleagues John Ermisch and Stephen Jenkins for advice
on the econometric models. Thanks also to Tony Atkinson (Nuffield College,
Oxford), Jonathan Bradshaw (University of York), Mike Brewer (Institute for Fiscal
Studies), Alan Marsh, Stephen McKay and Chris Whelan (Economic and Social
Research Institute, Dublin) for valuable comments on drafts.
As always, the analysis and interpretation are the responsibility of the authors, not of
the organisations or individuals whose contributions are acknowledged here.
ix
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The Authors
The Authors
Richard Berthoud is a Research Professor at the Institute for Social and Economic
Research, University of Essex.
Mark Bryan is a Chief Research Officer at the Institute for Social and Economic
Research, University of Essex.
Elena Bardasi was a Senior Research Officer at the Institute for Social and Economic
Research, University of Essex and is now at the World Bank.
Glossary of terms
Glossary of terms
(Italics indicate cross- references to other entries)
α)
Alpha (α
See Cronbach’s alpha.
Balanced panel
A subset of individuals or households in a
panel survey who provided the relevant data at
every wave.
Between cases
An analysis comparing each respondent’s
average level of deprivation, income, and so
on over a (seven year) period. We interpret it as
showing the ‘underlying’ relationships. See
also within-cases.
BHPS
British Household Panel Survey
Constant
The predicted value of the dependent variable
for a hypothetical case where the values of all the
explanatory variables are zero. See Regression
for beginners in Box B, Chapter 6.
Correlation coefficient
A measure of the extent to which two variables
are linearly associated with each other (e.g.
how consistently respondents with low incomes
report high deprivation scores). 0.00 means
no association; 1.00 means an exact match
between the two sets of values.
Cronbach’s alpha
A measure of the extent to which a package of
several variables are all associated with each
other. It also ranges between 0.00 and 1.00. A
high alpha (greater than 0.60) is interpreted to
mean that the package of variables represents
an underlying dimension.
xi
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Glossary of terms
Cross-section
A sample (of households) all interviewed at
about the same time. Most one-off surveys are
cross-sectional. Each wave of a panel survey
can be treated a new cross-section.
Cubic
A function based on the cube of (e.g.) income
i.e. income multiplied by income multiplied by
income.
Decile
In a representative group of 100 observations,
the lowest decile is the 10th from the bottom;
the highest decile is the 10th from the top. The
fifth decile is also the median.
Decile groups
The ordered distribution (e.g. of income) divided
into ten equal-sized groups – lowest tenth,
second tenth, etc.
Deprivation index
A continuous indicator of material living
standards, discussed in Chapter 4. The index
eventually used for this analysis averages zero:
well-off families tend to have negative scores,
low income families have positive scores.
‘Continuous’ means a scale with many points
ranging from very undeprived to very deprived.
See also hardship.
DWP
Department for Work and Pensions
DSS
Department of Social Security (predecessor of
the DWP).
Equivalent income
Net household income divided by a factor
based on the number and ages of the
household members to adjust for varying needs.
Sometimes referred to as ‘equivalised income’.
The factor is known as an ‘equivalence scale’.
See Chapter 5 for a discussion.
FACS
Families and Children Survey
FES
Family Expenditure Survey
FRS
Family Resources Survey
Hardship
We use this word to refer to the position of
being highly deprived – an either/or condition,
as compared with the numerically continuous
scale of a deprivation index (cf poverty and
income).
Glossary of terms
HBAI
Households Below Average Income: the
analysis of incomes, and of poverty, published
annually by the DWP.
ISER
Institute for Social and Economic Research,
University of Essex.
Mean
The conventional ‘average’: the sum of the
values divided by the number of cases.
Median
The mid-point of the distribution of values.
ns
Not significant (see statistically significant).
Panel survey
A survey in which the same sample (of
households) is interviewed repeatedly. In both
surveys used here, the interviews are annual.
Poverty
The position of having a very low income.
Although many commentators consider that
deprivation or hardship are the true, direct,
measures of poverty (see Chapter 1), this report
always uses the words ‘poor’ and ‘poverty’ to
mean income-poverty – defined as having an
equivalent income below 60 per cent of the
contemporary median income before housing
costs.
PSI
Policy Studies Institute.
Quadratic
A function based on the square of (e.g.) income
i.e. income multiplied by income.
R2
Pronounced R-squared. An estimate of the
proportion of the variance in the dependent
variable which is explained by the explanatory
variables in combination. See Regression for
beginners in Box B, Chapter 6.
Regression coefficient
An estimate of the rate at which the dependent
variable (e.g. a deprivation index) increases for
each unit increase in one of the explanatory
variables. See Regression for beginners in
Box B, Chapter 6.
Regression equation
An analytical procedure for estimating the
relationships between variables. See Regression
for beginners in Box B, Chapter 6.
xiii
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Glossary of terms
Shadow observations
Families who were screened out of the FACS
sample at waves 1 and 2, but for which we can
conclude on the basis of the screening
questionnaire that they were working couples
with children who were not in poverty.
Standard deviation
A measure of the range of variation between
respondents. The square root of the variance,
the particular property of the standard deviation
is that it is measured in the same units as the
variable itself (e.g. £s, age-years). If the variable
is divided by its standard deviation, it becomes
unitless, and this allows variables originally
measured in different units to be compared
directly with each other.
Standard error
A measure of the likely range of estimates of
the value of a statistic (e.g. a regression
coefficient), if many different samples were
selected. The larger the sample, the smaller
the standard error for a given estimate. See
also t-score and significant.
Stata
The statistical program used to analyse the
survey data and estimate the relationships.
(Statistically) significant
If measurements are based on a random sample
of households, rather than all households in
the population, the estimates will vary either
side of the true value, depending on chance
factors affecting which particular households
were chosen. The larger the sample, the lower
the risk of chance variation. An estimate is
judged to be ‘statistically significant at the
95% level’ if the probability of its having arisen
by chance is less than 5%. The 95% confidence
level has been applied throughout this report.
See also ns.
t-score
An estimate of the accuracy with which a
regression coefficient, mean, percentage (or
other statistic) has been measured on a sample
of a given size. The ratio of the statistic to its
standard error. A statistic (e.g. coefficient) is
significant at the 95 per cent level if its t-score
is 2 or greater.
Glossary of terms
Variance
A measure of the range of variation between
respondents. The square of the standard
deviation, the particular property of the variance
is that it can be partitioned into additive
components (e.g. the between-cases variance
plus the within-cases variance equals the overall
variance; a certain proportion of the variance
can be explained).
Within cases
An analysis comparing variations in each
respondents’ deprivation, income and so on,
either side of their average, over a (seven year)
period. We interpret this as showing the
‘longitudinal’ relationship. See also between
cases.
xv
Summary
Summary
Introduction
The government has pledged to eliminate child poverty by 2020, and has set itself a
series of intermediate targets for reducing the number of poor families between
now and then
Poor families experience low living standards. They are said to be ‘deprived’ or ‘in
hardship’. There is a long history of research indicating a strong relationship
between low income and indicators of deprivation at any point in time. This leads to
the expectation that a family’s living standards would rise and fall roughly in line with
changes in its income – exiting income-poverty should mean ending hardship. The
aims of this research are to promote our understanding of how people experience
deprivation over time, as their incomes rise and fall.
An index of material deprivation is an attempt to summarise the living standards of
families at different levels of income, based on survey questions about whether
people do or do not have certain items; can or cannot afford to participate in normal
daily activities; and find it easy or difficult to manage their budgets. A family’s
position on a deprivation scale is likely to depend on a number of factors, including
their income, their particular set of needs, their preferences, the ‘efficiency’ with
which they convert income into essential consumption, and imprecision in the
measurement scale.
Deprivation indicators have been interpreted in two distinct ways, depending on
what one means by the word ‘poverty’:
• One view is that poverty consists of a lack of resources (one of whose main
symptoms is a low standard of living). This view requires only a weak set of
assumptions about deprivation scores – they are just an indicator, used to identify
groups at risk of poverty or to calibrate a poverty line.
• An alternative view is that poverty consists of low living standards (one of whose
main causes is lack of resources). This view requires a much stronger set of
assumptions about deprivation scores – they have to be comprehensive enough
and reliable enough to be treated as an actual measure of poverty.
1
2
Summary
The analysis in this study is based on the view that no index can support the strong
set of assumptions required to treat it as a direct measure of poverty. It uses the weak
set of assumptions which treats the survey data as just an indicator. The analysis will
nevertheless be of interest to those who favour the direct measurement approach.
Source surveys
Two surveys have been used to unravel the relationships between income and
material deprivation over time.
The Families and Children Survey (FACS) has a large sample of families, and a very
detailed battery of deprivation indicators. It has followed the same sample of
families for four years. But working couples with middle or high incomes were not
fully interviewed in the first two waves, and this means that it is not possible to
analyse the experiences of a representative sample of families over the full period.
The British Household Panel Survey (BHPS) has followed a fully representative
sample of households over a long sequence of years. We analyse the seven-year
period 1996 to 2002 (waves 6 to 12), and focus our attention on non-pensioner
individuals who contributed data on at least five of those occasions. Because
households change their composition over time, we followed the position of
individuals, attributing to them the income and deprivation scores of the household
they were living in at each wave.
Poverty and hardship in 2002: some findings...and some
puzzles
The analysis started with a straightforward cross-comparison between ‘poverty’ and
‘hardship’ – both defined as positions at the disadvantaged end of their respective
scales of income and of deprivation. At first the findings were entirely in line with
what one might have expected. Poor families are much more likely to be in hardship
than others; while well-off families have a very low risk. Families who have been in
poverty for several recent years report more hardship than those for whom it was a
temporary experience.
But then some more puzzling findings emerged. Among families who had moved in
and out of poverty, the risk of hardship at the end of the period varied according to
the number of years poor, but it hardly mattered whether the experience of incomepoverty was recent or some time ago. Only a small proportion of families who moved
out of poverty between one year and the next, also moved out of hardship at the
same time. On the other hand, there was a general drift out of hardship over the four
year period, as levels of deprivation seemed to decline even among poor families.
Summary
Measuring material deprivation
A series of questions from each of the two surveys was used to develop an extended
index of deprivation for more detailed analysis. The questions were under four
headings: daily living, financial stress, consumer durables and housing. The housing
indicators were found not to perform so well as the other three, and that group of
questions was dropped.
The compilation of the index was based on six principles:
• many component indicators;
• components associated with each other (an underlying dimension);
• components, and index, associated with income (especially low income);
• analysable as a continuous variable;
• meaningful when compared across years, as well as in any year;
• simple and easy to understand.
The first four of these principles were not difficult to achieve, and followed
precedents set by previous analysts in this field. The new, and difficult, problem, was
in calibrating an index which would distinguish changes in individuals’ experience as
their incomes rose and fell, from underlying trends in the answers to the survey
questions used for the index. As expected, both the surveys showed a steep
downwards movement over the observation period in the number of consumer
durables which people did not have. We had not expected, though, that both
surveys would also show downwards trends in deprivation under the headings of
financial stress and daily living. In the latter case, the down-trend in the FACS data
was just as steep as for consumer durables. In both cases, the down-trend in the
FACS data was steeper than in the BHPS data. All these trends are over and above
any movement that might have been expected from changes over time in the
distribution of incomes and other characteristics associated with deprivation. It has
also been noted that the Irish deprivation index, which has been used as a model for
the development of UK approaches in this field, shows a rapid downward trend
which is difficult to explain in terms of improving incomes.
So it was decided to recalibrate the contribution of each component item of the
index each year, so that the overall average score was fixed. (But the distribution of
the overall score is not fixed.) This provides a measure of relative, rather than
absolute, deprivation, comparable in principle with relative measures of poverty.
The disadvantage of this solution was that the final item on the list of principles
above had to be sacrificed. The index used here is not simple and easy for nonanalysts to understand.
3
4
Summary
Measuring income
Both surveys provide measures of total net family/household income before housing
costs very similar to that used by the DWP for its Households Below Average Income
series. The FACS income data excludes the self-employed. No equivalence scale was
used, because the analysis was able to take direct account of the effects of family
structure on living standards.
Both of the surveys used here, as well as the Family Resources Survey (FRS) and the
Family Expenditure Survey (FES), appear to show that families/households with
extremely low incomes are much better off than one would have expected. These
lowest incomes may have been under-recorded. This is not a new finding, but it is
especially important for this research, and a correction factor was built into the
analysis to take it into account.
‘Cross-sectional’ relationships between material deprivation
and other factors, at one point in time
Although our ultimate interest is in the ‘longitudinal’ relationship between income
and deprivation over time, the analysis starts by focusing on the position in a single
year (2002). This replicates the approach taken by single-year surveys (such as the
Poverty and Social Exclusion Survey), and by repeated surveys using separate
samples (such as the Family Resources Survey). Multiple regression analysis has been
used to estimate the strengths of the associations between deprivation and each of
a series of other household characteristics, including income.
As expected, families with low incomes have high deprivation scores; and high
incomes are associated with low deprivation scores. The shape of the relationship is
curved, so that the rate of decrease in deprivation with increasing income is steep at
the lower end of the income distribution, and flatter at the upper end.
The relationship between income and deprivation is very steep if income is the only
set of predictor variables used. It is much flatter (though still significant) if the effects
of other characteristics such as family structure, sources of income (including
employment) and housing tenure are taken into account. This implies that some of
the apparent relationship between income and deprivation is explained by other
factors (which are associated with income) rather than by income in its own right.
The number and ages of family members are also directly related to deprivation
scores, even after taking income into account. These family effects are inconsistent
with the assumptions built into most equivalence scales:
• Couples report slightly lower deprivation scores (on a given income) than single
people or lone parents – it might have been expected that the extra person
might add to a family’s costs, but there appears to be some benefit associated
with being a couple which more than compensates for this in terms of deprivation.
Summary
• Young children have a larger adverse effect on deprivation levels than older
children.
• Families with one or two children are not much worse off than those with none;
a third or fourth child makes more of a difference; but it is families with five or
more children who record very high deprivation scores.
Families and households with at least one worker record lower deprivation scores
than those with no worker, even after allowing for the fact that they have higher
incomes. But the receipt of certain benefits (WFTC and IS) is often associated with
relatively high deprivation scores, after allowing for income. Since these sources of
income are obviously associated with the amounts of income, it is difficult to work
out what the exact effects are. It should also be noted, that the effect of incomesources was substantially greater in the FACS analysis than in the BHPS.
Households who own their home outright have below average deprivation scores;
tenants have above average scores; in both cases after allowing for income and
other characteristics. This may be a reflection of the different housing costs faced by
these groups. Another interpretation is that capital affects living standards
independently of the income it generates. But there may be a selection effect too, if
it is families with high deprivation risks who tend to live in rented accommodation.
Other variables associated with deprivation included age, educational qualifications
and region. But the four discussed above – income, family structure, income sources
and housing tenure – are the most important. Between them they accounted for
40% of the total variance in deprivation scores in the FACS, and 31% in the BHPS.
‘Underlying’ relationships over a period
If we take the seven consecutive years of data from the BHPS, each individual will
have recorded a range of incomes, and range of deprivation scores. It is useful to
consider their position as having two distinct components: their average income
(and average deprivation) over the whole seven year period; and variations in their
income (or deprivation) around that mean, from year to year within that period. The
distinction can be handled by splitting the analysis into two stages:
• Calculating the mean value of income, deprivation (and so on) for each member
of the sample, averaged across waves. This discounts variations across years,
and focuses on variations between individuals. The technique is referred to as
‘between-cases’ analysis: it can be interpreted as establishing the underlying
relationships.
• Calculating for each individual in each wave the difference between this wave’s
income, deprivation (and so on) and their average calculated at the previous
step. This discounts underlying differences between individuals, and focuses on
variations across years. The technique will be referred to as ‘within-cases’ analysis:
it can be interpreted as establishing the longitudinal relationships over time.
5
6
Summary
Analysis of the underlying relationships, using the first of these approaches, showed
that all the sets of variables that helped to predict deprivation in the ‘cross-sectional’
analysis were just as strongly associated when compared over a seven year period.
The measured effect improved substantially, so that income itself explained 24 per
cent of the overall variance in deprivation scores, even after allowing for the effects
of other variables (and 36 per cent if other variables are ignored). This is an
exceptionally strong relationship. But we still cannot be sure that this underlying
relationship is directly causal. The possibility remains that there is some unmeasured
characteristic of households which affects both their incomes and their deprivation,
so that if their income went up, their deprivation would not necessarily go down.
‘Longitudinal’ relationships from year to year
So the ‘within-cases’ analysis is designed to look directly at what happens to
people’s deprivation scores when their income changes. It turned out that the
strength of the link appeared to vary considerably, depending on whether we were
comparing a pair of consecutive waves, or a pair of waves six years apart. This was
not (mainly) because it took a long time for changing deprivation to catch up with
changes in income. It appeared to be mainly because the relatively small true
changes in income and deprivation between consecutive years were being masked
by also-small random changes in people’s report of their income and deprivation.
When a wider spacing of years was used, the true changes were larger, but the
random error remained small, so the true picture was more clearly visible. This is why
we used a sequence of seven waves of the BHPS, and a more complex within-cases
model, rather than simply compare changes in income and deprivation between
‘last year’ and ‘this year’.
The longitudinal relationship between income and deprivation was about half as
strong as the underlying relationship had been. That is, people with consistently low
incomes have consistently high deprivation scores; if someone’s income increases,
their deprivation reduces, but not enough to make them as well off as someone who
had had the higher level of income all along.
Part of the longitudinal relationship was ‘lagged’ – a change in income between one
wave and the next had an immediate effect, but also a further, delayed effect the
following year. But there was no sign of a continuing response beyond the second
year.
Looking across the range of predictor variables:
• some of the coefficients were just as high in the longitudinal analysis as in the
underlying analysis, and these can be interpreted as true causal effects – improving
the characteristic will lead to a reduction in deprivation. These robust indicators
include employment and marital status;
Summary
• other longitudinal coefficients were lower than their underlying equivalents. Only
part of the overall effect can be interpreted as truly causal, and investments in
these areas may pay a reduced dividend. These less efficient indicators include
(crucially) income, but also benefits received and housing tenure;
• a third group of variables had no longitudinal relationship with deprivation, and
have to be interpreted as reflecting permanent characteristics of the family, rather
than dynamic influences on living standards. These are educational qualifications
and (surprisingly) large family size.
The analysis concluded with a series of checks:
• comparing individuals living in households whose circumstances changed, with
individuals who moved between households in different circumstances;
• comparing the three groups of variables used to compile the index (daily living,
financial stress and consumer durables); and testing the effect of adding a fourth
group (housing);
• comparing families with and without children;
• comparing the BHPS and FACS.
These comparisons suggested some interesting differences of detail, but in broad
terms confirmed that the conclusions were robust with respect to these analytical
alternatives.
Review and conclusions
Working out the precise relationship between income and material deprivation over
time turned out to be a complex task, requiring some fairly sophisticated analytical
techniques. There are two main differences between the simplest possible and the
final complex measures:
1 The effects of other disadvantaging characteristics in their own right, as well as
income itself. It has been shown that family composition, income sources (as
opposed to income amounts) and housing tenure all have a direct association
with deprivation; and that some apparent effects of income are actually explained
by these other factors.
2 The distinction between underlying and longitudinal relationships. Underlying
relationships over a period of time are much more effective at explaining
deprivation scores than variations over time within that period. To the extent
that year on year changes in deprivation can be accounted for, the effect of
income is about half as strong as it appeared in the underlying model. But it was
still strong. People really do get better off when their income rises!
7
8
Summary
The research has identified a number of measurement issues, some of which may be
relevant for other analyses in this area:
• A general point is that small variations in reported income and reported
deprivation from year to year impose a background ‘noise’ which makes it very
difficult to base longitudinal analysis on a pair of consecutive years.
• The apparent unreliability of income data at the very bottom of the scale has
implications for a range of statistics derived from the foot of the distribution –
not only the poverty rate, but also (for example) take-up rates.
• The rapid year-on-year reduction in absolute measures of deprivation, unexplained
by changes in income or other characteristics, means that some form of
continuous recalibration is required if an index is to provide a valid measure of
relative deprivation over a period. Otherwise deprivation-poverty will disappear
of its own accord.
The findings of the analysis also indicate some potentially important lines of policy
strategy. For example, the fact that moving in and out of employment has a strong
effect on deprivation levels, independent of income, endorses the current view that
‘work is the best route out of poverty’. Some unexpected variations by family
composition might be taken into account in a review of scale rates for benefits and
tax credits. The variations by housing tenure support the view that owneroccupation is best, but also focuses attention on the plight of the dwindling group
of families who remain excluded from owner-occupation.
The relatively weak longitudinal relationship between income and deprivation
means that families who dip into poverty just for a short a period need not be a
primary area of concern. The converse, though, is that those in long-run poverty
suffer even more deprivation than might have been feared; and that a temporary
escape from poverty will do little to alleviate their position. The implication seems to
be that permanent improvements in poor people’s underlying economic positions
are required, not short-term fixes. That implies, on the one hand, policies to
encourage steady employment, high earnings (and perhaps even partnership
stability); and, on the other hand, an adequate income for those who are obliged to
remain on benefit for long periods.
Introduction
1 Introduction
1.1
Background and objectives
The government has pledged to eliminate child poverty by 2020, and has set itself a
series of intermediate targets for reducing the number of poor families between
now and then.
So what’s wrong with being poor? The modern concept of poverty is expressed in
terms of relative deprivation and social exclusion (Runciman 1965, Townsend 1979,
Hills and others 2002). A formal definition was adopted by the European Union in
1984:
‘The poor shall be taken to mean persons...whose resources...are so limited as
to exclude them from the minimum way of life of member states in which they
live.’
Poor families experience low living standards. They are said to be ‘deprived’ or ‘in
hardship’. ‘Deprivation’ and ‘hardship’ are clearly associated with a low income; but
there may be other factors which affect any particular family’s living standards.
Although the recent practical definition of poverty, both within the UK (DWP 2002)
and across the EU (Atkinson and others 2002), has been in terms of low relative
income (below 60 per cent of the contemporary median), the government has
recently proposed adding direct indicators of deprivation to the measures against
which progress towards the elimination of child poverty should be assessed (DWP
2003b). (The proposal is summarised in Box A)
The aims of this research are to promote our understanding of how people
experience deprivation over time, as their incomes rise and fall. The overall objective
is to contribute to the development and evaluation of the government’s policies to
eliminate child poverty.
There is a long history of research in which ‘deprivation’ or ‘hardship’ indicators have
been used to examine the relationship between family income and living standards
(see later in this chapter). These studies have varied in their theoretical and empirical
approaches, but all have suggested a strong statistical relationship between low
income and low living standards at any point in time.
9
10
Introduction
A household’s income is not constant over time. The Family Resources Survey shows
a recent trend towards higher incomes, and lower income-poverty rates among
families with children (DWP 2003a). Even without an overall trend, individual
families can rise and fall on the income ladder as (for example) their adult members
move in and out of work. Although a quarter of children were below the incomepoverty line in any particular year in the mid- and late-1990s, only one in ten were in
a continuous four-year spell of income-poverty (Jenkins and Rigg 2001). If a
significant proportion of low income is experienced over only a short period, the
question arises whether living standards also dip. It is often assumed that a short
period on low income might not matter; though an alternative hypothesis is that
income-poverty will be felt more acutely at the beginning of a spell than later on
(after budgets have adjusted to the new income level).
Box A
Measuring Child Poverty
The UK government’s proposals for Measuring Child Poverty were published
in December 2003 (DWP 2003b). Three measures were proposed:
1 Absolute low income: families with an equivalent income below 60 per
cent of the 1998/99 median.
2 Relative low income: families with an equivalent income below 60 per cent
of the contemporary median.
3 Material deprivation: families who are both materially deprived (lacking
certain goods and services) and have an equivalent income below 70 per
cent of the contemporary median.
New deprivation questions will be included in the Family Resources Survey
from 2004/05 onwards. There are eleven questions relevant to all households,
and nine relevant to children (though not all of the latter apply to all age
groups). Most of the questions are of the type referred to later in this report as
‘daily living’. At the time of writing (June 2004), no decision has yet been
made as to how the questions should be combined to define a threshold for
material deprivation.
There has been hardly any systematic research into the dynamics of living standards.1
The close association between current income and current measures of deprivation
or hardship leads to the expectation that living standards would rise and fall roughly
in line with income – exiting poverty should mean ending hardship. But the year-onyear relationship between changing income and changing deprivation is not
necessarily the same as the ‘cross-sectional’ relationship. A more complex hypothesis
is required to understand the links between the dynamics of income and of living
standards.
1
An exception, using European data, is Whelan and others, 2001. Vegeris and
Perry’s report on the Families and Children Survey (2003) briefly addresses the
issue.
Introduction
It can be assumed that one of the government’s main intentions in tackling child
poverty is to reduce the extent of deprivation associated with low income. On that
assumption, it is important to understand the links between the two problems.
There are two key questions:
• Families below the income-poverty line at any time can be divided into those
who are temporarily below the threshold, and those in persistent poverty. Do
the latter account for a high proportion of all those in hardship? Can a short
period on low income perhaps be discounted as having less serious consequences?
Or, alternatively, are the consequences of a sudden but temporary fall in income
more acute, or more long-lasting, than steady-state analysis would lead us to
expect?
• The government aims to eliminate family poverty by a combination of incomemaintenance and welfare-to-work policies. How far does an escape from incomepoverty lead directly to a reduction in deprivation for the family concerned?
The answers to both those questions may seem obvious. But the extent of the effects
has not been measured; and the outcomes are not always as ‘obvious’ as might have
been expected. Only careful longitudinal analysis can unravel the relationships.
1.2
Outline of the report
The research reported here is based mainly on two sources: the Families and
Children Survey (FACS) and the British Household Panel Survey (BHPS). Each survey
follows its sample of respondents from year to year, and can therefore be used to
assess the relative importance of underlying variations between households in their
income and in their experience of deprivation, and longitudinal variations over time.
The two surveys are described in the next chapter.
Chapter 3 uses the FACS data to present straightforward tables about the overlap
between ‘poverty’ (i.e. low income) and ‘hardship’ (i.e. high deprivation). Some of
the findings are exactly what would have been expected. Others are more
surprising, and therefore interesting. A third group of findings are so counterintuitive
that they require further investigation. We conclude that more complex analysis of
the details of households’ incomes, deprivation and other characteristics is needed
to unravel some of the puzzles.
Chapter 4 uses the answers from a large number of survey questions to assemble
deprivation indices for each of the two surveys, which are functionally equivalent
even though not based on exactly the same questions. The biggest challenge was
dealing with trends from year to year in the overall number of deprivation items
reported. Chapter 5 discusses the available measures of household income,
focusing especially on some apparent distortion at the very bottom of the distribution.
11
12
Introduction
Chapter 6 mainly uses the FACS data to paint a detailed picture of the relationships
between deprivation and income (and other household characteristics) at any point
in time. This ‘cross-sectional’ approach is similar to that of one-off surveys (such as
the recent Poverty and Social Exclusion Survey (Gordon and others 2000)), and of
repeated but independent surveys (such as the deprivation indicators planned for
the Family Resources Survey (DWP 2003b, McKay and Collard 2004)).
The analysis then uses panel data, mainly from the BHPS, to examine the same sets
of relationships over a period. Chapter 7 considers people’s average positions over
the course of the whole period, to contribute to an understanding of the ‘underlying’
associations. Chapter 8 then looks at people’s movements up and down the income
and deprivation scales from year to year (either side of their average), to assess the
‘longitudinal’ relationships. If the peaks and troughs in respondents’ incomes tend
to synchronise with the troughs and peaks in their deprivation scores, then a causal
link can be inferred: people actually do get less deprived when their income rises! It
turns out that such a link does exist, though it was not easy to identify, and is not as
strong as the ‘underlying’ relationships over a period might have led us to expect.
Chapter 9 reviews these findings, and discusses the implications both for the
measurement of income and deprivation, and for anti-poverty policy.
This is an unavoidably quantitative analysis, which has had to get quite technical at
times. We have tried to explain the analysis step by step, and use everyday English as
far as possible. The narrative is aimed at readers who are happy with numbers, and
have probably read other reports based on large-sample surveys, but assumes no
expertise in econometric analysis. A glossary of terms is available at the front of the
report, and a simple explanation of ‘regression for beginners’ is provided at the point
where we move from straightforward tables to multivariate analysis (in Chapter 6).
But the tables and notes also aim to offer enough technical detail for readers with
more statistical or econometric expertise to see how the analysis has been carried
out. It is hoped that the less-expert reader will skip over the specialist material, while
the more-expert reader will be patient with the step-by-step explanations.
The findings are summarised and discussed in the final chapter in terms which
require very little fluency with numerical analysis.
1.3
What is ‘material deprivation’?
Both quantitative and qualitative research have shown that families with low
incomes have to go without things that are widely regarded as essential, that this
restricts their lifestyle, and that it is difficult to balance their weekly budget (Adelman
and others 2003, Kempson and others 1996). ‘Deprivation’ and ‘hardship’ have
become code-words to refer to the unsatisfactory living standards and financial
stress associated with a low income.
An ‘index of material deprivation’ is an attempt to summarise variations in living
standards of families at different levels of income, so that the relationships between
Introduction
the two can be measured and assessed. Respondents to a large-scale survey are
asked to say whether they do or do not have certain items; whether they can or
cannot afford to undertake certain normal daily activities; whether they are in debt,
or find it difficult to make ends meet. The set of items covered is designed to be as
sensitive as possible to variations towards the lower end of the income scale. The
answers to the questions are added up (in a simple or a complex way) to form a scale
reflecting the number of problems each family faces. Although most indices have
been applied at a single point in time, it is important to note that the concept of
deprivation is essentially a relative one. Overall living standards might improve, but
people might still be found to be deprived in relation to the expectations and
conventions of the day.
A family’s score on a deprivation scale is likely to depend on seven sets of factors:
• Economic resources: The primary influence is assumed to be the family’s current
income. Most surveys offer a measure of current income, though this is not
certain to be an accurate figure. Other resources include previous income and
expectations of future income; savings and other capital assets; access to credit;
and the availability of contributions from less formal sources such as family or
friends
• Prices: Converting resources into consumption depends on the prices to be
paid. There is little evidence of major variations in the cost of living facing
individuals over the majority of goods and services, but certain items represent a
much heavier burden on some households’ budgets than others – notably housing
(varying between regions and by stage in the life-cycle) and transport (varying
between urban and rural areas).
• Needs: It is widely recognised that large families need more income than small
ones to maintain the same standard of living. The idea is embodied in the use of
equivalence scales to adjust income for varying needs. But other characteristics
which might have an independent effect on needs, and therefore on living
standards, include disability (Zaidi and Burchardt 2002), location and social
identity.
• Hypothecation: Some sources of income must be spent on certain compulsory
outgoings, and are not available to contribute to general expenditure. These
include child-care allowances built in to tax credit payments, and housing benefit.
• Preferences: A family’s position on the scale may depend on the consumption
priorities of the family, or of the person who has effective control of the budget.
A generalised deprivation index assumes that most people, in most social groups,
place broadly the same emphasis on the desirability of the component items.
• Efficiency: For any given set of circumstances, some families will convert resources
into essential consumption highly efficiently, with maximum value and minimum
waste. Others will be less efficient. This will be reflected in the respective families’
scores on a deprivation index at any given level of income.
13
14
Introduction
• Imprecise measurement: Families with broadly the same living standards will
vary in the answers they give to the questions contributing to the deprivation
index (many of which are fairly subjective). And the same family might give a
slightly different set of answers on two occasions, even though their circumstances
may not have changed.
Apart from income, few of these potential influences on living standards, and
deprivation scores, can be measured directly by surveys. Our research objectives are
particularly concerned with the role of income – partly because it can be measured
with a reasonable degree of accuracy, partly because of its obvious direct influence
on living standards, and partly because the distribution of income can be affected by
policy. But allowance is made for the potential effects of other factors by including
a range of other factual characteristics in the analysis, so that the net effect of
income can be identified more clearly.
The EU’s definition of the poor (see the opening paragraph of this chapter) does not
make it clear which of the two problems referred to constitutes the essence of
‘poverty’ (Figure 1.1). One view is that poverty consists of a lack of resources (one of
whose main symptoms is exclusion from a minimum way of life). Another view is
that poverty consists of social exclusion (one of whose main causes is lack of
resources). This uncertainty is reflected in empirical analysis of the relationships
between income, deprivation indicators and ‘poverty’. One interpretation is that the
poor should be defined as those with low incomes (and perhaps other economic
disadvantages such as high prices, high needs and so on). In that case, an index of
deprivation is used as an indicator to calibrate the poverty line. The opposite
interpretation is that the poor should be defined as those with high deprivation
scores, regardless of their economic position. In that case, the index is used as an
actual measure of poverty.
Figure 1.1
Two interpretations of the essence of poverty
Agreed process
Lack of resources
Exclusion from a
minimum way of life
Interpretation 1
‘Poverty’
Outcome of poverty
Interpretation 2
Cause of poverty
‘Poverty’
A leading example of the former approach is Townsend’s monumental study of
Poverty in the United Kingdom (1979). He used a multi-item index to track the
relationship between income and deprivation, looking for evidence that there was a
boundary line in the income distribution below which living standards plunged to
unacceptably low levels. Berthoud (1984) and Berthoud and Ford (1996) used
Introduction
deprivation indicators to compare the living standards of families with different
compositions but similar incomes, while Berthoud and others (1993) and Zaidi and
Burchardt (2003) looked at the effects of disability on living standards. A series of
reports from the Policy Studies Institute (e.g. Marsh and McKay 1993, McKay and
Vegeris 2001, Vegeris and Perry 2003) have shown the extent of ‘hardship’ among
low income families. Each of these studies used deprivation indicators to demonstrate
in one way or another that low income is a bad thing, and should be labelled poverty.
A contrasting perspective is that it is deprivation that is a bad thing. Ringen (1988)
argued that a low income was only an indirect measure of poverty, and that direct
measures of social exclusion were required. A second school of researchers has used
deprivation indicators to define poverty and count the poor (Mack and Lansley
1985, Gordon and others 2000). This perspective has entered the language of the
European Union, where households with an income below the conventional
threshold are now referred to, not as in poverty, but as at risk of poverty. Several
researchers have noted that those on low income and those with high deprivation
scores are not necessarily the same people. One interpretation is that income is a
poor predictor of poverty, though a compromise position is to define the poor as
households who combine low income with high deprivation scores (Nolan and
Whelan 1996, Layte and others 2001, DWP 2003b).
One might agree with Ringen that direct measures of social exclusion are required,
but not necessarily agree that a narrowly-based index of material deprivation is an
adequate measure of exclusion (McKay 2004). Some researchers have looked for
indices based on a much wider range of social and economic activities, not directly
related to consumption (Burchardt and others 2002, Bradshaw and Finch, 2002).
While arguments about what ‘poverty’ consists of may seem theoretical, or even
merely linguistic, there are important empirical implications. Using an index of
material deprivation as an indicator, to identify groups at risk of poverty or to
calibrate a poverty line, can be based on a fairly weak set of assumptions. The
principal requirement is that the items in the index should collectively reflect living
standards across all groups in the population, and be appropriately sensitive to
variations at the lower end of the income scale. It is just an indicator, whose job is to
tell us about the variations between households analysed by income, family
composition, employment status and so on. The fact that some income-poor
households are not also in hardship is not a problem – it is variation in the risk of
hardship that matters.2
In contrast, using an index as a direct measure of poverty requires a very strong set of
assumptions. The items in the index have to be identified as necessities, and it has to
2
By analogy, the employment rate for Bangladeshis is half that of white people
(of working age). This difference in probabilities signals labour market
disadvantage for Bangladeshis, even though some Bangladeshis have a job and
some whites do not.
15
16
Introduction
be established whether those who do not have them could not afford them (Gordon
and others 2000); but McKay (2004) strongly challenges the empirical validity of
either of these preconditions. In principle, the index should sample the whole range
of areas of consumption (including those where no deprivation is in fact experienced,
and others where deprivation is not associated with low income), in order to obtain
a balanced measure of inequality. A concept of secondary poverty may be required
(as originally proposed by Seebohm Rowntree in 1901) to account for people whose
high deprivation score is not associated with low income, and is presumably caused
by wasteful spending. And if the deprivation index is the direct measure of poverty,
governments would be advised to intervene directly (and enable families to ‘have
friends or family round for a drink or meal at least once a month’, for example) rather
than encourage employment, increase benefits and so on.
The analysis which follows is based on the weak set of assumptions required to treat
an index of deprivation as just an indicator of poverty. It aims to observe relationships
rather than establish thresholds. Our own view is that no index can support the
strong set of assumptions required to treat it as a direct measure of poverty. The
analysis will nevertheless be of interest to those who favour the direct measurement
approach.
One consequence of our approach is that the words ‘poverty’ and ‘poor’ will always
be used to refer to households with low incomes. The word ‘hardship’ will refer to
the position of households with a high score on the deprivation index.
Source surveys
2 Source surveys
The research is based on detailed analysis of two surveys, the Families and Children
Survey (FACS) and the British Household Panel Survey (BHPS). The strategy is as
follows:
• The FACS has a large sample of families with children, and a very detailed set of
questions on material deprivation. It will be used to provide a full analysis of the
relationship between income and deprivation among families with children in
2002.
• The BHPS has followed a sample of families (both with and without children)
over a long series of years. We switch to that source to unravel the complex
relationship between changes in income and changes in deprivation from year
to year.
It is quite unusual for research to use two different data sources to address the same
question. Each survey has its strengths and weaknesses. Several chapters of the
report mainly use one survey and then check the results with the other. One of the
challenges has been to address and explain the differences between the two sets of
findings, but the opportunity to test the robustness of the conclusions is eventually
a bonus.
This chapter provides a brief outline of each survey’s structure. Detailed discussion of
the deprivation and income data derived from the two surveys appears at relevant
points in the remainder of the report.
2.1
The Families and Children Survey (FACS)
This panel survey was launched in 1999; four waves have now been completed and
are available for analysis:
1 A complete sample of families with children was contacted at the first wave
(1999), but detailed interviews were undertaken only with families who were a)
lone parents, or b) non-working couples, or c) working couples with an income
below a defined level. So higher-income working couples were screened out.
17
18
Source surveys
2 At the second wave (2000), all the families (including those screened out at
Wave 1) were again approached: this time a full interview was undertaken either
if the family had been interviewed the year before, or if they now met the selection
criteria. But families who were higher-income working couples on both occasions
were again screened out.
3 In Wave 3 (2001), all the families in the original sample were approached and
interviewed, whatever their income.
4 The same full sample was interviewed in Wave 4 (2002).
A sample of new families (i.e. those whose first baby was born in the past year) was
also included in each new wave of interviews. Further technical details of the survey
are available from the National Centre for Social Research (Phillips and others 2003).
Sample families who had moved in to the sample areas after Wave 1 were also
interviewed in each wave of FACS interviewing, but are not included in the analysis
here. (But those who moved out of the sample areas were included in the survey,
and our analysis, after the move. It is not appropriate to include both movers in and
movers out in the same analysis.)
Table 2.1
Summary of the coverage of the Families and Children
Survey
Source: FACS Wave 1-Wave 4
✓ ) or screened out (✘
✘)
Included (✓
Percentage Wave 1
Wave 2
Wave 3
Wave 4
of all families 1999
2000
2001
2002
Lone parents
Not working
Working, low income
Working, higher income
17
12
2
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Couples with children
Not working
Working low income
Working, higher income
5
22
42
✓
✓
✘
✓
✓
✘
✓
✓
✓
✓
✓
✓
Note: the percentage of families in each group is derived from the Wave 3 data.
A total of 8,433 families with children took part in at least one wave of the FACS, and
were analysed for this study. Families were excluded from the analysis of any
particular wave if:
• one or other of the parents was self-employed, or if the family’s income was not
adequately recorded, at that wave;
• the family no longer had any dependent children at that wave.
Source surveys
The 8,433 families provided an average of 2.4 interviews over the four-wave period,
adding up to 20,018 family-wave cases. The composition of each wave’s sample is
shown in Table 2.2.
• Both the last two waves covered the full range of families with children, and
these are representative samples within the limits of sampling error and attrition.
They provide a representative record of transitions (e.g. in and out of poverty, in
and out of hardship) over a one-year period.
• The first two waves provide full samples of lone parents, and of non-working
couples. We therefore have a record of transitions across a three-year period for
families who started in one of those positions. But the first two waves do not
provide representative samples of working couples with children.3
Table 2.2
Sample of families in FACS Waves 1 to 4
Source: FACS
Sample numbers
1
1999
FACS Wave
2
3
2000
2001
4
2002
Total
Lone parent
Not working
Working
1,527
865
1,213
768
1,040
846
996
816
4,776
3,295
Couple
Neither working
One working
Both working
Total number of families
Average persons per household
534
985
334
4,245
3.6
353
988
637
3,959
3.6
315
1,680
2,257
6,138
3.7
293
1,494
2,077
5,676
3.7
1,495
5,147
5,305
20,018
3.7
Notes: ‘Working’ means in employment at least 16 hours per week. The cells shown in bold are
those which were not fully represented in Waves 1 and 2.
All the FACS analysis is based on calculations of the income, hardship and other
characteristics of whole families, treated as a unit. When a couple separated, the
survey followed the children, and this provides a sequence of ‘continuing families’,
although they may switch from couple to lone parent, and back again, in the course
of the sequence.
3
The boundary between ‘low/moderate’ income (included in the survey) and
‘higher income’ (screened out) was raised between Wave 1 and Wave 2 to take
account of tax credit policy changes. This means that the two waves do not
provide a consistent sample of ‘low/moderate’ income working couples, and
these groups in these years are effectively excluded from our analysis. That is,
analysis of Waves 1 and 2 is confined to lone parents and/or non-working couples.
19
20
Source surveys
But the data are weighted throughout by the number of adults and children in the
household.4 This means that the estimates refer to the number of individuals
experiencing the various combinations of income, deprivation and so on. This is
consistent with the Department for Work and Pensions’ official Households Below
Average Income (HBAI) analysis which counts the number of adults and children
below the poverty line (DWP 2004). As explained in the next section, following
individuals is the only way of tracking changes in income and deprivation across
households over a long series of years (using the BHPS), and this weighting of the
FACS results is designed to be consistent with that procedure. For longitudinal
analysis, the weighting is by the number of members of the household at the end of
the sequence under consideration.
Although the FACS data-set includes a complex set of weights designed to
compensate for variations in response rates at each wave, it was found that applying
the weights made little difference to the findings, and they were not used in the
analysis presented here.
2.2
The British Household Panel Survey (BHPS)
The FACS data has two substantial advantages for our purpose: it provides a large
sample of families with children who are the focus of the enquiry; and it includes
many questions of direct relevance to the analysis. But it has one substantial
disadvantage in its sample structure – the fact that high income couples with
children were omitted from the survey at the first two waves means that we have
only one pair of waves (3 and 4) on which to base analysis of changes over time for
the majority of families who have two parents. Even for lone parents, the longest
sequence of observations is only four waves. The BHPS is introduced to fill that gap,
because it offers a long sequence of annual observations for a representative crosssection of the population.
The BHPS was launched in 1991. A representative sample of households in Great
Britain was selected, and all the adults in participating households were interviewed.
Each of the adults has been followed up each year since then. Children of the panel
members are included in the data set, and join the panel itself when they reach the
age of 16. If a member of the panel joins a household with (an)other adult(s), each
co-resident is also interviewed for as long as they live in the same household as the
4
Note the distinction between a ‘family’ and a ‘household’. A household consists
of all the people who live and eat together, whatever their relationships. A family,
which coincides with the benefit unit used to calculate social security and tax
credit entitlements, is defined to consist of a single adult, or a couple, plus any
dependent children. A large proportion of ‘families’ which are not also
householders consists of single adults living with their parents, but who are no
longer defined as dependent children. Where data are available about both
family units and whole households (e.g. in the BHPS and the FRS, see below), it
has been found that analysis of families with children is not very sensitive to this
distinction; but it makes more difference to ‘families’ without children.
Source surveys
panel member, so that full household data is available. Further details of the survey
are available in Taylor and others (1996) and at www.iser.essex.ac.uk/bhps.
Although the full survey dates back to 1991, the analysis here picks up the data at
Wave 6 (1996) when a new series of deprivation indicators was added to the
questionnaire. The last available data refers to Wave 12 (2002), so the maximum
number of waves covered is seven.
• Households consisting entirely of people over pension age (at any particular
wave) have been deleted from the data, as many of the relationships between
deprivation indicators, and between deprivation and income, were weaker for
pensioners than for the working age population.
• Individuals above pension age (but living with younger people) were included in
the calculation of household characteristics (e.g. household size, total income)
but were not included in the analysis itself; the estimates are therefore based on
a representative sample of people of working age and below.
• Households which did not provide adequate details of their income, or who did
not fully answer the deprivation questions, were also deleted from the data for
the relevant wave.
After these exclusions, a total of 12,044 individuals below pension age (including
dependent children) contributed to the analysis (Table 2.3). Rather less than half
were covered by the complete sequence of seven waves, though these of course
contributed disproportionately to the total number of 57,650 person-year
observations available. The great majority of those analysed were included in the
sample for at least two waves, and therefore could make some contribution to the
longitudinal analysis.5
These individuals lived together in households – for example the 7,949 nonpensioner respondents covered in Wave 12 (2002) lived in 2,699 households, an
average of 2.7 per household.6 Forty-five per cent of the households included
dependent children, which provide the most direct comparisons with the FACS
analysis. All measures of income, of deprivation and of other characteristics used in
this report are derived at the household level. Effectively it is assumed that all
members of each household share each others’ income and consumption patterns.
5
An individual could have less than seven observations either because they left
the panel under analysis (by dropping out of the sample, or by passing pensionable
age); or because they joined the panel (by being born); or because they missed
one or more years (by not giving an interview, or because their household did
not provide full income/deprivation data).
6
See note 4 for an explanation of the difference between a ‘family’ and a
‘household’.
21
22
Source surveys
Table 2.3
The BHPS sample of individuals under pension age, by
number of waves of available data (Waves 6 to 12)
Source: BHPS
One
Two
Three
Four
Five
Six
Seven
Total
Sample numbers
Number of
individuals
Percentage of
individuals
Number of
person-waves
1,704
1,135
957
946
1,187
1,719
4,396
12,044
14
9
8
8
10
14
37
100
1,704
2,270
2,871
3,784
5,935
10,314
30,772
57,650
In principle, this means that the analysis should also be based on whole households,
and that is an appropriate approach for cross-sectional analysis. But while it is
straightforward to define a household as a group of people living together at any
wave, it is more problematic to keep track of continuing households across waves. If
a couple split up, and each finds a new partner, neither of the new households can
be considered a continuation of the previous one. This is an important issue for
longitudinal analysis of household characteristics, especially income and deprivation
– if a person moves from one household to another, he or she may experience a
change in the primary source of income, a change in the primary budget keeper, or
a change in the identity of the person who answers the deprivation questions. Any
of these types of change might unsettle the continuity required for longitudinal
analysis of household characteristics.
In spite of these complications, we decided to follow individuals from wave to wave,
regardless of any moves they might make between households. The sensitivity of the
conclusions to instability of household membership is tested at the end of Chapter 8.
For cross-sectional analysis, the calculated effects are exactly the same as if a
household level analysis was weighted by the number of individuals in each
household (the approach used for the FACS analysis). For longitudinal analysis, we
are comparing the experiences of the same individuals from year to year, ascribing to
each individual in each year the level of income, deprivation and so on experienced
by the household they were living in at the time.7
As with the FACS, we did not use the complex sample weights available in the BHPS
data-set in the analysis presented here, as it was found that they did not have much
effect on the findings and conclusions.
7
Calculations of statistical significance take account of the fact that several
members of the same household provide identical information in any wave.
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
3 ‘Poverty’ and ‘hardship’ in
2002: some findings...
and some puzzles
According to the official FRS-based estimates (DWP 2004), 2.6 million children were
in poverty in 2002/03 (defined as living in households with an equivalent income
before housing costs below 60 per cent of the national median). The number of poor
children had reduced by more than half a million over the previous six years. Just over
a fifth (21 per cent) of all children were poor in 2002/03, by the same measure. The
estimate of poverty taken from the FACS data is not exactly comparable,8 but it is
very similar in any case: 22 per cent of children were below the poverty line in the
same year (Wave 4).
3.1
The Policy Studies Institute hardship index
Our main objective is not to estimate levels of income and of income-poverty among
families with children, but to assess their living standards. For the preliminary
analysis of the FACS deprivation data in this chapter, we use the definition of
‘hardship’ developed by the Policy Studies Institute for its previous series of reports
(Vegeris and Perry 2003). The PSI team has contributed to the current project by
calculating the Wave 4 version of the index, using the principles previously applied to
Wave 3; and supplying us with the derived variables for all four waves. The index
8
All FACS income measures exclude the self-employed, whereas the official
Opportunities for All indicators include the self-employed. FACS income is based
on families, whereas FRS income is based on households. Since no national
median is available from FACS, we have had to import the benchmark from the
FRS. These variations affect comparisons of the exact poverty rate between surveys,
but do not invalidate our classification of poor families for this analysis.
23
24
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
identifies families reporting one or more of nine specific indicators, as shown in
Table 3.1.9
Table 3.1
Nine indicators in the PSI hardship index
FACS Wave 4
Percentages
Indicator
Incidence in Wave 4
Reports two plus problems with accommodation and
cannot afford to repair (if owner)
Lives in overcrowded accommodation
Cannot afford to keep home warm
Worries about money almost all the time and runs out
of money most weeks
Has no bank account and has two or more problem debts
Lacks food items
Lacks clothing items
Lacks consumer durables
Lacks social/leisure activities
9.2
13.3
2.1
5.9
4.4
6.0
6.5
5.9
5.6
Note: ‘lacks’ in the last four rows is defined as in the worst 7.5 per cent of the Wave 3
distribution of a more complex measure of the affordability of a number of items.
Counting the number of these adverse indicators recorded by each family provides
a score of between zero and nine, which can be used to define three groups of
families:
Not in hardship
(no indicators)
69 per cent in Wave 4
Moderate hardship
(1 or 2 indicators)
24 per cent
Severe hardship
(3 to 9 indicators)
7 per cent
This distinction between those in and out of hardship can be likened to the
distinction between those in and out of poverty: both provide simple categories to
summarise the position of families at the extreme end of a continuous indicator of
living standards – of deprivation in one case and of income in the other.
9
The PSI index analysed here was originally calibrated on the basis of Wave 3 data
(the first covering all families with children), and used whole families as the unit
of analysis. This chapter focuses on Wave 4 (the most recent), and weights families
by the number of household members. So the percentage of families recorded
as ‘in hardship’ varies slightly between the two reports, though the index is
identical.
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
3.2
Headlines
Table 3.2 compares the experience of hardship among three groups of families: the
poor (defined as those below 60 per cent of the median equivalent10 income), welloff families (defined as a group at the top of the scale of equivalent income exactly
the same size as the group of poor families); and a middle-income group between
these two extremes. The proportion of poor families who were in moderate
hardship in FACS Wave 4 was as high as 41 per cent; the proportion of poor families
in severe hardship was 17 per cent – so more than half of all poor families were in
some hardship on this measure – 58 per cent. The comparison shows exactly what
we would have expected: the poor are much more likely to be in hardship, and
severe hardship, than middle-income families. The well-off group are much less
likely to be in hardship than middle-income families; only nine per cent of them are
in moderate hardship, just one per cent in severe hardship.
Table 3.2
Hardship among poor, middle-income and well-off
families at Wave 4 (2002)
Source: FACS Wave 4
Not in hardship
Moderate hardship
Severe hardship
Sample size (families)
Column percentages
Poor
Middle-income
Well-off
42
41
17
1,266
70
24
6
3,112
90
9
1
1,302
Note: ‘well-off’ is defined as a group of families at the top of the equivalent income distribution
the same size (at Wave 4) as the group defined as poor. The sample sizes are slightly different
because the definitions were based on individuals, not households
Income is not the only factor that distinguishes between families with high and low
hardship risks. Table 3.3 shows that poor lone parents report much more hardship
than poor couples with children, even though in principle the use of equivalent
income to define poverty should mean that both groups have about the same level
of income in relation to their families’ needs. The same is true among middle-income
and well-off families: lone parents always have higher hardship rates than couples
with children with similar incomes.
It is often pointed out that not all poor families are found to be in hardship; and
indeed the converse is also true – only just over half of all families found to be in
hardship are poor. In general, the lack of an exact match between poverty and
hardship is not a problem – as discussed in Chapter 1, it is more helpful to think of
hardship rates as indicators of risk than as actual measures of welfare. But one would
10
All analysis of income and of poverty, in this and the next chapter is based on
income equivalised using the McClements scale. See Chapter 5, for a discussion
of equivalence scales.
25
26
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
certainly expect the very poor – families whose income was well below the poverty
line - to have higher hardship rates than those just below the threshold. Yet this
expectation is not substantiated: if the distribution of family income is divided into
ten groups with the same number of individuals in each group (decile groups), the
one-tenth of families with the lowest incomes appears less likely to be in hardship
than the next poorest group (Figure 3.1). (Both the lowest two decile groups are
below the poverty line, given an overall poverty rate of 22.5 per cent.) So this is the
first puzzle – why are those reporting the lowest incomes not also recording the
highest hardship rates?
Table 3.3
Hardship at Wave 4: couples and lone parents compared
Source: FACS Wave 4
Column percentages
Couples with children
Lone parents
Poor
Not in hardship
Moderate hardship
Severe hardship
Sample size (families)
52
36
12
547
30
46
23
701
Middle-income
Not in hardship
Moderate hardship
Severe hardship
Sample size (families)
77
20
3
2124
49
37
14
967
Well-off
Not in hardship
Moderate hardship
Severe hardship
Sample size (families)
92
8
0
1161
73
21
6
135
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
Figure 3.1
3.3
Hardship at Wave 4, across the full distribution of
equivalent income
Persistent poverty
Tables 3.2 and 3.3, and Figure 3.1, all refer to income and hardship measured at one
point in time – Wave 4 (2002). One of the key questions for this research is whether
the time dimension matters – whether persistent poverty carries a more serious risk
of hardship than short-term poverty.
The DWP’s favoured definition of ‘persistent poverty’ is families who were poor in at
least three of the last four years, and this requires a complete history of each family’s
poverty status over a four year period. That needs to be based on respondents who
took part in all four waves (known technically as a ‘balanced panel’).
The structure of the FACS, in which couples who had a job and a reasonably high
level of income were not fully interviewed in Waves 1 and 2, causes a difficulty in
constructing this balanced panel, since we do not have full data for a large section of
the original sample. We do, though, have three key items of information for those
who were screened out in the earlier waves, derived from the screening interview:
those not interviewed in full were couples, they were in work, and they were not
poor. The following analysis is based on families who either provided full information,
or who were screened out, in each wave. The latter are referred to as ‘shadow
27
28
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
observations’.11 Of the 5,680 families who were interviewed (and provided income
and hardship data) in Wave 4, 3,757 provided data for the complete sequence of
four waves if shadow observations are included.12
The first four lines of Table 3.4 show that counting the overall number of years of
poverty over a four year period is an effective way of discriminating between highand low-hardship risk families. Only 14 per cent of those who had no experience of
poverty over the four year period reported moderate hardship, and just one per cent
reported severe hardship in Wave 4. The risk of hardship rose sharply and fairly
steadily for those with one or two years experience of poverty; a third and a fourth
year of poverty increased the risk further, but not so seriously. It is helpful to
summarise these variations by calculating a ‘weighted hardship’, adding together
moderate and severe hardship, but counting severe hardship double to take
account of its more serious implications. On this measure, families rose from a
hardship risk of 16 per cent if they had no recent experience of being in poverty, to
94 per cent if they had no recent experience of being out of poverty.
Table 3.4
Hardship at Wave 4, by total number of waves in poverty
over four-wave period
Source: FACS Waves 1-4, balanced panel
with shadow observations
Not in hardship
Moderate hardship
Severe hardship
(Weighted hardship)
Only one wave of (non) poverty
Wave 1
Wave 2
Wave 3
Wave 4
Sample size (families)
Column percentages
None
One
Two
Three
Four
85
14
1
(16)
68
25
7
(39)
42
42
16
(74)
38
42
21
(83)
31
45
25
(94)
2,102
38
43
37
36
637
414
87
87
87
75
330
274
Note 1: see text for explanation of balanced panel and shadow observations. Weighted hardship
is calculated as the percentage in moderate hardship, plus 2 multiplied by the percentage in
severe hardship.
Note 2: In the wave-by-wave analysis (lower panel) column One shows the hardship risk at Wave
4, for families who were poor just once, according to which wave that was. Column Three shows
the weighted hardship at Wave 4, for people who were poor three times, according to which
was the one wave when they were not poor.
11
Some sample members did not take part in Waves 1 or 2 for reasons other than
screening-out, but were nevertheless interviewed in Waves 3 or 4. These have
not been included as shadow observations in the balanced panel.
12
The balanced panel necessarily covers those who were families with children
throughout the four year period. So it does not include families whose first child was
born after Wave 1, or whose last child ceased to be dependent before Wave 4.
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
The analysis in Table 3.4 still measures hardship in Wave 4, at the end of the
observation period. It would be natural to suppose that the longer ago a period of
poverty was experienced, the less impact it would have on current hardship risk. But
this hypothesis is not supported by detailed analysis. The lower half of Table 3.4
(column One) compares the hardship risk in Wave 4 of families who had only one
wave in poverty, according to which one of the four waves that was. We would
expect the figures to rise steadily from a lower level of current hardship associated
with poverty experienced in Wave 1 (i.e. three years ago) through to a higher level of
hardship associated with poverty experienced in Wave 4 (i.e. now). But the rates are
essentially steady, whichever the single wave of poverty was. Then the opposite
approach is taken to families who had three years in poverty (column Three), and,
therefore, only one wave out of poverty. This time we would expect the hardship
rates to move down from Wave 1 (three years since the families were not in poverty)
to Wave 4 (not in poverty now). There is a significant dip at the end of the sequence
showing a lower risk of hardship associated with a recent exit from poverty. Even so,
here is a group of people, not now in poverty, who have a very high risk of hardship
associated with their recent history of poverty.
So the analysis of families’ recent income histories begins to suggest another puzzle:
while poor families have a much higher hardship risk than non-poor families, at any
one point in time, the timing of when they were poor does not seem to make much
difference to the timing of when they were in hardship. The point is re-emphasised
by Figure 3.2. Each of the pair of columns shows how much higher the risk of
hardship is among poor families (black) than among non-poor families (grey). But
the hardship is always measured at Wave 4, while each of the four pairs of columns
uses a different wave to distinguish between the poor and the non-poor. If hardship
was sensitive to recent income, we would have expected much less of a difference
between the grey and the black columns on the left of the graph than on the right.
Direct analysis of movements in and out of poverty, and in and out of hardship,
suggests similar conclusions. Table 3.5 is based on families who were interviewed in
both Wave 3 and Wave 4. The headings of the columns allocate the sample to
groups according to whether they moved into or out of poverty between the third
and the fourth wave, or whether they remained in the same position in both years.
The headings of the rows makes a parallel allocation according to whether the
families moved into or out of hardship (moderate and severe combined). So the first
column records that of those who remained in poverty over the pair of years, 55 per
cent also remained in hardship, 10 per cent moved into hardship, while 11 per cent
moved out of hardship – and so on. At the foot of each column the figures show the
entry rate to hardship (as a proportion of those at risk) and the exit rate.
The table shows a fair degree of movement both into and out of hardship between
years (some of which may have been caused by respondents changing just one
answer to the 40-odd questions taken into account in the definition.) But the
patterns are a very long way from supporting a view that people who leave poverty
also leave hardship at the same time, or that people who start a spell of poverty also
enter hardship.
29
30
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
Figure 3.2
Hardship risk at Wave 4, by whether in or out of
poverty at each wave
Table 3.5
Movements in and out of hardship between Waves 3
and 4, in relation to movements in and out of poverty
Source: FACS Waves 3-4
Remained in hardship
Moved into hardship
Moved out of hardship
Remained out of hardship
(Entry rate to hardship)
(Exit rate from hardship)
Sample size (households)
Column percentages
Remained in
poverty
Moved into
poverty
Moved out
of poverty
Remained out
of poverty
55
10
11
23
(30)
(17)
583
39
14
13
34
(29)
(24)
479
40
10
15
35
(22)
(27)
380
14
7
8
72
(9)
(36)
3,340
Note 1: Highlighted cells are those consistent with moves in and out of hardship occurring at the
same time as moves in and out of poverty.
Note 2: Entry rate to hardship is the number of respondents who moved into hardship between
Waves 3 and 4, expressed as a proportion of the number who were not in hardship at Wave 3.
Exit rate from hardship is calculated equivalently.
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
3.4
Trends in hardship rates from year to year
Almost all the analysis reported in the tables and figures so far presented is based on
respondents’ reports of hardship in the fourth wave of FACS (2002). This is true even
when the income against which it is being compared was derived from an earlier
wave. A different question is whether the overall risk of hardship increased or
decreased across the four years covered by the survey. The left hand section of Table
3.6 measures hardship in each period, for those who were poor in the same period.
The right hand side does the same for those who were not poor in Waves 3 and 4,
but omits Waves 1 and 2 because a full sample of non-poor families was not
available at that stage. The results for poor families are most striking: the proportion
of poor families defined as in any hardship reduced from 76 per cent to 58 per cent
between Waves 1 and 4; the proportion in severe hardship more than halved, from
36 to 17 per cent. The figures in brackets at the foot of the table confirm that this
reduction in the hardship measure occurred even among the families who remained
poor in all four waves. On the face of it, these families appeared to be improving their
living standards as the duration of their spell in poverty lengthened.
There was also an apparent reduction in hardship among non-poor families
between Waves 3 and 4 (right hand section of table), but the difference is too small
to matter.
Table 3.6
Hardship among poor and non-poor families, by wave
of observation
Source: FACS Waves 1-4
Average equivalent income
Column percentages
Poor families
Wave 1 Wave 2 Wave 3 Wave 4
1999
2000
2001
2002
£129
£136
£146
£143
Not in hardship
24
Moderate hardship
40
Severe hardship
36
Weighted risk of hardship
among those poor all four waves (130)
Sample size (families)
2,168
Non-poor families
Wave 3 Wave 4
2001
2002
£367
£375
30
39
30
38
41
21
42
41
17
75
21
5
76
20
4
(116)
1,694
(106)
1,233
(94)
1,266
na
4,905
na
4,414
Note: hardship rates cannot be measured among non-poor families at Waves 1 and 2 because
many of them were screened out
The reduction in hardship among poor families over only three years is remarkable –
and welcome – but it is not easy to explain. There were increases in rates of child
benefit, Working Families’ Tax Credit and the Income Support rates for children
between 1999 and 2002 (to use the terminology of the period before the current
child- and working-tax credit schemes were introduced). But these policies were
aimed at lifting families with children out of poverty, and the findings in Table 3.6
31
32
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
refer to families who nevertheless remained in poverty. It is true that the real
equivalent incomes of those below the poverty line increased over the period, from
an average of £129 per week in 1999 to £146 in 2001, though they fell back to £143
in 2002 (see first line of Table 3.6). Even so, the proportion of poor families in
hardship seems to have fallen by 10.4 percentage points for each £10 increase in the
average income of poor families over the period.13 This compares with a reduction of
only 2.4 percentage points for each £10 increase in average equivalent income at
the steepest point in the graph of hardship against income reported in Figure 3.2.14
So we have another puzzle: why did the measure of hardship fall so rapidly between
waves? If the 1999-2002 trends continued in a straight line, severe hardship would
have disappeared altogether by 2006 (Wave 8), even though poverty would
continue.
3.5
Discussion
The analysis of the Families and Children Survey in this chapter has clearly
demonstrated that poor families are at risk of hardship – a risk much greater than
that faced by middle-income and well-off families. It has also shown that families
who remain poor over a period have higher hardship rates than those poor for only
a year or two. These are important findings in their own right, and both conclusions
are entirely in line with what might have been expected. But there are also some
important puzzles:
• why do the households with the very lowest incomes record lower hardship
rates than those only just below the poverty line?
• why is the risk of hardship in any particular year so insensitive to the date at
which families were in poverty; and why do people exiting poverty not escape
from hardship at the same time?
• why has the measured risk of hardship decreased so rapidly over the last few
years, even among those whose incomes remained below the official poverty
line?
13
Calculated from a simple regression equation predicting annual hardship rates
from annual average incomes among poor families, based on four units of analysis
(waves).
14
The mean equivalent income in the third decile group in Table 3.1 was £33
higher than in the second decile group. The difference in hardship rates was
eightper cent. That works out as a reduction of 2.4 percentage points for each
£10 increase in income.
‘Poverty’ and ‘hardship’ in 2002: some findings...and some puzzles
Much of the remainder of this report will be devoted to unravelling these puzzles.
This will be done using three shifts of analytical focus:
• First, we will move from a simple distinction between ‘poverty’ and ‘non-poverty’
to an analysis of the whole distribution of family incomes; and from a simple
distinction between severe, moderate and no hardship to an extended distribution
of deprivation scores.
• Second, we will introduce a range of other variables which appear to be associated
with a family’s level of deprivation, rather than rely simply on ‘equivalent income’
as the sole explanatory variable.
• Third, we will use the longer run of annual observations from the BHPS, as well
as the larger sample of families with children in the FACS, to assess the impact
of the time dimension.
33
Measuring material deprivation
4 Measuring material
deprivation
The original FACS hardship scale used in the previous chapter (see Table 3.1) has
nine indicators, and the summary divides families into just three categories (no
hardship, moderate hardship and severe hardship). One potential advantage of that
method is that it is relatively easy to explain the concept of adding up nine items to
lay readers (though not so easy to explain how the nine items were derived). Another
potential advantage is that by focusing always on the most deprived families in each
dimension, the scale might be especially sensitive to variations in living standards at
the lowest end of the income scale. A potential disadvantage of the nine point scale
is that the cut-off points on each indicator were inevitably rather arbitrary. But the
main difficulty for the analysis proposed here is that there is no differentiation within
the two-thirds of families who were classified as ‘not in hardship’, nor within the
quarter of families in moderate hardship. These large groups of families do not
necessarily all have the same living standards, but the fine grain of the data is lost in
the construction of the simple index.
The original FACS hardship scale was entirely appropriate for the job it was initially
designed to do – illustrating variations in the incidence of hardship between poor
and non-poor families in a particular year. It is very difficult to use, though, for
longitudinal analysis, measuring variations in the experience of families between
one year and another. In principle one can subtract the number of hardship
indicators reported ‘last’ year from the number reported ‘this’ year to come up with
a scale of change ranging from +9 to -9. But with the majority of families moving
from zero to zero, the distribution is too ‘lumpy’.
We have therefore developed an alternative index which is designed to be a
continuous indicator of living standards, ranging from no-problem at one end of the
scale to extreme deprivation at the other. (Note the switch of language: we use
‘deprivation’ to label the continuous index, keeping ‘hardship’ as a label for a
category at the top end of the distribution. By the same token ‘income’ is continuous
and ‘poverty’ a category.)
35
36
Measuring material deprivation
4.1
Approach
Many researchers have developed deprivation indicators in recent years (Burchardt
and others 2002, Calandrino 2003, Desai and Shah 1988, DWP 2003b, Gordon and
others 2000, Halleröd 1994, Jensen and others 2003, Layte and others 2001, Mack
and Lansley 1985, Marsh and McKay 1993, McKay 2004, McKay and Collard 2004,
Nolan and Whelan 1996, Townsend 1979, Vegeris and Perry 2003). The principles
adopted for the new index used for the current study have been:
1 Use of as large a number of component indicators as possible, to reduce the risk
that the index is too sensitive to the choice of one set of questions rather than
another.
2 The components should be closely enough associated with each other to suggest
that they are all elements of some single underlying dimension.
3 The index should be as sensitive as possible to variations in household income,
especially at the lower end of the income scale.
4 The index should be analysable as a continuous numerical variable, rather than
as a simple distinction between in and out of hardship.
5 It should make sense when compared across years, as well as within any year.
6 The index should be as simple and easily understood as possible.
The second and third points are important, and deserve some comment at this
stage. The fifth point, which has never had to be addressed before, turned out to be
even more important, but will be discussed later in this chapter. The sixth remained
an important consideration, but it has to be accepted the resulting index used here
is not as simple and easily understood as had been hoped.
Associated with each other
We are looking for an indicator of an underlying dimension (which we will label
‘deprivation’). The parallel is with the development of attitude scales in psychology
or political analysis, which use batteries of questions to divide subjects into introverts
and extroverts, or between right and left wing opinion holders (Nunnally and
Bernstein 1994). Analysts feel confident that there is an underlying dimension if
there is one group of people who all give similar answers to a set of questions, and
another group of people who give the opposite set of answers. A simple measure of
similarity between people’s answers to a pair of questions is the correlation
coefficient. The approach can be extended using a measure known as Cronbach’s α
(alpha), which shows the extent to which a package of questions are all associated
Measuring material deprivation
with each other.15 If alpha is high (a common threshold using factually-based
material is 0.60), then a dimension is judged to have been identified. The key issue
here is how should a deprivation index deal with a social characteristic which is
undoubtedly ‘bad’ but which does not tend to be more common among families
who also face the other problems thought to comprise deprivation. The analytical
answer is that the social characteristic which does not fit the pattern should be
excluded from the index of deprivation, as evidently not a symptom of the same
underlying social phenomenon.
Sensitive to income
Following the ‘weak’ assumptions explained in Chapter 1, the index is designed to
be an indicator, not an actual measure, of material well-being or deprivation.
Neither we, nor the general public, nor the respondents themselves, have expressed
any opinion on which of the items on the list are or are not essential for full
participation in society, the lack of which would be deemed poverty. The only
requirement for the index as a whole, and for each component of it, is that
households with high incomes should be shown to be systematically ‘better off’
than households with low incomes – where ‘better off’ simply means having a
higher probability of possessing particular items or avoiding particular problems. It
does not matter that some rich people lack some items on the list, or that some poor
people possess many of them – as long as income is shown to have a strong effect on
households’ probability of possessing them. The definition is empirically circular –
the object of this analysis is to identify the relationship between income and
deprivation, so it is essential that deprivation is defined to highlight such a
relationship.
15
Analytical readers unfamiliar with alpha should consult the Stata manual for
details. It is calculated as:
kc .
v + (k-1)c
where
k is the number of variables contributing to the scale
c is the average covariance
v is the average variance.
37
38
Measuring material deprivation
4.2
Components of the new FACS index
Table 4.1 lists all the items which were included in the new index based on the FACS
data.16 All items are expressed as deprivations: that is the lack of an item, or a
problem which should be avoided attracts a high score. Each was initially expressed
as a simple score, derived in one of two ways:17
• The questions under daily living and durables were asked in two stages: do you
have a (washing machine)?; if not, is that because you do not want one or
because you cannot afford one? The indicators were initially scaled as a ½ point
if the family did not have the item, and 1 point if they confirmed that they could
not afford it. (It is often argued that these items should only count as deprivation
indicators if the family cannot afford them; but in fact the simple lack of items is
also correlated with income, and adds to the effectiveness of our index.)
• The questions under financial strain offered respondents a range of answers on
a four or a six item ordinal scale, which were initially allocated fractional points.
For example:
How are you and your family managing financially these days?
Manage very well
21%
0 pt
1
Manage quite well
35%
/5 pt
2
Get by alright
33%
/5 pt
3
Don’t manage very well
3%
/5 pt
4
/5 pt
Have some financial difficulties
6%
In deep financial trouble
1%
1 pt
The individual indicators are organised into four groups, according to the subject
matter of the questions asked of respondents. We could have divided the longer lists
into sub-groups: for example the items of daily living can easily be split into food,
clothing and social activities; lists of durables sometimes distinguish between
labour-saving devices and sources of home entertainment. But since our objective
was eventually to add all the groups together, this did not seem important. The
groupings are not based on a full factor analysis (see Calandrino 2003 and Layte and
others 2001 for examples of this approach), but the internal consistency of each
group is examined by showing the average correlation between each item and all
the other items in that group, and the value of alpha for the group as a whole (at
Wave 4). The correlation between each item and equivalent income (at Wave 4) is
also shown in the table.
16
Within each group, the sub-index was declared missing (i.e. unknown) if more
than one of the component questions had not been answered (i.e. one don’t
know was allowed and treated as a non-problem). When the groups were added
together, the overall index was declared missing if any one of the sub-indices
was missing.
17
The simple points systems described here were initial scales within each
component; we discuss later how the scales were added together.
Measuring material deprivation
Table 4.1
Detailed components of the FACS index of material
deprivation
Source: FACS Wave 4
Correlation coefficients
Correlation with
Other items in group
Equivalent income
α = 0.88
Daily living
Cooked meal
Meat or fish
Joint of meat
Vegetables
Fruit
Cakes
Branded food
Adults’ coats
Children’s coats
Adults’ shoes
Children’s shoes
New clothes
Best outfit
Branded clothes
Celebrations
Toys
Outings
Holiday
Night out
Friends round
0.28
0.46
0.38
0.47
0.47
0.39
0.60
0.46
0.35
0.58
0.49
0.55
0.45
0.60
0.51
0.49
0.62
0.52
0.45
0.57
Financial strain
Money worries
Trouble with debts
Run out of money
Number of debts
Difficulty managing
0.67
0.73
0.65
0.60
0.72
-0.08
-0.12
-0.06
-0.15
-0.15
-0.04
-0.23
-0.15
-0.09
-0.20
-0.11
-0.21
-0.14
-0.25
-0.17
-0.16
-0.30
-0.35
-0.23
-0.23
α = 0.86
-0.29
-0.26
-0.27
-0.24
-0.33
α = 0.66
Durables
Car
Freezer
Washing machine
Tumble drier
Dishwasher
Microwave
Telephone
Cable/satellite
Video
Hi fi
Computer
0.46
0.27
0.20
0.37
0.44
0.22
0.23
0.33
0.28
0.22
0.41
Housing
Poor condition
Overcrowding
Difficult to heat
Central heating
0.17
0.07
0.14
0.16
-0.29
-0.12
-0.07
-0.15
-0.34
-0.05
-0.10
-0.11
-0.09
-0.10
-0.23
α = 0.27
-0.11
-0.20
-0.08
-0.10
Note: Central heating was originally asked as part of the durables sequence, but did not fit well
there. Colour TV and Fridge were also removed from the durables index, because they did not fit
well. (‘Did not fit’ means that they were not correlated with the other items in the group, and
reduced, rather than increased, the value of alpha.)
39
40
Measuring material deprivation
The details in Table 4.1 are summarised in Table 4.2. Each of the 20 items in the daily
living group is correlated fairly strongly with the other 19, and the measure of overall
fit of the items was high at 0.88. The five items in the financial strain group also fitted
together well, with an alpha of 0.86. The tendency for families lacking one
consumer durable also to lack the other was not quite so strong, but still high
(α=0.66). But the four housing variables were not closely associated with each other
(α=0.27), and failed to obtain a good measure of internal consistency.
Some of the specific items in the daily living and durables groups were not very
closely associated with income – notably ‘cakes’ and ‘washing machine’. But both
groups as a whole were associated with income – that is, those who frequently said
that they lacked these things tended to have low incomes. The components of the
financial strain group were all associated with low income, as was the group as a
whole. The housing group was also associated with low income, but less strongly
than the others.
Table 4.2
Overview of four FACS deprivation sub-indices
Source: FACS Wave 4
Coefficients
No. of
Group’s
components internal alpha
Daily living
Financial strain
Durables
Housing
20
6
11
4
0.88
0.86
0.66
0.27
Correlation with
Equivalent
Other
income
groups
-0.31
-0.35
-0.32
-0.22
0.66
0.63
0.55
0.37
Note: For reasons to be explained later, within-group alphas are based on annually standardised
scores for each component; between-group alphas are based on the means of the group scores,
without restandardisation.
The right hand column of Table 4.2 takes each of the four groups of indicators, and
shows how far it is correlated with the other three. Thus we look at the association
between groups in much the same way as we considered the association between
components within groups in the first column of Table 4.1. The daily living, financial
strain and durables sub-indices are very highly associated – again, this means that
people with bad scores on one tend to have bad scores on the others. But housing is
once more the odd one out, showing a much weaker association with the other
groups.
The first three sub-indices have passed all three tests set of them: they are internally
consistent, correlated with low income, and associated with each other. If these
three are added together, the value of α for the combined index is 0.65. The housing
group performed less well on each of the three tests. If an index was based on
adding all four together, the value of α would fall to 0.61. So the analytical logic
points to a three-group overall index, excluding housing. Most of the remainder of
this report is based on that three group index.
Measuring material deprivation
The exclusion of housing from the index is open to challenge. The counter-argument
is that if poor housing is a social problem, it should be included in the overall package
of items attempting to measure welfare. If the problem is also widely experienced
(by a set of people who do not necessarily face other problems), then those people’s
exclusion needs to be recognised in the measure. And if it is true that poor housing
is not correlated with low income, then the overall estimate of the association
between income and deprivation will be biased upwards by selecting only the highly
correlated indicators.
These points are all true; but they can probably be applied with equal force to a
whole series of other social problems which turn out not to be strongly associated
with either low income or the other members of the deprivation package – lack of
public transport, inadequate education and health services, environmental pollution.
These are all things which detract from people’s well-being, and should be included
in any overall measure of welfare based on ‘strong’ assumptions about the role of
deprivation indicators (see Chapter 1). It is not clear why housing should be
included, when these other factors are not. Note that the Irish deprivation index,
used as a model for UK approaches to this issue, also excluded housing indicators
explicitly because the factor was not closely associated with income (Nolan and
Whelan 1996).
An analysis of the relationships between income and each of the four separate subindices (including housing) will be provided at Table 8.4, so that the sensitivity of the
conclusions to the choice of indicator can be assessed.
4.3
Components of the BHPS index
The index just described refers to the FACS data. Although the BHPS was not
originally set up to measure living standards, it has always included some relevant
questions, and these were expanded in Wave 6 (1996) to include 30 potential
indicators of deprivation. A few of the questions are very similar to those asked in the
FACS, but it is more appropriate to consider them as a functionally equivalent set of
indicators of the underlying dimension, rather than directly comparable measures of
what items respondents do and do not have. The details of the questions on which
the BHPS index is based are in Table 4.3, and the summary in Table 4.4 is directly
equivalent to the FACS version in Table 4.2. The BHPS indicators are not as internally
consistent as those derived from the FACS (though the BHPS diagnostics would be
slightly stronger if confined to families with children). Again, the overall index has
been derived by adding together the daily living, financial strain and durables subindices. The BHPS housing and area group performs better than its FACS equivalent,
but it has again been left out of the overall index, partly on the grounds of
consistency with the FACS version, and partly because (as we will show) it shows
very weak relationships with income once other factors have been taken into
account.
41
42
Measuring material deprivation
Table 4.3
Detailed components of the BHPS index of material
deprivation
Source: BHPS Wave 12
Correlation coefficients
Correlation with
Other items in group
Equivalent income
α = 0.64
Daily living
Meat
Clothes
Furniture
Holiday
Friends round
0.29
0.39
0.47
0.44
0.36
Financial strain
Saving
Housing payments
Consumer debts
Difficulty managing
0.25
0.32
0.25
0.45
Durables
Car
Washing machine
Dishwasher
Microwave
Telephone
Colour TV
Cable/satellite
Video
Hi fi
Computer
Housing and area
Condensation
Leaky
Damp
Rot
Space
Difficult to heat
Central heating
Noisy neighbours
Noisy street
Light
Pollution
Crime
-0.08
-0.15
-0.19
-0.29
-0.18
α = 0.53
-0.25
-0.14
-0.11
-0.36
α = 0.65
0.29
0.38
0.28
0.32
0.32
0.29
0.24
0.41
0.28
0.34
-0.21
-0.05
-0.25
-0.01
-0.10
-0.02
-0.01
-0.03
-0.12
-0.17
α = 0.63
0.40
0.20
0.37
0.29
0.24
0.16
0.26
0.27
0.35
0.25
0.26
0.28
-0.09
0.00
-0.07
-0.04
-0.13
-0.06
-0.07
-0.07
-0.07
-0.05
-0.03
-0.12
Note: Variables with the same name as one of the FACS components did not necessarily use the
same question.
Measuring material deprivation
Table 4.4
Overview of four BHPS deprivation sub-indices
Source: BHPS Wave 12
Coefficients
No. of
Group’s
components internal alpha
Daily living
Financial strain
Durables
Housing and environment
4.4
5
4
10
12
0.64
0.53
0.65
0.63
Correlation with
Equivalent
Other
income
groups
-0.27
-0.32
-0.20
-0.13
0.51
0.37
0.28
0.31
Trends in the prevalence of deprivation components
The description of the development of the deprivation indicators has so far been
based on data for a single year – FACS Wave 4 or BHPS Wave 12 (both referring to
2002). Given our focus on relationships over time, it is crucial that the indices should
also be robust when compared from year to year. Most deprivation analyses in the
past have had only one year of data available to them, and the issue of year-on-year
changes in overall living standards was a theoretical rather than a practical and
empirical question.
One view is that measures of deprivation have an absolute validity: that if the
number of families unable to afford a colour TV or unable to have cooked main meal
each day reduces over time, then that is an improvement in living standards, a
reduction in deprivation, and, therefore, an alleviation of the social exclusion which
underlies the concept of poverty. That view is effectively identical to the view that an
absolute money income (after allowing for inflation) is the best yardstick for
measuring poverty. But it is now widely accepted that poverty should be defined
relatively, in comparison with the current incomes of the population as a whole.
It would certainly be difficult to rely on a set of fixed and absolute deprivation
indicators in the long run. That is obviously true of consumer durables: twenty or
thirty years ago only privileged families had a car, a fridge, a washing machine or a
colour TV, and many of the other items on the current list were only just entering the
market. Lack of these durables would not appear on any deprivation index if we took
a long-run and absolute view. But we are living in a period when ownership of these
goods is rapidly spreading up the income distribution, and there must come a time
when possession ceases to be a privilege and absence starts to be a deprivation.
Durables are probably a special case, but other aspects of normal daily living are
likely to change over time, too. The index developed by Peter Townsend and his
team in the 1960s, for example, included having a cooked breakfast every day
(Townsend 1979); fashions have changed, and no-one would now suggest that the
absence of a cooked breakfast should be considered a deprivation.
One suggested solution to this issue is that we should agree on an initial set of
indicators; treat them as having an absolute meaning over the short term, and then
43
44
Measuring material deprivation
change them periodically to deal with long-term changes in the items that are
regarded as ‘essential’. But if the index simply counts the number of indicators, that
solution is essentially an absolutist one, since short-run improvements for the
population as a whole would be interpreted as an immediate reduction in hardship
among the poor. Moreover it fails to grasp the nettle of how changes in social
behaviour should be reflected in a measure of relative deprivation.
The speed at which access to electrical and electronic equipment is increasing for all
income groups means that it would be essential to recalibrate an index annually if
durables were included among the contributory components. Among non-working
families in FACS (a group fully represented at all four waves), the average number of
consumer durables missing from the eleven in the index fell steadily from 4.5 per
family to 3.6 per family in just three years, from 1999 to 2002 (Waves 1 to 4). In the
BHPS, non-working families with children showed almost exactly the same rate of
fall over the same period if the two indices (with some differences in the durables
covered) are recalibrated to the same scale (Figure 4.1). And the longer run of BHPS
data shows that a similar trend had already been in progress since at least 1996.
Similar analysis of the FRS (not shown here) is entirely consistent with both the
smaller surveys. None of this is surprising, but it does emphasise the need to adjust
the deprivation index for changing norms. The largest change between FACS Wave
1 and Wave 4 (still for non-working families) was an increase in ownership of home
computers, from 24 per cent to 49 per cent. We cannot pretend that lack of a
computer was as clear an indicator of disadvantage in both periods.
Figure 4.1
Trend in lack of consumer durables among
non-working families with children, 1996 to 2002
Measuring material deprivation
Ownership of electrical and electronic gadgets is known to be in a period of rapid
growth (which may continue as more new equipment is invented and becomes
widespread). We had assumed that the other two main groups of indicators
included in the overall deprivation index would be less sensitive to year-on-year
change. After all, it might be argued, the wish to have friends or relatives round for
a meal, or to have money to put aside at the end of the week, would be the same in
all periods. But analysis of the trends provided surprising and inconsistent findings.
The two panels of Figure 4.2 are both plotted on the same scale as Figure 4.1 (and
are still confined to non-working families with children), so that the three subindices can be compared directly. According to the longer sequence of observations
in the BHPS, there was a steady but slow reduction in the prevalence of the problems
included in the daily living and financial strain indices. The shorter run of FACS data
suggested that the trend was much steeper. For both groups of indicators, the
reduction over a three year period recorded by the FACS was greater than the
reduction over six years recorded by the BHPS. In the case of daily living, the rate of
decline in deprivation recorded by the FACS was actually steeper than the rate of
decline in lack of durables.
It has been suggested that the apparent improvement in non-working families’
living standards might be attributable to the generous increases in Income Support
rates awarded in 1999 and 2000 (Marsh 2003). But the BHPS data shows that the
trend was already in progress well before that, and there is no obvious kink in the
lines at 1999. In fact versions of the BHPS durables and financial strain sub-indices
can be replicated right back to 1991. Both showed a remarkably steady decline in
deprivation from year to year across the full eleven-year period, though it was much
steeper for durables than for financial strain.
Multivariate analysis confirmed that very little of the trend could be attributed to
such improvements. As an illustration, the dashed line in the daily living panel of
Figure 4.2 shows what the FACS trend would be after correcting for changing
income and family composition (using the regression equation reported in Table
6.5). It is virtually identical to the unadjusted trend represented by the solid black
line.
A third source supports the view that absolute measures of deprivation tend to
decline over time, even for disadvantaged families. The proportion of Irish households
reported to be deprived fell steadily from 1994 to 2001 (Figure 4.3). A first instinct is
to explain this in terms of the increased prosperity of the Irish population as a whole
– more people with jobs, higher salaries for those in work. But the reduction in
deprivation was just as great among people without jobs – among unemployed
households, the proportion fell from 58 to 27 per cent in nine years. It is hardly likely
that the real incomes of unemployed people in Ireland have increased fast enough to
explain that trend.
45
46
Measuring material deprivation
Figure 4.2
Trends in daily living deprivation and financial
hardship among non-working families with children,
1996 to 2002
The findings with respect to durables are entirely predictable; those with respect to
daily living and financial strain are more surprising, and the difference between the
trends observed in the two surveys is inexplicable.18 Whatever the detailed explanation,
18
One hypothesis about the trend was that there might be a conditioning effect –
that respondents who had answered the same questions in previous years would
become less and less likely to report problems. Another hypothesis was that
respondents with high deprivation scores might be more likely to exit the panel,
leaving behind those with lower scores. Analytical tests of these hypotheses
failed to support them. In any case, neither hypothesis could explain the difference
between the two panel surveys.
Measuring material deprivation
the overall conclusion is that trend changes in the absolute frequency of the
problems included in the index cannot be taken as direct evidence of reducing
deprivation or increasing welfare. Some form of year-by-year recalibration is
required, not just for durables, but for other components of the index.
Figure 4.3
4.5
Proportion of households scoring one or more on the
Irish basic deprivation index, by economic activity of
household reference person, 1994-2001
Formulating the index
The recalibration approach needs to be based on a long-run view of what a
deprivation indicator represents. It can be argued that being deprived means not
having what other people do have. In that case, the more other people have
something, the more depriving the absence of it might be. If so, the index could
compensate for the reduction in the number of families lacking durables (and so on)
by increasing the weight given to each ‘lack’ on the overall scale. This calibration
should be based on an estimate of the proportion of all families recording the
possession or absence of the item, so the approach works best for the full samples of
families with children in Waves 3 and 4 of the FACS, and of all non-pensioner
families in the BHPS, rather than for the partial samples of low income families in
Waves 1 and 2 of the FACS.
19
Figure 4.3 is taken from Table 5.5 of the Irish report. The table is missing from
the printed version, but is available in electronic copies.
47
48
Measuring material deprivation
Instead of using prevalence weighting, the approach adopted here uses annual
standardisation. Each family’s score, on each component deprivation item is
transformed as follows:
Family’s raw item score – Overall average item score
Overall item standard deviation
where both the average and the standard deviation are specific to the year of the
observation, as well as the variable under consideration. This formula sets up a value
for each item whose average is 0 every year and whose standard deviation is 1 every
year.
Readers familiar with handling data will instantly recognise this formula as a ‘Zscore’ – the established technique for converting variables with different distributions
into a form as nearly as possible comparable with each other. It is common practice
to standardise variables in this way before adding them together into an overall
index. So the approach neatly combines the solutions to two problems: how to take
account of trends over the years in the overall level of living; and how to combine
variables in any one year, without giving undue weight to one rather than another.20
In detail, the full sequence of operations to assign a deprivation score to each family
in the FACS (or household in the BHPS) was as follows:
1 calculate the family’s weighted score on each component item, standardised
year by year as just described;
2 sum the scores within each group (daily living, financial strain and durables), and
divide by the number of components in the group to obtain a group average;
3 sum the scores across the three groups, and divide by three to obtain an overall
average;
4 multiply the result by 100 simply to make the numbers easier to read.
Note that there is no annual recalibration at stages 2 and 3, only at stage 1.
4.6
Properties of the index
The two surveys’ indices, calculated by the same method, should produce broadly
similar ranges of scores, though the fact that the sub-indices include different
components, and different numbers of components, will affect the distribution to a
certain extent. Figure 4.4 illustrates the distributions for the most recent wave from
20
The PSI hardship index analysed in the previous chapter used ‘prevalence
weighting’ (Vegeris and Perry 2003): the absence of each item was weighted by
the proportion of all families who possessed that item. This has the advantage
of conceptual clarity, but still allows the overall quantity of deprivation to fall
over time.
Measuring material deprivation
each data source, both representing 2002. They are continuous (the distributions
are smooth rather than jerky or spiky). And the scales are more sensitive to variations
at high levels of deprivation than at low levels (nearly half of the FACS observations,
for example, are concentrated between -59 and -16, the other half are spread out
between -16 and 163).21
The deprivation index is fairly stable over time – the correlations between each
individual’s score in 2002 and the same person’s score the previous year were 0.83
(FACS) and 0.69 (BHPS). The graph in Figure 4.4 also illustrates the range of changes
affecting individuals between consecutive years (using the BHPS as the example).
Figure 4.4
Distribution of the three-group deprivation indices
in 2002
Figure 4.5 confirms that, as intended, the deprivation indices discriminate well
between families who are high and low in the income distribution. The correlations
between the index and equivalent income were -0.40 (FACS Wave 4) and -0.37
(BHPS W12). Both indices were more closely associated with income than any of
their member groups were, and much more closely associated than most of their
component items – this is a sure sign that the index is effectively summarising the
symptoms of low income.
21
-59 and 163 are the 1st and 99th percentiles of the Wave 4 distribution.
49
50
Measuring material deprivation
Figure 4.5
Mean deprivation score in 2002, by quintile groups of
equivalent income
Standardising the index to reflect changes in the distribution of each component
problem in each year creates a fixed average deprivation score – the overall mean is
necessarily zero in each year. It does not follow, though, that the proportion of
people in hardship (i.e. with relatively high deprivation scores) is fixed. If the
experience of deprivation were to become more concentrated on a small group of
families over time (that is, if the correlations between components, and the values of
alpha, were to increase), then the distribution of the index scores would spread out,
and there would be a clearer distinction between the highly deprived and the not-atall deprived. Similarly, if the experience of deprivation became more focused on
families with low incomes over time (that is, if the correlation with income were to
increase), there would be a stronger tendency for the poor also to experience high
deprivation scores. So if ‘hardship’ is defined as a score above a fixed point in the
deprivation index, it is just as much a relative measure of deprivation as is the current
definition of poverty in relation to the distribution of income. In fact the BHPS index
shows that if hardship is redefined as a score of more than 30 points on the overall
index (about the worst one-fifth of all scores) the risk of hardship among poor
households drifted rather unsteadily down from 52 per cent in 1996 to 42 per cent
in 2002 (Figure 4.6).
Measuring material deprivation
Figure 4.6
4.7
Proportion of poor and non-poor BHPS respondents
scoring more than 30 points on the continuous
deprivation index, by wave
Discussion
This chapter set a series of technical objectives, to develop a deprivation index which
was based on a large number of survey questions, internally consistent, sensitive to
variations in income, numerically continuous and robust to changing overall living
standards. These aims have been achieved, and functionally equivalent (though
clearly not numerically identical) indices have been derived for the samples of all
families with children in the FACS, and of all non-pensioner households in the BHPS.
Every analyst who has ever worked on deprivation indicators (and many of those
who have no experience in the field) will point to aspects of the development which
they would have done differently. Actually, the development work involved much
experimentation with variants, so it is possible that we have already tried some of the
alternatives that might be recommended, and identified unexpected difficulties. It is
not suggested, though, that this is an ‘ideal’ approach; it is an index which achieves
certain aims and works, at least according to the criteria of the ‘weak’ assumptions
discussed in Chapter 1. One lesson is that all sensibly-calculated measures of
material deprivation will produce roughly the same findings about the relationships
with income. But (we argue) none of them will bear the weight of too literal an
interpretation in terms of trends in ‘hardship’ or ‘direct’ measurement of poverty.
51
52
Measuring material deprivation
The feature of the new index which distinguishes it from its predecessors is the
annual recalibration of the relative contribution of each of the components. This is
clearly essential if durables are to be included in the index (though an alternative
solution would be to omit durables for that very reason). The groups of daily living
and financial strain indicators might have been expected to have a longer-term or
even absolute validity. But long-run decline in deprivation recorded by these
indicators by the BHPS, the very rapid rate of reduction recorded by the FACS, and
the inexplicable difference between the two surveys, meant that annual recalibration
was essential for them too.
An early objective was that the index should be as simple as possible, so that it could
be clearly understood by non-specialists and the general public. Indeed, a simple
count of the number of missing items of daily living and consumer durables, plus an
equivalent count of aspects of financial strain, produced an index which met the first
four of our objectives as long as analysis was confined to a single year. But it failed
the fifth test, because the straight counts suggested so rapid a fall in absolute
deprivation and hardship levels from year to year as to make a nonsense of any
attempt to measure changes over time in relative deprivation. We have corrected for
changing average standards, without eliminating the opportunity to identify
reductions in hardship. But the cost, at this stage, is an index whose numerical value
is difficult to relate to the specific experience of poor families. This is an issue which
needs to be discussed further.
Measuring income
5 Measuring income
5.1
Defining income
The income data used for this analysis were drawn from the two surveys’ existing
estimates of net household income, calculated on principles as close as possible to
those used for the DWP’s HBAI estimates. All current sources of income (including
benefits, and subtracting direct taxes) are added across all members of each
household or family. All income is measured before housing costs. Monetary
amounts have been deflated to December 2001 prices, and expressed in terms of
pounds per week. Extreme values were top- and bottom-coded as follows:
• incomes of less than £10 per week were treated as missing;
• incomes between £10 and £50 per week were treated as £50;
• incomes between £2,000 and £4,000 per week were treated as £2000;
• incomes above £4,000 per week were treated as missing.
The FACS data set does not include a summary income calculation for families where
either adult was self-employed, and these families have therefore been omitted
from the FACS analysis.
The FACS covers the income of members of the family (benefit unit), and does not
include resources provided by other household members such as adult children.
Checks with the FRS (which can be used to calculate income on both bases) showed,
though, that the distributions of ‘family’ income and the distribution of ‘household’
income are very similar among families with children, and this turned out not to be
an important difference between the sources in practice.
The mean net household income in the BHPS data (for which we have a long
sequence of full samples) rose from £424 in Wave 6 (1996) to £487 in Wave 12
(2002), an average rate of increase of 2.3 per cent per annum. Figure 5.1 shows that
the range of inequality between households was steady and very similar for nonpensioner households with and without children over the period 1996 to 1999.
53
54
Measuring income
Both groups became less unequal between 1999 and 2001 – that is, low incomes
increased a bit faster than high incomes between those years – but the improvement
was twice as good for families with children compared with those with no children.
Figure 5.1
5.2
Trends in inequality of equivalent household incomes:
BHPS non-pensioner families with and without
children
Equivalence scales
Estimates of poverty and inequality, and analyses of the relationship between
income and deprivation, almost invariably adjust income to take account of the
varying needs of households of different sizes, using ‘equivalence scales’. Some
preliminary analysis in this and previous chapters have been based on equivalent
income, using the McClements scale almost always applied by UK analysts,
including the standard HBAI poverty estimates (DWP 2003a). All equivalence scales
incorporate a set of assumptions about the expected effect of the number of
household members on the amount of individual welfare that can be obtained from
a given overall income. In the case of the McClements scale, the main assumptions
are that:
a each additional adult imposes an additional cost, but less than the base cost of
the first adult;
b each child represents an additional cost, lower than that of an additional adult,
which is the same whether it is the first or the fifth child in the family; but
c older children cost more than younger ones.
Measuring income
The DWP has recently announced (DWP 2003b) that it is switching to the ‘modified
OECD’ scale for its child poverty measurements. The OECD scale incorporates
assumptions a and b, but not c. This enables comparisons to be made with EU and
other international statistics. The recent improvement in benefit rates for young
children, relative to older children, is consistent with this switch from the McClements
to the OECD scale (though there is no evidence that the two decisions were
connected to each other).
Rather than making assumptions about the additional costs associated with
additional household members, though, we can measure the actual effects of
variations in household composition on deprivation scores, controlling for raw (i.e.
unequivalised, but deflated) income (Berthoud and Ford 1996). All the analysis in
the next and subsequent chapters uses raw income, but also includes variables
which describe the composition of the household.
The use of equivalence scales has been discussed in detail elsewhere (e.g. Buhmann
and others 1988, DSS 1992). It is not the aim of the current project to assess the
validity of scales currently in use, but it can be noted (Table 6.2) that the relationships
with household structure are very different from the assumptions on which such
scales are based.
5.3
Very low incomes
Discussion of poverty often incorporates an explicit or implicit assumption that ‘the
poorest of the poor’ – families with incomes well below the poverty line – will be
substantially worse off than the marginally poor. A detailed analysis of the
relationship between income and material deprivation must address this issue.
But the question is dealt with here in this technical chapter, rather than in the
substantive analysis, because there are clear indications that some of the incomes
recorded at the bottom of the scale may be unreliable. These findings are consistent
with previous findings (Davies 1995, Goodman and others 1997), but they are
especially relevant to our current analysis of living standards. Figure 5.2 plots the
average deprivation score (after controlling for household composition and other
factors22) for individuals in each two per cent range of the distribution of household
income. Both surveys show an impressively consistent inverse relationship between
income and deprivation across the main range of low and middle incomes. But the
relationship peters out at low levels of income – just where we would expect the
most acute deprivation to be observed. In the BHPS, the slope of the line flattens
slightly for families without children below about £150; it is unsteady but broadly
flat for families with children below about £200. In the FACS, those on the lowest
incomes actually report lower levels of deprivation than families with only moderately
low incomes.
22
The complete list of control variables is shown in Table 6.5. In summary, they
are: household composition, age, employment status, benefits claimed, education/
occupation, housing tenure and region.
55
56
Measuring income
Figure 5.2
Estimated average deprivation scores for families/
households in each two per cent range of the
distribution of income (up to £500)
This twist in the tail of the relationships between low income and indicators of
consumption can be identified in other surveys. The only indicator of living standards
in the FRS is the number of consumer durables possessed; the left hand panel of
Figure 5.3 shows a slow but steady increase in ownership with increasing income
from about £175 upwards, but a reversal of the relationship at the lowest end of the
distribution.23 The Family Expenditure Survey provides even more telling evidence:
the right hand panel of the figures shows that households with a reported total
(unequivalised) income of less than about £90 per week spend significantly more
then they earn, and more than those with slightly higher incomes.24
23
Many thanks to Simon Lunn and Chris Read of the DWP for supplying this FRS analysis.
24
Many thanks to Andrew Leicester and Alissa Goodman of the Institute for Fiscal
Studies for supplying this FES analysis.
Measuring income
Figure 5.3
Measures of resources among households with very
low incomes based on the Family Resources Survey
and the Family Expenditure Survey
Why do households with very low incomes have higher living standards than might
be expected? A special survey of families reporting very low incomes in the FRS
suggested a variety of reasons (Elam and others 1999). Three broad types of
explanations can be considered:
• Perhaps there is a group of families with a very low interest in material
consumption. They willingly work for very low wages and/or do not claim all the
benefits they are entitled to. They use what little money they have extremely
efficiently, waste nothing, and substitute home-production for income to provide
what they need. They experience little deprivation, because they demand so
little. This would be consistent with low levels of deprivation on the daily living
and financial stress components of our index. But an unmaterialistic group would
probably not have plenty of consumer durables, nor would they spend in excess
of their income. So this seems an unlikely explanation for the patterns observed.
57
58
Measuring income
• An alternative explanation which is commonly put forward (Goodman and others
1997, McKay and Collard 2004) is that the lowest income band may contain
many households who are experiencing a temporary shortage of income during,
perhaps, a brief period of unemployment. They are able to smooth their
consumption to tide them over this period, so their lack of current income is not
experienced as hardship. It is entirely plausible that short-term fluctuations in
income are not immediately reflected in deprivation indicators, and this is one of
the key issues addressed later in this report. What this hypothesis does not explain,
though, is why those in temporary difficulties should appear below the
permanently poor in the overall income distribution.
• A third possibility is that a proportion of those reporting incomes at the very foot
of the distribution of income have understated their resources in some way –
that their true income is actually much higher than that measured by the survey
on this particular occasion. This could occur either if they omitted a key source
of income from the total, or if the amount was misinterpreted (e.g. a weekly
amount was registered by the interviewer as monthly). This type of measurement
error seems to us the most likely explanation.
Whatever the explanation, the flattening or even reversal of the relationship
between income and deprivation at very low levels of income causes an analytical
difficulty. If we simply wanted a more reliable estimate of the distribution of income,
we might use other data about each household, especially last year’s income and its
current deprivation score, to calculate a revised estimate for the doubtful cases. But
since our analytical objective is concerned with the relationship between deprivation
and changing income over time, using those very variables to predict income would
be impossibly circular.
The alternative is to give special consideration to the very low income group in the
multivariate analysis, rather than allow them to bias the overall conclusions. The true
FACS cross-sectional relationship at fairly low levels of income seems to be that
illustrated by the straight line drawn in the right hand panel of Figure 5.2, which
implies a reduction of about 0.8 deprivation points for each £10 increase in income.
If the lowest income households were allowed to influence the calculations with no
correction for the switch in slope, the estimate of the overall relationship would be
biassed downwards – the measured slope would be flatter. The first line of Table 5.1
confirms this – the estimated slope at around £200 is about half as steep as the visual
pattern in the graph would lead us to expect.
The table then shows the effect of three alternative ways of adjusting for this:
• the first effectively draws a reverse-slope link between income and deprivation
at incomes below £125;
• the second effectively assumes that those below £125 are a fixed distance below
where they would otherwise be expected;
• the third discounts the data from families below £125 altogether.
Measuring income
All three adjustments produce a very similar estimate of the slope of the relationship
between income and deprivation at around £200. The remainder of the FACS
analysis uses the categorical variable ‘below £125’ as the regular adjustment factor,
as this seemed the most efficient way of taking account of the available information.
The factor is included in all remaining FACS analysis.
Table 5.1
Estimated slope of the cross-sectional relationship
between income and FACS deprivation score, with and
without adjustment for very low incomes
Source: FACS Wave 4
Regression estimates
Estimated effect of a £10
difference in income at £200
No adjustment
Adding number of £s income below £125 as
an extra numerical variable
Adding income ‘below £125’ as a categorical variable
Omitting cases with an income below £125
-0.41
-0.71
-0.78
-0.82
Note: based on the full equation recorded in Table 6.5, with the variants shown.
A similar analysis of the BHPS data showed that once all the control variables were
included in the regression analysis, adding a factor to adjust for very low incomes did
not improve the fit, and no adjustment was made in the remaining BHPS analysis.
5.4
Discussion
Measuring household income and analysing its distribution are not primary objectives
of this research, but it has been important to assess the reliability of the income data
as a key component in the analysis of deprivation. Four different surveys have all
shown that households with very low incomes seem to experience higher living
standards (measured in various ways) than households just below the poverty line. If
this is true, then it has important implications for an understanding of the nature of
poverty, and especially of extreme poverty. If it is not true (that is, if the very low
incomes recorded in surveys are systematically biased), then there are important
implications for estimates of poverty rates and benefit take-up rates, which will be
discussed in the concluding chapter. For the moment, the key requirement is to take
account of this twist in the observed relationship between income and deprivation,
to avoid distorting the picture.
59
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
6 ‘Cross-sectional’
relationships between
material deprivation and
other factors, at one point
in time
Although our eventual objective is to demonstrate the effect of year-on-year
changes in a household’s income on changes in its experience of material deprivation,
it is important to start with an analysis of the situation at a fixed point in time. There
are two motives for this cross-sectional analysis:
• first, several straightforward cross-sectional surveys have demonstrated the fact
that low income households experience higher levels of deprivation. The DWP
now plans to add a set of deprivation questions to the FRS, and use cross-sectional
measures to help monitor progress towards the elimination of child poverty. The
inference has been drawn from those surveys that an increase in a household’s
income would lead to a reduction in its deprivation; it is that inference that
requires to be tested by analysis of the longitudinal data, but it is helpful to start
by establishing precise measures of the cross-sectional relationship to set against
the analyses derived from ad hoc surveys;
• second, it is important to check how much of the apparent cross-sectional
relationship with income is independent of such other potential correlations of
both income and deprivation as (for example) housing tenure.
This chapter develops cross-sectional regression equations predicting scores on the
deprivation index using the FACS Wave 4 data. The narrative proceeds in three
sections, establishing first the precise shape of the relationship with income; second
incorporating the effect of variations in family structure; and third taking account of
61
62
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
a series of other potential predictors. At each stage the effect of one set of variables
is discussed in detail, holding the other two sets constant. The full final FACS
equation appears at Table 6.5, and is compared with an equivalent cross-sectional
equation for the BHPS Wave 12 data in Table 6.7. A brief explanation of regression
equations is provided in Box A, for those who are unfamiliar with this approach.
Box B
Regression for beginners
The starting point is the hypothesis that families with low incomes experience
more deprivation than those with high incomes. The two key initial questions
are:
• how much less deprivation is associated with each additional £100 of weekly
income?
• how accurately do variations in income explain variations in deprivation?
Figure 6.1 illustrates a hypothetical group of ten families whose incomes range
from £150 to £800 per week (average £400). Their scores on a deprivation
index range from -20 to +15 (average 0). The family with the lowest income
has one of the highest deprivation scores; the family with the highest income
has easily the lowest deprivation score. But the other families are not lined up
exactly between those two cases. In general, high incomes are associated
with lower scores, but in detail the score of each family cannot be predicted
exactly from its income.
Figure 6.1
Stylised relationship between income and
deprivation
Continued
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Box B
continued
A regression equation calculates a line of best fit between the points on the
graph, illustrated by the downward sloping line. The slope of the line shows
the best estimate of the rate of fall in deprivation with increasing income,
taking all the data points into consideration. It can be seen that a notional
family with zero income would score 15 deprivation points. At £400 the
expected deprivation score is zero. At £800 the expected score is -15. This set
of results can be expressed as a formula or equation:
Deprivation = -3.75 x Income (in £100s) + 15
Deprivation is the dependent variable (the variable we are trying to explain).
Income is the explanatory or predictor variable. The slope of the line is -3.75;
this is known as the coefficient on income – the minus sign indicates that it
slopes downwards. 15 is the point at which the line crosses the vertical axis,
the predicted value at £0 income; it is known as the constant.
If all the data points had been exactly on the line, it would be possible to
predict exactly how much deprivation a family with a given income would
have. If the data points had been randomly distributed, there would be no
relationship, and no sloping line. The regression equation’s calculation of how
much closer the data points are to the sloping line than they would be to a
horizontal line is called R2. It can be interpreted as a measure of the proportion
of the original variance in the dependent variable that is explained by the
predictor variable. In the case illustrated in the graph, income explains 40 per
cent of the variance in deprivation.
This simple regression equation using only one explanatory variable provides
answers to the two initial questions set out at the beginning of this box.
Multiple regression uses a series of other explanatory variables (as well as
income) to address two other sets of questions:
• what other factors help to explain variations in families’ deprivation scores,
in combination with income?
• how far are the effects of the explanatory factors independent of each other?
So the equation becomes (for example):
Deprivation = A x Income + B x Number of children + C x Working family + Constant
6.1
Income
The first step is to work out the precise shape of the relationship between income
and deprivation at different levels of income. Most deprivation indices are
designed to be sensitive to variations at low levels of income; one of the
considerations in the design of our own index was that it was at least capable of
showing variations higher in the income scale. The black diamonds in Figure 6.2
63
64
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
represent the estimated deprivation score (controlling, as explained, for
household structure and other covariates, see Table 6.5) for each 2 per cent band
across the entire income distribution.25 The diamonds form a fairly straight line,
indicating a constant relationship, across a fairly broad range of lower incomes.
But they bend away to the right at higher levels of income, indicating that
deprivation is less sensitive to variations in the upper ranges.
Figure 6.2
FACS deprivation index by income – three metrics
compared
The straight grey dashed line in the graph represents the line of best fit if the
regression equation used a simple term for income (plus the adjustment factor for
incomes below £125 discussed in the previous chapter). The details of that simple
linear model are shown in the first column of Table 6.1. The coefficient on income
suggests that a household with an income £10 per week higher than some other
household can expect to be a third of a point lower in the deprivation index.
25
That is, income was recoded as a set of 50 categories, and submitted to the
regression equation as a set of dummy variables, in place of continuous income.
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Table 6.1
Cross-sectional regression equations for the FACS
deprivation index using alternative measures of current
income
Source: FACS Wave 4
Regression coefficients
Controlling for other factors
Linear
Quadratic
Cubic
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
(Below £125)
Effect of a £10 difference in income:
at £200
at £800
-3.3
-7.9
0.3
-16.5
-0.33
-0.33
No other
controls
Cubic
-23.5
-10.0
0.58
-0.011
-25.5
-34.8
2.8
-0.070
-60.5
-0.68
-0.33
-0.78
-0.28
-2.45
-0.38
Note 1: Additional controls for household composition and other factors are included in the
equations reported in the first three columns – for details, see Table 6.5.
Note 2: The effect of a £10 difference is calculated as the slope of the curve at each point. In the
case of the cubic relationship, this is:
(b[income/100] + 2*b[income/1002]*income/100 + 3*b[income/1003]*income/1002)/10
where b represents the coefficient on each term. £200 is close to the lowest decile of the income
distribution, and £800 is close to the highest decile.
The straight line clearly does not describe the relationship well across the complete
range of incomes: the slope is not steep enough at lower levels of income, but it is
too steep at higher levels of income. The second and third columns of Table 6.1
show what happens if more complex measures of income are used. Adding the
square of income is a common way of putting a bend into a regression curve, and
this improves the accuracy of the prediction (second column, quadratic). But in
practice the quadratic formula imposes too much of a bend, so that predicted levels
of deprivation actually appear to increase as incomes rise above £1,350 per week.
Adding the cube of income to the formula (third column of Table 6.1) effectively
straightens out the bend slightly, and provides the most accurate description of the
relationship. The cubic function is plotted as the solid curve in Figure 6.2. It can be
seen not only that the cubic function provides a better fit than the linear one; it also
shows how much more sensitive deprivation is to variations at low levels of income
than the linear formula suggested. The slope of the curve clearly varies with income,
but at £200, the cubic function suggests that a £10 higher income (say between
£195 and £205) is associated with a three-quarter point lower deprivation score –
more than double the effect estimated from the simple linear formula.26
26
It can be recorded that two other ways of expressing the relationship were almost
as accurate as the cubic function shown in the final column of Table 6.1. One
was the logarithm of income, which is much more sensitive to variations between
low incomes than between high incomes. The other was the respondents’ position
in the percentiles of the income distribution. The cubic formula was preferred
though, because the use of three terms makes it more flexible. It performed
slightly better than the alternatives both here and in the longitudinal analysis.
65
66
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
It should be noted that the relationships between income and deprivation shown in
Figure 6.2 and the first three columns of Table 6.1 are calculated after also taking
account of the relationships between deprivation and all the other factors to be
discussed in this chapter. That is, we are estimating the variations in deprivation
scores between families which have different incomes but are identical in all the
other respects included in the analysis. The final column of Table 6.1 shows what the
cubic formula would have looked like if none of those other factors had been taken
into account. The more detailed analysis shows that deprivation scores are much less
sensitive to variations in income than they appeared to be on the basis of a simple
analysis which took no account of other variables. The two versions are illustrated in
Figure 6.3. This is an important point – not least because the control variables include
characteristics which are strongly predictive of income such as economic activity and
benefits claimed. The implication is that part of the explanation for low deprivation
scores among higher income working families (compared with lower income nonworking families) is associated with the fact that they are in work, and part with the
fact that they have higher incomes.
Figure 6.3
Estimated FACS deprivation scores by income: with
and without controls for family structure and other
factors
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
6.2
Family structure
The previous chapter discussed the role of equivalence scales in adjusting incomes to
take account of variations in household size. All the analysis in this and subsequent
chapters uses raw income rather than equivalent income, but includes specific
measures of household structure which allow the impact of additional members on
deprivation scores to be measured directly. All the analysis holds income, employment
and other characteristics constant, so we are looking at the net effect of household
composition. The results are shown in Table 6.2. Many of them are inconsistent with
the assumptions incorporated in equivalence scales: this does not show that the
scales are wrong, though it does encourage us to re-examine the assumptions.
The level of deprivation is slightly lower in two-parent families than it is for lone
parents with a similar income and other characteristics. This is a only a small effect,27
but it is clearly inconsistent with the standard assumption that additional adults
represent a drain on income and might be expected to lead to an increase in
deprivation, other things being equal. Although the FACS data refer only to couples
with children and lone parents, the BHPS analysis will confirm the same relationship
between partnered and single householders for all non-pensioner households
(Table 6.7). The same unexpected relationship has been identified in several other
surveys (Berthoud and Ford 1996).
When households are analysed by the age of the children (first column of Table 6.2)
the analysis suggests that children below school age have more effect (leading to
increased deprivation, other factors held constant) than older children – again, this
is not in line with the assumptions in most equivalence scales.
When the number of children in the family is analysed as a sequence (second column
of the table), it appears that the marginal effect of each child increases with the
number of other children in the family. This finding is also inconsistent with most
equivalence scales, which assume that each additional child represents the same
additional cost to the family. This non-linear effect can be captured quite effectively
by using the square of the number of children in the regression equation (third
column).
27
The reduction in deprivation associated with being a couple appeared much
larger in versions of the regression equation with fewer covariates.
67
68
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Table 6.2
Cross-sectional regression equations for the FACS
deprivation index using alternative measures of family
composition
Source: FACS Wave 4
Regression coefficients
Children by age
Children by number
Children squared
Two parent family
-2.3
Number of children:
aged 0-1
+7.7
aged 2-4
+7.9
aged 5-10
+3.6
aged 11-15
+5.4
aged 16-17
+1.5
2
R
45.5%
Two parent family -1.6ns
Number of children:
second
+0.0ns
third
+5.5
fourth
+6.4
fifth
+20.5
Two parent family
-1.9
Number of children:
squared
+1.5
R2
R2
32.2%
32.0%
Note: Additional controls for income and for other factors are included in the equations – see
Table 6.5 for details. All FACS families have at least one child. The effects of second, third etc
children were calculated by including terms for each number of children, and subtracting each
coefficient from its predecessor. There were too few sixth and seventh children to enable their
effect to be estimated.
6.3
Other factors
The analyses in Tables 6.1 and 6.2 focus on the ‘obvious’ influences on a family or
household’s living standards, namely their income and the number of family
members requiring support out of that income. These are the same variables
(though we have used them in different ways) as are included in the equivalent
income measure used to define income poverty. But there may be other characteristics
of families and households which affect their deprivation, even after controlling for
the ‘obvious’ effects. Table 6.3 shows the factors which turned out to be significant
in the FACS analysis. The list has emerged after a period of experimentation, but we
have not shown all the variants tested in the table.
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Table 6.3
Cross-sectional regression equation for the FACS
deprivation index: other factors
Source: FACS
Age per year
Up to 40
40 onwards
Qualifications
GCSE/O level
Further qualifications
Regression coefficients
-0.77
+0.34
-5.8
-7.4
Income sources
Employment
Working Families’ Tax Credit
Income Support
-13.1
+15.7
+30.0
Housing tenure
Outright owner
Tenant
-7.5
+18.8
Region
London
North East
+10.6
-7.9
Note 1: Additional controls for income and for household composition are included in the
equation – see Table 6.5 for details.
Note 2: Age and qualifications based on the older/better qualified parent in couples.
‘Employment’ means that either parent works 16 hours or more. For qualifications, income
sources, housing tenure and region, the comparison is between members of each category and
families who fell into none of the categories listed
The level of deprivation decreases steadily with the age of the householder, down to
a low point at age 40; then the tendency reverses, and deprivation scores increases
slowly with each year of increasing age between 40 and pension age.28
Families where either parent had GCSE level qualifications are less deprived than
might otherwise have been expected; and further qualifications beyond GCSE
standard are associated with a further reduction.
Families where either parent (or both) has a job report substantially lower levels of
deprivation than might have been expected just from the level of their income. Of
working families, however, those claiming Working Families’ Tax Credit (WFTC) are
more deprived, and the WFTC effect more or less cancels out the employment effect
compared to those out of work but not claiming IS. Income Support claimants, on
the other hand, are much more deprived (compared with non-workers not on IS)
than even their very low incomes could explain; so families on WFTC are still in a
28
The equation uses a pair of variables, recording each year up to age up to 40,
followed by each subsequent year of age after 40. The technique is known as a
spline.
69
70
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
better position than those on IS. Thus the FACS survey confirms findings from
previous studies of low income families, that those on in-work means-tested
benefits/tax credits are worse off than those in work but not on such benefits, over
and above the effect of their lower incomes (Marsh and McKay 1993)
It is potentially confusing to combine employment and benefits in the same analysis,
when benefit entitlements are so closely associated with employment status. Table
6.4 clarifies this by tabulating the four main possible combinations. The majority of
families were in employment and not receiving Working Families’ Tax Credit. They
have the highest average income, and the lowest average deprivation score. At the
opposite end of the scale, 16 per cent of families were on Income Support; they have
low (though not the lowest) income, and the highest deprivation score. The
contribution of the regression analysis is that it sorts out how much of the
deprivation difference between these groups can be explained by the income
differences, and how much, unexplained by income (or other characteristics),
appears to be directly associated with employment and with benefit receipts.
Table 6.4
Incomes and deprivation scores by income sources
Source: FACS Wave 4
In employment
No WFTC
WFTC
Percent of families
Mean income
Mean deprivation score
Mean score predicted by
regression equation taking
account of income sources
No employment
No IS
IS
60%
£556
-22
19%
£350
14
5%
£224
20
16%
£247
60
-22
14
18
61
Note: The table shows the four main logical combinations. A few employed families appeared to
be receiving Income Support; some non-employed families were receiving WFTC.
The small number of families who already own their home outright have low
deprivation scores (return to Table 6.3), while tenants (both social and private) are
more deprived than other similar families in other tenures (most of whom were
mortgage-holders).
Deprivation scores are substantially higher (i.e. worse) in London, and lower in the
North East of England, than in other regions. These differences may be associated
with variations in housing costs, rather than with direct regional effects.
Some of these effects imply a big impact of the new variables on the estimated level
of material deprivation. Take the largest of the coefficients: Income Support
claimants score 30 more deprivation points than families with otherwise identical
incomes, household structures and other characteristics. That is equivalent to the
deprivation difference between an income of £150 and an income of £650 (see
Figure 6.3).
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
6.4
Strength of the relationships
The full FACS equation, containing the three sets of variables introduced in Tables
6.1-6.3, is shown in Table 6.5, which also provides measures of statistical significance.
The calculation of R2 (at the foot of the table) shows that these variables explain more
than 45 per cent of the variance in deprivation scores, which is an impressively high
figure for family-level data of this kind.
Table 6.5
Full cross-sectional regression equation for the FACS
deprivation index
Source: FACS Wave 4
Coefficients
Coefficient
t
Current income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
(Below £125)
-10.0
+0.6
-0.01
-25.5
11.5
5.2
2.6
14.0
Family composition
Two parent family
No. of children: squared
-1.9
+1.1
2.3
18.3
Age per year:
Up to 40
40 onwards
-0.8
+0.3
13.5
3.8
Qualifications
GCSE/O level
Further qualifications
-5.8
-7.4
8.2
9.3
Income sources
Employment
Working Families’ Tax Credit
Income Support
-13.1
+15.7
+30.0
9.4
19.4
20.4
Housing tenure
Outright owner
Tenant
-7.5
+18.7
6.6
23.9
Region
London
North East
+10.6
-7.9
11.4
7.4
Constant
Sample size (families)
R2
56.9
5,612
45.5%
20.2
Note: the column headed t shows the ratio of the coefficient to its standard error. The coefficient
is significant at the 95% level if t is 2 or more.
71
72
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Given that deprivation has been found to be associated with 17 variables, under
seven headings, it is important to work out which of the factors are the important
ones. The coefficients themselves, which simply show the increase or decrease in the
deprivation index associated with a unit increase in each variable, do not indicate
how much difference the variable as a whole makes, still less the effect of a whole
package of variables such as ‘current income’. Table 6.6 provides calculations of the
impact of each of the seven groups of variables on the prediction of deprivation
scores. (The calculations are explained in Box C at the end of the chapter.)
• The first column records what proportion of the overall variance in deprivation
scores can be explained by each group of variables after allowing for the maximum
possible effect of all the other variables. This can be interpreted as the minimum
effect of each factor.
• The middle column records the proportion of the variance explained by this
group of variables, if each is allocated half of the effect of its combinations with
other variables (and the other variables are assigned the other half). This can be
interpreted as the central estimate of the power of each group of variables. The
sum of the variances explained by each group of variables is the total variance
explained by the equation as a whole (R2), as already reported in Table 6.5.
• The right hand column shows the maximum effect of the group of variables,
allowing each one to claim all the predictive power associated with its combination
with other variables. Clearly these estimates cannot all be correct, and it is likely
that they are overestimates.
Table 6.6
Proportion of cross-sectional variance in FACS
deprivation index explained by each group of factors
Source: FACS Wave 4
Current income
Family composition
Age
Qualifications
Income sources
Housing tenure
Region
Total
Variances and covariances as proportion of total
Minimum
estimate
%
Central
estimate
%
Maximum
estimate
%
4.2
1.0
0.6
0.3
9.6
3.1
0.6
10.3
2.4
2.1
2.2
18.8
9.3
0.4
45.5
16.4
3.8
3.7
4.0
28.0
15.4
0.3
Note: derived from the equation in Table 6.5. See Box C for explanation of calculations.
This is important evidence. It shows that the cubic series of income variables
developed in Table 6.1 explains at least 4 per cent of the between-family variance in
deprivation scores, and at most 16 per cent, with 10 per cent the most likely answer.
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Income is more important in this respect than all three basic family characteristics
(composition, age and qualifications) combined. On the other hand the simple
comparison between outright owners, tenants and ‘other tenures’ (mostly mortgage
holders) is almost as effective a predictor as income is. And the group labelled
‘income sources’ seems to be a more powerful predictor than the amount of income
in pounds per week. The evidence suggests that families with jobs experience low
levels of deprivation, and income-tested benefit claimants experience high levels of
deprivation, not just, or even mainly, because the first group has high incomes and
the second group has low incomes. Their positions in the economic hierarchy seem
to have an important direct effect – or, alternatively, some unmeasured family
characteristics that are associated with those positions.
6.5
BHPS comparison
This chapter has so far been based on the FACS data. A similar regression equation
establishes the relationships between deprivation and other factors in the BHPS
(Table 6.7). There are some differences in detail, partly because the BHPS sample is
about half the size of the FACS sample, so some variables which were significant in
one model failed to reach significance in the other. The age of the head of household
and the region of residence fell out of the BHPS analysis for this reason. The BHPS
equation as a whole explained rather less of the overall variance in deprivation than
the FACS version did (shown in grey). Nevertheless, the two models are broadly
similar, and both show the same shape, and the same order of magnitude, for the
key relationship between deprivation and income.
Table 6.7
Full cross-sectional regression equation for the BHPS
deprivation index
Source: BHPS Wave 12
Regression coefficients
FACS
Coefficient
Current income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
(Below £125)
Effect of a £10 difference in income:
at £200
at £800
Family composition
Couple householder
Number of other adults
Number of children: squared
BHPS
Coefficient
-10.0
+0.6
-0.01
-25.5
-12.1
+0.9
-0.02
-0.78
-0.25
-0.89
-0.27
-1.9
na
+1.1
-10.5
+3.5
+0.7
t
5.9
3.7
2.8
4.6
2.3
2.6
Continued
73
74
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Table 6.7
Continued
Source: BHPS Wave 12
Regression coefficients
FACS
Coefficient
Age per year
Up to 40
40 onwards
Qualifications
GCSE/O level
Further qualifications
Any qualifications
BHPS
Coefficient
t
-0.8
+0.3
-5.8
-7.4
-7.6
2.7
Sources of income
Employment
Working Families’ Tax Credit
Income Support
-13.1
+15.7
+30.0
-5.9ns
+8.2
+16.6
1.8
2.8
3.9
Housing tenure
Outright owner
Tenant
-7.5
+18.7
-6.9
+22.2
3.8
9.2
Region
London
North East
Constant
Sample size (households)
R2
+10.6
-7.9
56.9
5612
45.5%
49.4
2846
34.4%
8.9
Note: the column headed t shows the ratio of the coefficient to its standard error. The coefficient
is significant at the 95% level if t is greater than 2. Blank cells represent non-significant variables.
As before, it is possible to estimate the power of each group of variables in
explaining variation in deprivation scores. Income explains slightly more variance in
the BHPS deprivation index than it did in the FACS index. Other packages of variables
appeared to be performing slightly better in one data-set than the other, but it is
probably not safe to place too much weight on these small differences. Strikingly,
though, the set of variables recording the sources of the household’s income
explains much less variance in the BHPS. It is not at all clear why the two surveys
should have produced such different estimates on this important point.
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Table 6.8
Proportion of cross-sectional variance in BHPS
deprivation index explained by each group of factors
Source: BHPS Wave 12
Variances and covariances
FACS
central
estimate
%
Current income
Household composition
Age
Qualifications
Income sources
Housing tenure
Region
Total
10.3
2.4
2.1
2.2
18.8
9.3
0.4
45.5
Minimum
estimate
%
BHPS
Central
estimate
%
Maximum
estimate
%
8.2
1.6
13.0
3.5
17.9
5.5
0.4
2.3
5.6
1.1
6.5
10.2
1.8
10.7
14.7
34.4
Note: derived from the equation in Table 6.7. See Box C for explanation of calculations.
Box C
Attributing variance to groups of explanatory variables
The group variances in Table 6.6 and 6.8 are calculated in two steps.
Create group summaries
The first step is to convert groups of variables into single numerical variables
reflecting the observed relationships between each component and the
dependent variable. This is done by calculating, for each respondent, the
contribution of the set of variables to the prediction, multiplying the value of
each component variable by its regression coefficient. For example:
Pincome = income*binc + income2*binc2 + income3*binc3 +below125*bbelow125
If the set of these group summaries is included in a new regression equation
predicting deprivation, all the coefficients are 1 and the whole-equation
diagnostics are identical to those of the original equation.
Calculate variances
The second step is to calculate the variances and covariances of the variablegroups. Each variable-group has its own single-variance, and a covariance
with each other group. The total variance explained is the sum of the single
variances, plus twice the sum of all the covariances.
• The minimum estimate of the predictive power of Pincome (and so on) is its
own single variance, with no assumed contribution from the covariances.
Continued
75
76
‘Cross-sectional’ relationships between material deprivation and other
factors, at one point in time
Box C
Continued
• The central estimate of the explanatory power of each variable-group is
calculated as the sum of its single-variance plus one set of its covariances
(effectively allowing the other variables each to keep their share of the other
set). The sum of these central estimates is the total variance explained.
• The maximum estimate is calculated as the sum of the variable-group’s single
variance plus both of its sets of covariances (effectively allowing this variablegroup to claim all the joint predictive power which it shares with other
groups).
‘Underlying’ relationships during a period
7 ‘Underlying’ relationships
during a period
The cross-sectional analysis in the previous section considered the relationship
between deprivation and income (and other household characteristics) in any
particular year, using Wave 4 of the FACS, and cross checking it with Wave 12 of the
BHPS, both referring to the same year, 2002. Much the same results would have
been expected if any other year had been chosen. No direct use has yet been made
of the panel data which follows the same households and individuals from year to
year.
7.1
Approach
The FACS panel covered a representative sample of families with children only in the
third and fourth waves. Although in principle that allows measurements of changes
in income, and in deprivation, between years, it turns out (see Chapter 8, Table 8.1)
that consecutive pairs of observations provide an unreliable base for longitudinal
analysis, and a reasonably long period of years is needed to disentangle underlying
relationships and the effects of changes over time. The analysis in this and the next
chapter therefore switches to the seven-wave period covered by the BHPS. The
lessons learned will then be applied to the FACS sample of families with children
right at the end of Chapter 8.
Remember (see Chapter 2) that although all the measures of deprivation, income
and other characteristics under consideration are defined for whole households in
each year, it is not possible to follow households as such from year to year, because
they change their composition. Instead we follow individual BHPS sample members
across survey waves, and attribute to them the income, deprivation and so on of the
household they are living in on each occasion. So an individual could be seen to
increase their income between waves either because the household they were living
in increased its income, or because they moved out of a low-income household and
joined a high-income household. We will test the sensitivity of the results to the
77
78
‘Underlying’ relationships during a period
assumption that these are equivalent to each other, towards the end of the next
chapter, once the form of the models has been established.
It is now well-established (Jenkins and Rigg 2001) that a sample of individuals
studied in any one year will include some people who have steady low or high
incomes, others whose low or high incomes are just a temporary stage, and others
again whose income fluctuates widely from year to year. Looking over the whole
seven year period covered by this analysis, it is useful to consider each individual’s
income as having two distinct components: their average income over the whole
seven year period; and variations in their income around that mean, from year to
year within that period. Thus we distinguish between an individual’s underlying
position and fluctuations in that position. The distinction can be handled quite
neatly by splitting the analysis into two stages:
• calculating the mean value of income, deprivation (and so on) for each member
of the sample, averaged across waves. This discounts variations between years,
and focuses on variations between individuals. The analysis can be interpreted
as establishing the underlying relationships;
• calculating for each individual, in each wave, the difference between this wave’s
income, deprivation (and so on) and the individual’s average calculated at the
previous step. This discounts underlying differences between individuals, and
focuses on variations across years. It can be interpreted as establishing the
longitudinal relationships over time.
It can be calculated that nearly two-thirds (65 per cent) of the overall seven-year
variance in deprivation scores in the BHPS can be accounted for in terms of
underlying variation between individuals’ personal averages over the period as a
whole (between cases), and the remaining one third (35 per cent) is accounted for by
variations from year to year in individuals’ experience (within cases). The statistics for
between – and within – case variance in income are almost identical. The analytical
questions addressed in this and the next chapter are:
• To what extent are underlying (between-case) variations in deprivation over the
period as a whole associated with underlying variations in income and other
characteristics?
• To what extent are longitudinal (within-case) rises and falls in deprivation from
year to year synchronised with parallel changes in income and other
characteristics?
Multivariate regression techniques are available to split the analysis into these two
components. The analysis of underlying relationships based on means will be
referred to as the between-cases model, as it focuses on differences between
sample members, using data from all waves. The analysis of longitudinal relationships
from year to year will be referred to as the within-cases model, because it ignores the
‘Underlying’ relationships during a period
underlying variation between individuals and then analyses variations over time
within each person’s experience.29
7.2
Estimating underlying relationships
This chapter looks at the underlying picture, using the between-cases model. All the
analysis in this and the next chapter is confined to members of the BHPS sample who
provided data for at least five of the seven possible waves, so that we can establish
their long-run position (and deviations from it) with a fair degree of reliability.
Remember that the BHPS sample includes households without children, whereas
the FACS only covers families with children.
Table 7.1 compares the effectiveness of predicting this year’s deprivation from this
year’s income and other items of information (cross sectional column, in grey), with
the effectiveness of predicting period deprivation using income and other items of
information over the period.30 The between-cases equation increased its predictive
power (R2) by half compared with the simple point-in-time model. Indeed, the
analysis shows very strong relationships – it is quite unusual to see nearly 50 per cent
of the variance explained by regression equations based on household level data.
The relationship between deprivation and income is especially strengthened by the
switch of time period, with a substantial increase in the estimated marginal effect of
a £10 increase in weekly income at £200. The central estimate of the power of
income to explain variations in income rises from 13 per cent to 23 per cent (Table
7.2).
Some of the other predictors also increase their coefficients as we move from the
cross-sectional to the period analysis. The set of variables labelled ‘sources of
income’ also improved its predictive power (though it remains weaker than it
appeared from the FACS analysis).
29
The within-cases analysis is also known in the economics literature as a ‘fixedeffects’ model. That name is intended to reflect the fact that underlying individual
(‘fixed’) characteristics are held constant, in order to isolate the longitudinal
(‘variable’) effects. Because of our focus on longitudinal effects, we prefer the
‘within-cases’ terminology.
30
Although Stata provides an automatic program for between-effects models (xtreg,
be), the analysis was done by the longhand method, calculating the mean value
of each variable for each sample member, and then running a straightforward
regression using the first observation per individual. This enabled calculation of
standard errors and t-scores which took account of the clustering of individuals
within households. It also enabled calculation of the variances associated with
variable-groups (see Table 7.2). The two methods produced identical coefficients
and estimates of R2.
79
80
‘Underlying’ relationships during a period
On the other hand, some other predictors have very similar coefficients in both
analysis formats. Qualifications retained their small effect and housing tenure
retained its large one. Some predictors were rather less relevant to the period
analysis than to the point-in-time analysis. This demonstrates that there is no
automatic improvement in fit between the deprivation index and all predictors as
one looks at the longer time period.
Table 7.1
Between-cases regression equation for the BHPS
deprivation index
Source: BHPS Waves 6-12
Regression coefficients
Cross-sectional
Coefficient
Income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
Effect of a £10 difference in income:
at £200
at £800
Between cases
Coefficient
t
-12.1
+0.9
-0.02
-16.3
+1.2
0.0
7.7
4.6
-3.2
-0.89
-0.27
-1.41
-0.88
Family composition
Couple householder
Number of other adults
Number of children: squared
-10.5
+3.5
+0.7
-8.4
+5.1
+0.7
4.5
4.6
3.2
Qualifications
Any qualifications
-7.6
-4.8
2.3
Sources of income
Employment
Working Families’ Tax Credit
Income Support
-5.9
+8.2
+16.6
-7.2
+17.2
+17.6
2.3
4.1
4.6
Housing tenure
Outright owner
Tenant
-6.9
+22.2
-10.9
+16.0
6.6
8.4
Constant
Sample size (households)
R2
49.4
2,846
34.4%
56.6
3092
49.6%
11.8
Note: Analysis based on individuals providing income and deprivation data in at least five waves.
‘Underlying’ relationships during a period
Table 7.2
Proportion of between-cases variance in BHPS
deprivation index explained by each group of factors
Source: BHPS Waves 6-12
Variances and covariances
Cross-section
central
estimate
%
Current income
Household composition
Qualifications
Income sources
Housing tenure
Total
13.0
3.5
1.1
6.5
10.2
34.4
Minimum
estimate
%
14.5
1.6
0.2
4.0
4.5
Between cases
Central
Maximum
estimate
estimate
%
%
22
4.1
1.0
11.4
10.2
49.6
Note: derived from the equation in Table 7.1; see the note to that table. See Box C for
explanation of calculations of variance.
31.2
6.7
1.7
18.9
15.8
81
‘Longitudinal’ relationships from year to year
8 ‘Longitudinal’ relationships
from year to year
The previous chapter analysed the underlying experience of deprivation during the
seven year BHPS panel period. This chapter analyses variations in their experience
from year to year. We know that the period difference between cases accounts for
nearly two thirds of the total variance in deprivation scores; we will now look to see
how far changes over time in income, or other characteristics, can explain the
remaining one third of the variance which is attributable to fluctuations over time
within cases. Members of the sample recorded variations from year to year in their
deprivation scores, in their income and in other characteristics – how far did the rises
and falls in deprivation coincide with falls and rises in income, or with changes in
other factors?
We cannot be sure that the ‘underlying’ relationship is truly causal. The possibility
remains that there is some unmeasured background characteristic of households
which affects both their incomes and their deprivation. But we can be fairly
confident that a ‘longitudinal’ relationship would be a true income effect – that is,
changes in income would be a direct cause of any changes in deprivation happening
simultaneously.
8.1
Testing alternative longitudinal models
Before presenting and interpreting the substantive results based on the preferred
model, though, it is necessary to compare alternative formulations of the analysis. At
first sight they appear to give very different answers to the same question, and we
have to decide which one gives the most accurate results. For this technical stage, all
the analysis (in Table 8.1) is confined to the ‘balanced panel’ of sample individuals
who provided data in all seven BHPS waves between Wave 6 and Wave 12. The
advantage of using the balanced panel for this technical comparison is that it is the
exactly the same 4,332 individuals being analysed on every occasion; the variations
in approach refer to which combinations of their annual observations are being
compared.
83
84
‘Longitudinal’ relationships from year to year
The simplest and perhaps the most natural way of looking at changes over time is to
compare two consecutive years. To what extent is an increase in income between
‘last year’ and ‘this year’ associated with (and a probable cause of) a reduction in
deprivation over the same pair of years? The outcomes of this approach are reported
on the left hand side of Table 8.1. Taking the first row of that side, an analysis of the
difference between consecutive years, using all seven waves of data, means
comparing Wave 7 with Wave 6, Wave 8 with Wave 7, Wave 9 with Wave 8 and so
on, and then pooling all the paired comparisons to get an average effect of moving
from one year to the next. This analysis suggests that an increase in income of £10
per week for an individual whose income is around £200 per week is associated with
a change in deprivation of -0.53 points. This compares with equivalent figures of
-0.89 in the cross-sectional analysis, and -1.41 in the between-cases analysis. If the
underlying association is greater than the current association (as the latter figures
imply), it is inevitable that the year on year association will be less than the current
association. Nevertheless, -0.53 seems a surprisingly low estimate.
The right hand side of Table 8.1 reports the results of a full within-cases analysis – the
underlying differences between cases (in mean income, mean deprivation score and
so on) are set on one side, and an estimate is calculated of the relationships over time
within each case.31 All seven years of each individual’s experience are included in the
analysis. The within-cases equation, using exactly the same seven-wave data as the
differences equation, suggests that the marginal effect of £10 at £200 is substantially
higher, at -0.75 (top right). Both versions of the longitudinal model explain much
less variance than the static models did, but the within-cases version explains nearly
twice as much as the differences version. Yet both are, in principle, measures of the
same relationship, using the same information about the same sample.
Table 8.1
Comparison of differences equations and within-cases
equations using various combinations of waves (all
confined to members of the balanced seven-wave panel)
Source: BHPS Waves 6-12
Regression estimates
Differences equations
Income effect
at £200
R2
All seven waves
-0.53
Wave 10 compared with Wave 9 -0.44
Wave 12 compared with Wave 6 -0.90
4.4%
3.5%
13.0%
Within-cases equations
Income effect
at £200
R2
-0.75
-0.44
-0.90
8.5%
3.5%
13.0%
Note: the equations include all the covariates shown in Table 7.1, but only the income effects at
£200 are reported.
31
Stata provides three ways of calculating within-cases equations, all of which
produce identical coefficients. We used ‘areg’ to calculate standard errors and t
scores (clustered by household), ‘xtreg, fe’ to calculate the overall explanation of
variance; and the longhand version, using the deviation of the current wave
from the overall mean, to calculate the variances attributable to variable groups.
See also footnote 30.
‘Longitudinal’ relationships from year to year
The differences analysis is based on a series of comparisons between two consecutive
years, whereas the within-cases analysis in the first row of Table 8.1 compares each
year’s deprivation and income (and other characteristics) net of the individual’s
seven-year average. The second row of the table shows that if both types of model
are confined to the same pair of consecutive years (the pair in the middle of the
available sequence) instead of the full set of seven, then they yield identical estimates
of the relationship between income and deprivation – and both suggest that the
relationship over two waves is weaker than the seven-wave comparison had
estimated. The two versions are indeed the same when confined to just two
consecutive years. It is the availability of a wider spread of years in the full withincases comparison that enables it to pick up a stronger income effect. This hypothesis
is supported when the pair of years under consideration is shifted to the first and the
last available waves (third row of table). Both estimates of the association between
income and deprivation double if the gap between observations is six years instead
of only one; the fit of the equation nearly quadruples. This seems to explain why the
within-cases model produces a clearer relationship when all seven waves of data are
included – it includes widely- as well as narrowly-spaced comparisons, whereas the
differences model is confined to a series of narrowly-spaced comparisons.
Although both methods of analysing changes over time should in principle provide
the same answer, the within-cases method has superior statistical properties, and
also takes account of a wider spread of waves of data. We therefore use that model
as our preferred estimate of the relationship between income and deprivation over
time. A technical conclusion is that pairs of consecutive waves produce underestimates
of the strength of this relationship (whichever method is used); and that the
differences approach fails to pick up the full strength of the associations revealed by
the within-cases model.
One possible explanation for the improvement in measured associations with the
introduction of wider gaps between observations in the within-cases regression, is
that relying solely on narrowly-spaced comparisons may be more sensitive to
possible measurement error than widely-spaced comparisons. Any estimate of the
strength of a longitudinal relationship is likely to be biased downwards if there are
fluctuations between years in the accuracy of an individual’s reported income (or
deprivation). If error strikes at random, it will make neither more nor less contribution
to the between-wave variance, whether the gap between waves is one year or six.
On the other hand, the variance between waves in respondents’ true income (or
deprivation) is bound to be wider if there is a wide gap between waves. Thus the
observed variance in income-difference (measured in hundreds of pounds per week)
rises from 3.8 if the gap is between consecutive waves, to 7.0 if the gap is between
Wave 6 and Wave 12; the observed variance in deprivation-difference rises from 891
to 1,524. So if measurement error contributes the same absolute variance to each
comparison, it represents a smaller proportion of the true variance when more
widely-spaced comparisons are included in our estimated model (using the withincases procedure).32 This implies that the widely-spaced estimate is more accurate.
32
An analogy is with physical measurement. If we have a ruler which is accurate to
within ±1 cm, the potential error is ±10 per cent if the object being measured is
10cm long, but ±1 per cent if the object is one metre long.
85
86
‘Longitudinal’ relationships from year to year
8.2
Estimating longitudinal relationships
With these important measurement issues in mind, we can now show more detail of
the preferred analysis. This uses the within-cases model and all seven waves of data.
But for this substantive analysis, individuals recording five or six observations are
included, as well as the balanced panel of respondents who provided data at all
seven waves. This provides both a larger and a more representative sample.
The results are presented in Table 8.2. The first (grey) column repeats the findings of
the underlying (between-cases) model (from Table 7.1).33 The new within-cases
model still shows a clearly determined negative relationship between changes in
respondents’ income and changes in their deprivation score. This is the expected
result – people become better off when they get more money, and worse off when
their income falls! The key point, though, is that this longitudinal relationship
between changes in income and changes in deprivation is much weaker than the
underlying tendency for households and individuals with steadily high incomes to
experience less deprivation than those with steadily low incomes.
The longitudinal model shows that some of the change in deprivation between one
year and the next (i.e. between t-1 and t) is also associated with a change in income
over the preceding year (i.e. between t-2 and t-1). The delayed effect is smaller than
the current effect, but makes a significant additional contribution to the longitudinal
relationship (see the note at the foot of the table). The possibility of a second year of
lag (i.e. income changes between t-3 and t-2) was tested, but the set of coefficients
was not statistically significant.34 It seems likely that different elements of the
deprivation index might respond faster or slower to changes in income, and that
issue will be addressed later (Table 8.4) .
33
A Hausman test of a random effects model confirmed that the between-effects
and the within-effects estimates were significantly different from each other.
34
Surprisingly, the coefficients on a third year of lag were substantially larger (and
in the expected direction) than those on the second year. The longer the series
of lags analysed, the fewer the number of observations with the relevant sequence
of data, and we cannot be confident of conclusions about slow-moving dynamics.
‘Longitudinal’ relationships from year to year
Table 8.2
Within-cases regression equation for the BHPS
deprivation index
Source: BHPS Waves 6-12
Regression coefficients
Between cases
Coefficient
This year’s income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
Last year’s income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
Effect of a £10 difference in
income at £200
This year only
This year and last year together
-16.3
+1.2
0.0
Within cases
Coefficient
t
-8.5
+0.7
-0.02
8.9
6.6
5.6
-1.5ns
+0.1ns
-0.002ns
1.7
0.9
0.5
-1.41
-0.71
-0.85
Family composition
Couple householder
Number of other adults
Number of children: squared
-8.4
+5.1
+0.7
-11.0
+0.4 ns
-0.2 ns
6.4
0.5
-0.7
Qualifications
Any qualifications
-4.8
-0.4 ns
-0.2
Sources of income
Employment
Working Families’ Tax Credit
Income Support
-7.2
+17.2
+17.6
-10.5
+3.5
+6.6
6.3
2.2
3.5
Housing tenure
Outright owner
Tenant
-10.9
+16.0
-3.4
+13.8
2.7
8.3
Constant
Sample size (households)
R2
56.6
3092
49.6%
41.6
3092
8.2%
11.7
Note: Analysis based on individuals providing income and deprivation data in at least five waves.
Coefficients marked ns are not significant in their own right (t is less than 2), but the group of
variables of which they are a member has a significant effect.
87
88
‘Longitudinal’ relationships from year to year
Some of the other sets of characteristics are of interest in their own right:
• The longitudinal association between partnership and deprivation is even stronger
than the underlying version. That is, becoming single increases deprivation,
forming a partnership reduces it.
• Other adults, and children, in the household make a difference to the underlying
position, but changes in family composition from year to year seem to make no
difference.
• Changes in deprivation are not associated with changes in the householder’s
qualifications – but then, hardly any such educational changes occurred.
• Moving into and out of employment is shown to be just as important in the
longitudinal model as being in or out of employment had been in the underlying
model. Movements on or off WFTC or IS still have an effect (though much smaller
than before).
• Moving into rented accommodation increases households’ deprivation scores,
and vice versa; though the longitudinal effect is rather smaller than the underlying
one.
8.3
An illustration
The main conclusion about the difference between the underlying and longitudinal
relationships is an important one, but may be difficult to explain. Figure 8.1 provides
a stylised illustration. The graph is artificial in that it uses straight lines for clarity,
rather than the curves which more accurately represent the relationships at different
levels of income (see Figure 6.2). But the slopes of the lines are derived from the
analysis; the slopes chosen are those calculated at an income of £200 per week.
• The black dashed line representing the underlying effect shows the range of
deprivation experienced by four individuals whose income over the panel period
averaged £200, £400, £600 and £800. The higher their average income, the
lower their average deprivation.
• The series of grey solid lines representing the longitudinal effect shows how
each of those individuals’ deprivation score would fall, if their incomes increased
by £100 from one year to the next. The flatter slope of these lines illustrates how
much slower the rate of fall in deprivation is, than might have been expected
from the period comparisons.
The implication of the analysis is that if a household increased its income by (say)
£100 per week, its deprivation score would fall, but the household would still be
more deprived than some other household which had been £100 per week better
off all the time.
‘Longitudinal’ relationships from year to year
Figure 8.1
8.4
Stylised representation of the underlying and
longitudinal relationships between income and
deprivation
Stable versus unstable households
As explained in earlier chapters, both income and material deprivation are
characteristics of households (or, at least, that is how they are measured). A difficulty
for longitudinal analysis is how to measure changes in household characteristics
when households themselves dissolve and reform. One solution is to confine the
analysis to the subset of households which do not change their membership at all
over the panel period, but these are not likely to be representative of all households.
Another solution is to follow individuals from year to year, ascribing to them the
characteristics of the households in which they live at each wave; this provides a
representative sample, but raises questions about the validity of comparisons of
household characteristics when it is the household itself which changes. The BHPS
analysis up to this point has taken the latter route and followed individuals. It is now
possible to check whether the preferred model provides similar findings for
individuals who lived in the same household throughout the period, and for
individuals who moved between households.
For this purpose, the analysis is confined to individuals who not only contributed at
least five waves of data, but also had no gap in their sequence. At each wave after
their first contribution, the exact details of their current household were compared
with the exact details of their last-year’s household:
89
90
‘Longitudinal’ relationships from year to year
• ‘No change’ in the last year was strictly defined in terms of all the household
members being identical in both consecutive years.
• ‘Small change’ in the last year was defined as involving the addition or subtraction
of one household member, but not if that member was either the householder
or the householder’s partner. This would encompass, for example, births of new
children, and older children leaving home, as long as no more than one movement
happened in any year, and as long as the parents remained together.
• ‘Major change’ in the last year was defined as a change more substantial than
that.
These tests were carried out on each individual separately, and could lead to
different answers for members of the same household. If a child left home (for
example) that would be recorded as a small change for the parents and siblings, but
a major change for the child.
The tests were carried out for each wave (compared with the last). Individuals were
then classified for the period as whole as having experienced no change at any wave;
a small change at least once but no major change, and a major change at least once.
Just over half (55 per cent) of the continuous sample of individuals had no change
over the panel period (of at least five years); just over a quarter (27 per cent)
experienced a small change; just under a fifth (19 per cent) experienced a major
change. As might have been expected, major change most commonly affected
people in their early 20s (40 per cent) and least common in their early 60s (7 per
cent).
There is no reason to expect a change in household composition to be associated
with either an increase, or a decrease, in hardship. The most probable consequence
would be a change in hardship, with increases and decreases balancing out. There
would also be higher than usual rates of change in income, and in other household
characteristics. The key analytical question is whether the relationships between
characteristics and deprivation hold up when individuals cross household boundaries.
That is, does moving into a higher-income household have the same effect on an
individual’s deprivation experience as remaining in a household which increases its
income.
Rather than present the full models in all their detail, Table 8.3 provides key outputs
from between- and within-cases equations similar to those reported in Table 8.2.
The between-cases results are broadly similar for both stable and unstable households,
but we would not have expected the underlying model to be very sensitive to this
point. As predicted, individuals who experienced a major change over the period
had a substantially wider variance between years in both their deprivation scores
and their income, and this helps to validate the legitimacy of our concern about the
issue. Those who changed households recorded a rather stronger than average
relationship between changing income and changing deprivation; this is consistent
with our developing hypothesis that income-differences between households are
more important than changes in income over time within households. But the
‘Longitudinal’ relationships from year to year
overall conclusion is that the analytical approach holds up when applied to unstable
as well as to stable households, and this provides encouraging evidence of its
robustness.
Table 8.3
Between- and within-cases regression equations for the
BHPS deprivation index: individuals in stable and
unstable households
Source: BHPS Waves 6-12
Between-cases
Effect of £10 difference in
income at £200
R2
Within-cases
Within-case variance as a
proportion of total:
Deprivation
Income
Effect of £10 difference in
income at £200
R2
Regression estimates
No change
Small change
Major change
-1.44
47%
-1.09
52%
-1.70
48%
33%
29%
35%
34%
45%
49%
-0.87
4.4%
-0.87
4.4%
-1.03
15.6%
Note: based on equations with all the covariates shown in Table 8.2. The income effect for the
within-cases model includes one year of lag, and is equivalent to the ‘this year and last year
together’ row of Table 8.2. See text for definitions of ‘change’.
8.5
Components of the deprivation index
The combination of survey questions used to define the index of material deprivation
was discussed in Chapter 4 (see especially Tables 4.1-4.4). In summary, three sets of
questions were added together: inability to afford items of daily living, questions
about financial stress, and absence of consumer durables. A further set of questions
relating to housing was omitted from the composite index, because the housing
component failed many of the tests imposed. The four sub-indices, and the overall
index, will now be compared to address three questions:
• whether the components are similarly associated with income;
• whether some components exhibit a delayed response to changes in income;
• whether it was appropriate to combine the three selected components into a
single index, and to omit the fourth.
The three sub-indices which were actually used in the overall index (first three
columns of Table 8.4) all yield rather similar findings – similar to each other, and
similar to the overall index (fifth column). But the overall index performs better on
several counts than its components – larger coefficients and better explanation of
variance. These findings quite strongly support the use of a generalised index to
summarise evidence drawn from different areas of household activity.
91
92
‘Longitudinal’ relationships from year to year
In detail, the coefficients suggest that the sub-index of daily living is most closely
related to income in the underlying model, but its response in the longitudinal model
is sluggish. The sub-index of financial stress shows the most rapid response to
changing income. The equations as a whole explain more of the variance in
consumer durable ownership than the other sub-indices, though since the income
coefficients were not very high, this must be partly because of associations with
other characteristics.
Table 8.4
Effects of income in the between- and within-cases
regression equations, using the components of the
deprivation index as dependent variables
Source: BHPS Waves 6-12
Daily
living
Between-cases
Effect of £10 difference
in income at £200
-1.53
R2
38%
Within-cases
Within-case variance as
a proportion of total: 45%
Effect of £10 difference
in income at £200
Current
-0.52
Lagged
-0.27
Overall
-0.78
R2
4.0%
Regression estimates
Financial
stress
Durables
Housing
3-item
index
4-item
index
-1.02
31%
-1.67
36%
-0.21
16%
-1.41
50%
-1.10
49%
49%
42%
50%
35%
33%
-0.88
0.03
-0.84
3.1%
-0.74
-0.17
-0.91
8.2%
-0.03
0.02
-0.01
1.5%
-0.71
-0.13
-0.85
8.2%
-0.53
-0.11
-0.64
8.3%
Note: the 3-item index is the overall deprivation score used in other analyses. It includes daily
living, financial stress and consumer durables, but not housing. Other co-variates are the same as
in Table 8.2.
One might have expected changes in housing to respond to changes in income
much more slowly than the other indices, and this would have suggested a much
stronger underlying relationship than longitudinal relationship in this case. But in
the event, the housing deprivation sub-index (fourth column of Table 8.2) shows an
exceptionally weak underlying relationship with household income, and no
longitudinal relationship at all. This strongly endorses the decision to omit housing
from the overall index – housing problems may be perceived as a form of deprivation
in the generalised sense of the word, but the evidence suggests that they are not
part of the package of problems included in the overall index, which are so closely
associated with low income.35
35
An obvious question is whether housing tenure was associated with the housing
deprivation sub-index. It was, but the association with housing deprivation was
no stronger than with the other three sub-indices.
‘Longitudinal’ relationships from year to year
The final column of the table shows what the overall results would have looked liked
if all four groups of questions had been included in the final index, rather than just
the three actually chosen. Adding in the weaker associations with housing has the
expected effect of reducing the coefficients: the underlying effects of a £10 income
difference falls from -1.41 to -1.10; the longitudinal effect falls from -0.85 to -0.64.
One the other hand the overall predictive power of the models, and indicated by R2,
is hardly affected by the choice of overall index. So the overall conclusions of the
analysis are not very sensitive to this issue.
8.6
Households with and without children
Much of the policy concern about poverty and hardship focuses on families with
children, and the Families and Children Survey, the BHPS’s partner in the current
project, was designed specifically to examine the experience of those with children.
So we need to show whether the overall conclusions derived from the seven wave
BHPS analysis are broadly similar for households with and without children.
We are still following individuals, classifying them as with or without children on the
basis of the membership of the household in which they live. Obviously children
themselves are all included in the with-children category; so are their parents; and so
would any other adults be if they lived with children. Most of the latter are likely to
be the older (now-non-dependent) brothers and sisters of the children. Each
individual is classified afresh at each wave, so they could move from with-children to
without in the course of the panel period. The analysis is now confined to those who
provided at least four waves of data as a non-pensioner with children, or as a nonpensioner without children, respectively (because sample sizes would be too small if
we maintained the five wave requirement used for other analyses). Table 8.5
presents the comparison. As before, the underlying between-cases model is
compared with the longitudinal within-cases version.
Overall, the two types of household recorded broadly similar sets of relationships.
There was no variable for which families with children had a significant positive
association and families without children had a significant negative one, nor vice
versa. The smaller sample sizes in the two groups help to explain why some of the
coefficients which were significant in the main equations are now not significant.
To make a large table easier to read, coefficients that are substantially larger in one
family type than the other are highlighted in bold. As far as income is concerned,
both family types have very similar single-year longitudinal relationships with
deprivation, though families without children also have a small lagged effect. But
the difference between the two measurements is relatively narrow for households
with children, and relatively far apart for those without children. At the £200 level,
for example, the between-cases effect is only marginally stronger than the withincases effect for families with children, but the underlying difference is more than
double the longitudinal effect when no children are present.
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94
‘Longitudinal’ relationships from year to year
Table 8.5
Between- and within-cases regression equations for the
BHPS deprivation index: households with and without
children
Source: BHPS Waves 6-12
Regression coefficients
With children
BetweenWithincases
cases
This year’s income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
-9.5
0.3ns
0.003 ns
-8.1
0.7
-0.020
Last year’s income
Income (in £100s)
Not applicable Not significant
Income (in £100s) squared Not applicable Not significant
-Income (in £100s) cubed Not applicable Not significant
Effect of a £10 difference
in income at £200
This year only
-0.90
-0.68
This year and last year together
Family composition
Couple householder
Number of other adults
Number of children: squared
-7.0
8.0
0.7
Without children
BetweenWithincases
cases
-22.5
2.0
-0.058
-8.4
0.7
-0.02
Not applicable
Not applicable
Not applicable
-1.3
0.0
0.001
-1.87
-0.70
-0.82
-9.1
1.7 ns
-0.2 ns
Qualifications
Any qualifications
-9.3
-11.9
4.1
-1.3 ns
Not applicable
Not significant
Sources of income
Employment
Working Families’ Tax Credit
Income Support
-9.4 ns
16.9
17.8
-11.5
4.5
7.0
-7.9
-7.9
Not applicable
20.2
2.6 ns
Housing tenure
Outright owner
Tenant
-10.3
16.4
-8.4
10.7
-11.5
18.9
-0.7 ns
14.6
Constant
Sample size (households)
R2
39.4
1,531
48.1%
39.2
1,531
7.2%
65.2
1,819
48.1%
34.3
1,819
8.8%
Note: Analysis based on individuals providing income and deprivation data in at least four waves
as the relevant household type. Coefficients marked ns are not significant in their own right (t is
less than 2), but the group of variables of which they are a member has a significant effect. Bold
type highlights coefficients which were at least 50% larger in one family type than the other (i.e.
comparing the left and right hand sides of the table).
‘Longitudinal’ relationships from year to year
Other points of interest include:
• ‘Other adults’ have a stronger underlying association with deprivation among
families with children than among childless households. In the former case they
are likely to be older ‘children’.
• The new table confirms what Table 8.2 had already indicated – that changes in
the number of other adults in a household from year to year have virtually no
effect in deprivation. Nor do changes in the number of children.
• Income Support has a clear longitudinal relationship with deprivation among
families with children, but no relationship among those without. This helps to
explain the strong income-sources effect observed earlier in the FACS data.
These are interesting variations, but they should probably be seen as details in the
context of the main conclusions of the analysis by family type. The overall shapes of
the equations are similar. They explain similar proportions of the between-case and
within-case variance. And, crucially, the relationships between income and deprivation
remain similar both in shape and size. Families with children are rather less sensitive
to underlying income variations, but the basic conclusions are the same for both
categories.
8.7
Lone parents in FACS
The whole of this chapter so far has been based on analysis of the BHPS, because it
provides a sequence of observations on a representative sample of households long
enough to disentangle the underlying and the longitudinal relationships. One of the
key lessons learned (Table 8.1) is that changes between two consecutive years
provide an underestimate of the sensitivity of deprivation scores to changing
incomes. This means that the two available waves of FACS which cover all families
(Waves 3 and 4) are not a reliable source for the analysis of longitudinal effects.
It is possible, though, to replicate the between-cases and within-cases models for a
subgroup of families who were covered by all four FACS waves. Table 8.6 is confined
to families who were lone parents at Wave 1, and who then provided income and
deprivation data in all three subsequent waves. (Lone parents who acquired a
partner during that period are retained.) It was not possible to calibrate the
deprivation index according to the annual distribution of component scores across
all families in each wave (see Chapter 4), so a revised index was calibrated according
to the annual distribution of scores among lone parents.
Given the different make-up of the two indices, and the restricted composition of
the FACS sample, it would be surprising if the two surveys produced identical results.
The between- and within-cases models based on the FACS are nevertheless
remarkably similar to those derived from the BHPS. In particular, the analysis of
underlying relationships explains far more of the variance, and records higher
income coefficients, than the longitudinal model.
95
96
‘Longitudinal’ relationships from year to year
Table 8.6
Between- and within-cases regression equations for the
FACS deprivation index: families who were lone parents
at Wave 1
Source: FACS Waves 1-4
Regression coefficients
Between-cases
Within-cases
-20.9
1.6ns
-0.032ns
-20.0
-7.6
0.7
-0.021ns
-2.8ns
Not applicable
-1.50
Not significant
-0.49
Family composition
Couple family
Number of children: squared
7.7ns
1.3
Not significant
Not significant
Qualifications
Any qualifications
-7.3
Not significant
Sources of income
Employment
Working Families’ Tax Credit
Income Support
-6.1ns
14.5
32.6
-6.5
5.0
11.8
Housing tenure
Outright owner
Tenant
-17.6
5.3ns
-11.9
9.6ns
Constant
Sample size (families)
R2
17.9ns
1087
32.8%
1.9ns
1087
6.7%
This year’s income
Income (in £100s)
Income (in £100s) squared
Income (in £100s) cubed
Below £125
Last year’s income
Effect of a £10 difference in income at £200
Note: analysis based on lone parents at Wave 1 who provided data at all four waves. Coefficients
marked ns are not significant in their own right (t is less than 2), but the group of variables of
which they are a member has a significant effect.
Review and conclusions
9 Review and conclusions
The findings of the research will be reviewed in this chapter in three stages. The first
section summarises the key conclusions about the relationship between income and
deprivation over time. The second raises some issues about the measurement of
income, and of deprivation, which have implications not only for further research,
but also for the recently announced ‘official’ measures against which progress
towards the elimination of child poverty will be assessed. The third section considers
the potential implications of the findings for future policy development.
9.1
Analytical conclusions
A starting point for this study, derived from most of the previous research in this
field, is an expectation that low household income was closely associated with, and
a probable cause of, high levels of deprivation; and that an increase in income over
time would probably lead to a reduction in deprivation.
Two surveys have been used to unravel the relationships between income and
material deprivation over time. The Families and Children Survey (FACS) has a large
sample focused on those most at risk of child poverty, and a very detailed battery of
deprivation indicators. The British Household Panel Survey (BHPS) has followed a
fully representative sample of households over a long sequence of years. Each
source has been used at points in the analytical sequence where it was especially
useful. Where direct comparison has been possible, there have been some surprising
differences of detail which tend to undermine confidence in the approach; but the
overall conclusions about relationships are reassuringly similar.
The analysis started with a straightforward cross-comparison between ‘poverty’ and
‘hardship’ – both defined as positions at the disadvantaged end of their respective
scales of income and of deprivation. At first, the findings were entirely in line with
what one might have expected. Poor families are much more likely to be in hardship
than others; while well-off families have a very low risk of hardship. Families who
have been in poverty for several recent years report more hardship than those for
whom it was a temporary experience. But then some more puzzling findings
emerged. Among families who had moved in and out of poverty, the risk of hardship
97
98
Review and conclusions
at the end of a period varied according to the number of years poor, but it hardly
mattered whether the experience of income-poverty was recent or some time ago.
Only a small proportion of families who moved out of poverty between one year and
the next, also moved out of hardship at the same time. On the other hand, there was
a general drift out of hardship over the four year period, as levels of deprivation
seemed to decline even among poor families.
Dividing survey observations into two groups in each dimension (poor/not poor, in
or out of hardship, last year/this year) provides clear outputs, but risks
oversimplification. It does not make full use of the mass of detailed information
about families’ incomes, their exact position on a scale of deprivation, and a range of
other characteristics which may help to explain the patterns. A series of questions
from each of the two surveys was used to develop an index of deprivation which had
three key characteristics:
• pooling information about daily living, financial stress and consumer durables
(but excluding housing);
• year-by-year recalibration to convert an absolute to a relative measure;
• a continuous numerical score with an overall range between about -50 and
about +150 (and an average of zero).
It is not possible to explain the units of this scale in terms of a comparison between
specific example families. But it was shown that the poorest fifth of families/
households averaged a score between 30 and 40 (depending on the survey), while
the best-off fifth of households (in terms of equivalent income) averaged between
-20 and -30.
Working out the precise relationship between income and material deprivation over
time turned out to be a complex task, requiring some fairly sophisticated analytical
techniques. The litmus statistic has been the estimate of the effect on deprivation of
an income difference between £195 and £205. This statistic has had something of
a roller-coaster ride as the analysis moved from the simplest possible approach
towards an eventual final estimate (Figure 9.1). Sticking to the BHPS for the sake of
consistency, a straight calculation of income against deprivation suggested a
reduction of 0.61 index points for each £10 increase in income. The relationship is
not straight, though, but curved – it is steeper at low levels of income than at high
levels. This means that a £10 increase in income has a greater downward effect on
deprivation at lower levels of income, compared to higher income levels. Using a
‘cubic’ measure of income trebled the apparent slope of the formula at £200.
Introducing other factors such as family composition, sources of income and
housing tenure reduced the strength of the effect apparently attributable to income
itself. But when families’ experience over the whole period of seven years was
averaged in the ‘between-cases’ model, the ‘underlying’ relationship proved to be
stronger than the ‘cross-sectional’ one. In contrast, the ‘longitudinal’ relationship
measured by the within-cases model was much weaker (although initial estimates
based on consecutive pairs of years underestimated it). And the delayed effect of a
change in income the previous year added to the estimate of the longitudinal effect.
Review and conclusions
Figure 9.1
Reduction in BHPS deprivation score associated with a
£10 increase in income at £200: sequence of improved
estimates
The irony is that the final best estimate of the rate of fall in deprivation associated
with a £10 rise in income is not so very different from the initial rough estimate based
on straight income and cross-sectional analysis. The value of the much more detailed
treatment is that we can be much more confident that the links measured at the end
of the analytical sequence are true ones. And the distinction between the ‘underlying’
and the ‘longitudinal’ relationships provides much clearer insights into the processes
at work.
In fact there are two main differences between the simplest possible and the final
complex measures of the income-deprivation relationship:
• the effects of other disadvantaging characteristics in their own right, as well as
income itself;
• the distinction between underlying and longitudinal relationships.
The idea that factors other than income might play a role is a familiar one, built in to
the standard use of equivalence scales to adjust household income for variations in
needs. As Table 9.1 reminds us, the combination of family composition, sources of
income, housing tenure and other factors is actually more powerful than income
itself. Since most of these other variables are themselves correlated with income, it is
difficult to sort out exactly which factors are pulling and which are pushing.
Nevertheless, the signs are that income in pounds per week is not the only influence
on deprivation.
99
100
Review and conclusions
Table 9.1
Proportion of variance in deprivation indices explained
by each group of factors
Source: FACS Wave 4, BHPS Waves 6-12
Variances as proportion of total
FACS
Income
Family composition
Income sources
Housing tenure
Other factors
Cross-section
BHPS
10.3%
2.4%
18.8%
9.3%
4.7%
13.0%
3.5%
6.5%
10.2%
1.1%
Underlying
BHPS
22.8%
4.1%
11.4%
10.2%
1.0%
Note: ‘central estimates’ from Tables 6.5, 6.7 and 7.2.
Some of the non-income correlations of deprivation are interesting. In particular:
• Couples experience less deprivation than unpartnered individuals with the same
income. This is true of families both with and without children. This might have
been interpreted as a selection effect (people with low deprivation risks tend to
find, and keep, a partner). But the longitudinal relationship is as strong as the
underlying one – that is, people reduce their deprivation score when they find a
partner, and increase it when they lose one. The strength of these effects varies
between sources, but it is quite at odds with the assumption that two adults
have higher needs than one adult. Perhaps couples are highly efficient at
converting income into consumption: two really can live for the price of one!
• Younger children have more of an adverse impact on a family’s living standards
(as measured by the deprivation score) than older children – this is again at odds
with the assumption built in to equivalence scales. The between-cases analysis
showed that deprivation is especially acute when the number of children in the
family exceeds four. But the within-cases analysis showed no sign that deprivation
rises and falls as children are added to or subtracted from the total. This may
mean that it is the types of people who have large families who are at high risk,
rather than that the number of children makes a direct difference.
• Households with at least one adult working 16 hours per week or more have
low deprivation risks, while those claiming WFTC or Income Support all have
high risks. The apparent direct effect of Income Support is especially strong for
families with children. Obviously workers have much higher incomes than benefit
or even tax-credit claimants, and this is an area where the causal effects are
especially difficult to unravel. Nevertheless, income sources do make a difference,
and moving into and out of work is just as important as being in and out of work
(compare the between- and within- coefficients in Table 8.2).
• The equations persistently show that outright home-owners have low deprivation
scores and tenants have high scores, for any given income. This may be a reflection
of the different housing costs faced by the two groups, and that is an area for
Review and conclusions
further study.36 Another interpretation is that capital might enhance living
standards independently of the income it generates, for example by providing
an opportunity to borrow. But there may be a selection effect too: if the needsassessments associated with entry into social housing (for example) tend to favour
families with high deprivation risks, then there will be unobserved factors which
are not taken into account in our analysis.
The second overarching analytical conclusion is that underlying relationships over a
period of time are much more effective at explaining deprivation scores than
variations over time within that period. Of the overall variation in deprivation
between people and between years, two thirds can be attributed to underlying
differences between people’s average position, and one third to longitudinal
differences affecting the same people from year to year. Half of the variation
between people in their average deprivation score can be explained by differences
between those people in their average incomes and other characteristics (Table 9.2,
middle line, left column). But less than one tenth of the variations experienced from
year to year, either side of their period average, can be explained by changes in their
incomes or other characteristics occurring at the same time (middle line, right
column). The combination of these sets of estimates means that the underlying
relationships are ten times as predictable as the longitudinal ones (32 per cent vs 3
per cent, bottom line of Table 9.2).
Table 9.2
Attribution of variance in the deprivation index to
underlying and longitudinal relationships
Source: BHPS Waves 6-12
Proportion of variance attributable to each effect
Proportion of that effect explainable by income
and other factors
Overall proportion of variance explained
Variances as proportion of total
Between-cases
(Underlying)
Within-cases
(Longitudinal)
65%
35%
50%
32%
8%
3%
Note: the first row add across to 100% and is taken from text page 78. The middle row is taken
from Tables 7.1 and 8.2. The cells in the bottom row are the product of the other figures in each
column.
It is important to distinguish, though, between the predictive power of the analysis,
and the slope of the relationship between income and deprivation. The average
deprivation score of an individual with an average income of £205 is 1.41 lower than
someone with an average income of £195 (see Figure 9.1). If the same individual
increased their average income from £195 to £205 over a couple of years, their
36
Adding an estimate of housing costs to the FACS equations did not turn out to
be very helpful. The existing set of BHPS net income variables does not include
an estimate of housing costs.
101
102
Review and conclusions
deprivation score would fall by 0.85 points. On this measure the longitudinal effect
is rather more than half (60 per cent) as strong as the underlying one.
What the coefficients show is the average change between years for all individuals
whose income rises or falls. The point about variance is that each individual’s
deprivation score also fluctuates from year to year in ways which cannot be
explained by income or any of the other characteristics included in the analysis. We
can interpret this in terms of ‘noise’ – small inaccuracies of measurement of both
income and deprivation which produce fluctuating measures of essentially the same
situation. This is not unexpected; the only implication is that too much weight
should not be placed on short-term movements into and out of ‘poverty’ or
‘hardship’ (i.e. across an arbitrary boundary line in the distribution of income or
deprivation score).
9.2
Measurement issues
All surveys provide a broadly accurate description of the population under study,
though all also deviate from strict accuracy because of a combination of measurement
error and sampling error. All the surveys referred to here have large samples (though
not always large enough for our purpose) and have been designed by experts who
know how to minimise the risk of the various kinds of inaccuracy. In general this
analysis has been more concerned with identifying the overall shapes of relationships,
than with the kind of precise accuracy required, for example, to estimate changing
poverty rates. But it has also identified three sets of measurement issues which may
be of wider importance, especially in the light of the DWP’s recent consultation on
the measurement of poverty (DWP 2003b). The three issues concern general
measurement error, very low incomes and relative deprivation.
A general point is that estimates of income and of deprivation over a period seem to
be more effective than a single measure of income taken at the same point in time as
a single measure of deprivation. The implication seems to be that a single year’s
estimate is far from ideal.37 This is partly because a household’s long-run position is
more important than this year’s particular situation. And partly because any
tendency for respondents occasionally to misreport either measure will be ironed
out by the averaging process. Measures of the distribution of income, the prevalence
of poverty, and their relationship with deprivation, are not reliable if based on a
single observation. The FRS, the base for the official HBAI estimates, is the gold
standard in other respects, but the absence of repeat observations looks like a
disadvantage in this context.
37
In principle income accumulated over the whole of a 12-month period should
provide a more reliable estimate of resources than income during the week or
month of interview. But an annual figure may be even more difficult to measure
accurately. The European Community Household Panel survey offers estimates
of both annual and current income. The former are based on much more detailed
questioning, but the latter are more closely associated with measures of
deprivation (Berthoud 2004).
Review and conclusions
A specific point about measuring income is the twist in the tail of the income
distributions identified in four separate surveys, all of which suggest that households
reporting very low levels of income are not exceptionally badly off, but surprisingly
well off (Figures 5.2 and 5.3). This is by no means the first time that the problem has
been identified and discussed (Davies 1995, Goodman and others 1997, Elam and
others 1999), and the DWP’s official income analyses regularly carry a health
warning about very low incomes (DWP 2004). But it seems to us that the potential
consequences of the problem have not been taken sufficiently into account in
official or in academic discourse on income and poverty analysis. There are two
possible explanations. If the disparity is caused by these low-income households
being in temporary straits, that adds to the strength of the conclusion that long-run
resources, rather than spot income, determine living standards. But if the disparity is
caused by occasional serious underestimation of some households’ incomes, then
there are some important implications for measurement:
• the poverty rate would be overestimated;
• estimates of the poverty gap would be even more affected;
• it would be impossible to eliminate the last few percentage points of measured
poverty;
• the data would obscure the experiences of those truly the poorest of the poor;
• estimates of working poverty would be exaggerated (an unexpectedly high
proportion of the very low income group appear to be in work);
• benefit take-up rates would be underestimated, if no allowance was made for
measurement error (the possibility is that the apparently low-income households
failing to claim benefit are not actually entitled to them).
As far as deprivation is concerned, the crucial measurement issue is how to deal with
trends over time in the overall frequency of the components of the proposed official
index (DWP 2003b). (At the time of writing, the DWP has decided what deprivation
questions should be included in the FRS, but not how they will be combined into a
score.) If consumer durables had been in the list, that issue would have been obvious
and unavoidable, and perhaps that is why durables were not included. But the BHPS
shows a long and steady, if gentle, downward trend in the frequency of deprivation
items in both the daily living and financial stress groups of indicators. The FACS
indices (similar in function though containing different specific items) shows a trend
which is both steady and steep.
Some analysts place much weight on checking that respondents ‘cannot afford’ an
item before accepting its absence as an indicator of deprivation, and it might be
argued that this check allows indicators to be given an absolute rather than a relative
interpretation. Valuable though the check question may be, the FACS panel does
not suggest that unaffordability is a very stable, and therefore rigorous, concept.
Table 9.3 shows that, of the long-term non-working families who said that they
could not afford money for trips or a home computer (for example) at the first wave,
103
104
Review and conclusions
about a quarter actually had enough money for trips, or a computer, the very next
wave (even though they were still out of work), and more than half had gained these
things within three years (still without work).
Table 9.3
Access over time to money for trips and a computer,
among FACS non-working families
Source: FACS Waves 1-4
Proportion who could not afford this at Wave 1
Of those, proportion who actually had this:
by Wave 2
by Wave 3
by Wave 4
not by Wave 4
Percentages
Money for trips
Computer
73%
58%
29
44
54
46
21
41
55
45
Note: analysis confined to families who were interviewed, and were not in work, in all four
waves.
The measurement problem is a double one. First, there seems to be a trend in
deprivation scores much greater than can be explained by changes in employment
rates or in incomes. Second, two surveys give very different accounts of the rate of
change, especially in the arena of ‘daily living’ which is the focus of the official list of
indicators. Until we know which of the two surveys was ‘right’, and what was
‘wrong’ with the other survey, we cannot know for sure which version of the trend
the FRS will eventually provide. But whether the underlying trend is slow or fast,
some method of continuous recalibration is required if the new index is to provide a
valid measure of relative deprivation over a period. Otherwise deprivation-poverty
will disappear of its own accord.
9.3
Considerations for policy
The theoretical discussion in Chapter 1 distinguished between weak and strong
assumptions about the role of a deprivation index in identifying the poor. The weak
assumptions are that the information about daily living, financial strain and durables
are merely indicators of living standards, which can be used to calibrate more
objective measures of income-poverty, and to monitor variations between groups or
over time. The strong assumptions are that the index is a direct measure of the actual
experience of poverty, which can be used to count the poor. The analysis in this
report has remained within the limitations of the weak assumptions, though much
of it can no doubt be applied to strong interpretations. Either way, it can be assumed
that the objective of policy is to reduce the number of families who are relatively
deprived, or in hardship. The findings of the analysis indicate some potentially
important lines of strategy.
Review and conclusions
The summary of analytical conclusions in the first section of this chapter emphasised
two departures from the simple low-income-means-high-deprivation account. One
was that a series of other factors, besides income, is associated with deprivation; the
other was that the longitudinal relationships are different from, sometimes weaker,
and much less well-determined than, the underlying relationships. These two sets of
conclusions have distinct policy implications.
The use of equivalence scales has become so familiar that their assumptions are
taken for granted. It is often argued that assigning the same tax credit allowances to
lone parents and to couples with children penalises the couples, given their greater
needs. So it would, if couples really were worse off than lone parents at any given
level of income. Deprivation analysis is by no means the only relevant consideration,
but suggests that the opposite is true, and the policy conclusion might be to increase
the rate of benefits to non-working lone parents, rather than adjust the rate for
working couples.
The finding that pre-school children have a stronger adverse effect on a family’s
living standards than older children (for a given income) provides strong support for
the present government’s decision to level up rates of benefit – indeed it might be
argued that young children should attract higher, rather than equal, allowances.
The very high deprivation scores recorded by families with four or more children are
difficult to explain simply in terms of the number of mouths to feed. Year on year
changes in family size have little effect on deprivation scores, and there may be some
unobserved characteristic of large families which creates an exceptional risk of
hardship. In any case, it may be appropriate to focus policy attention on this group.
Perhaps the most important finding in the current policy context is that employment
is associated with reduced levels of deprivation, independently of its effect on
income. The relative strength of the income and employment effects may be difficult
to measure, but there is no doubt that the employment effect is strong (especially for
families with children); and the longitudinal analysis supports the view that it is a
causal one. This seems to provide strong support for the current view that ‘work is
the best route out of poverty’.
Households who receive various benefits and tax credits for long periods have
persistently high levels of deprivation, and this should not be interpreted as simply
the converse of the employment effects. Moving on and off benefit has immediate
consequences, but it is the underlying relationship which is more important. The
implication may be that long-term dependence on benefits creates its own poverty.
That conclusion might encourage policy makers to increase their commitment to
both halves of the mantra, ‘work for those who can, security for those who cannot’.
That is, families for whom work is not a realistic option need more stability and a
higher income, not more conditions and higher incentives.
Further research is needed before we fully understand the apparent relationship
between housing tenure and deprivation. Perhaps not being a home-owner is a
marker for other unmeasured forms of social disadvantage. One reaction would be
105
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Review and conclusions
to encourage even more families to acquire their own home; but the housing and
other positions of the dwindling group of families who remain excluded from
owner-occupation should also be a priority for policy.
The other, and primary, conclusion of the research concerns the difference between
‘underlying’ and ‘longitudinal’ relationships. The outcome of changing characteristics
(income, family structure, employment tenure and so on) is much less predictable
than analysis of underlying relationships might have led us to expect. This is partly
because families’ records of their situation wobbles about from year to year in ways
which are inherently unpredictable. It may be more helpful to focus on the scale and
direction of changes in deprivation associated with changing characteristics:
• Some of the coefficients were just as high in the longitudinal analysis as in the
underlying analysis, and these can be interpreted as causal effects – improving
the characteristic will lead to a reduction in deprivation. These robust indicators
include employment and partnership status.
• Other longitudinal coefficients were lower than their underlying equivalents.
Only part of the overall effect can be interpreted as causal, and investments in
these areas may pay a reduced dividend. These less efficient predictors include
(crucially) income, but also benefits received and housing tenure.
• A third group of variables had no longitudinal relationship with deprivation, and
have to be interpreted as reflecting permanent characteristics of the family, rather
than dynamic influences on living standards. These are educational qualifications
and (surprisingly) large family size.
It is tempting to interpret the underlying analysis as representing the long run, while
the longitudinal analysis represents the short run. The analysis suggests that part of
the effect of an increase or decrease in income will be delayed by a year; there is no
convincing evidence for any further long-run adaptation to changing circumstances.
Nevertheless, there are some encouraging as well as some discouraging signals for
policy makers. The relatively weak longitudinal relationship between income and
deprivation means that families who dip into poverty just for a short a period need
not be a primary area of concern. The converse, though, is that those in long-run
poverty suffer even more deprivation than might have been feared; and that a
temporary escape from poverty will do little to alleviate their position. The implication
seems to be that permanent improvements in poor people’s economic positions are
required, not short-term fixes. That implies, on the one hand, policies to encourage
steady employment, high earnings (and perhaps even marital stability); and, on the
other hand, an adequate income for those who are obliged to remain on benefit for
long periods.
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