tion can be summarised in three points Boyce, 1994.
1. In a situation where there are benefits as well as costs of environmental degradation, the ex-
tent of the degradation will depend on who is most powerful the winner or the loser. As
power and wealth are often correlated, it is likely that the rich will be the ones with power.
If these are the ones who benefit from the degradation, there will be greater environmen-
tal degradation since the difference in distribu- tion leads to some groups in society not
having the power to counteract the costs. This is the main argument in Torras and Boyce
1998.
2. Greater inequality leads to less concern for the future, i.e. a higher rate of environmental time
preference. The poor have a high environmen- tal time preference as they are concerned with
day-to-day survival rather than future environ- mental degradation. The rich, Boyce argues,
also experience high rates of environmental time preference because political and economic
inequality pose threats to the legitimacy of the powerful for instance, through social unrest.
This prompts those in power to pursue the extraction of short-term profits even if this is
at
the expense
of future
environmental degradation.
3. Environmental degradation is often valued in willingness to pay, which is related to the
ability to pay — income will affect the valua- tion of the costs and benefits. Greater inequal-
ity raises the benefits to the rich, relative to the costs of the poor.
There are clearly a number of other complex relationships between income distribution and the
environment, exemplified, for example, by the ex- tent to which security in low income families in
developing countries is often gained through larger families, which in turn leads to higher
environmental impacts Markandya, 1998, or by the
extent to
which identity
in developed
economies is developed through materially inten- sive consumption patterns Jackson and Marks,
1999. The underlying issue in all of these rela- tionships is the question of the distribution of
benefits versus the distribution of costs. Higher consumption patterns benefit richer communities,
but the cost of these consumption patterns often impact most on poorer communities.
It is clear from these considerations that the relationships between intra-generational equity
and sustainable welfare are complex, but of con- siderable importance. As the UNDP 1996 has
pointed out: ‘average material welfare can be defined by the per capita GDP. However, statisti-
cal averages can mask the diversity that exists within any country. Therefore, from a sustainable
development perspective, it is informative to ex- amine income and wealth distribution throughout
a population.’ This brings us to the issue of how to measure inequalities and how to include con-
sideration of these inequalities into measures of national well-being. This is the subject matter of
the following two sections.
3. Measuring income inequalities
There are several different types of inequality measures. Coulter 1989 divides inequality mea-
sures into four distinct types, according to the mathematical model on which they are based.
These are:
measures based on the combinatorial model;
measures based on the entropy model;
measures based on deviation models;
measures based on the social welfare model. The first type of measure, based on combinatorial
analysis, ‘reflects the probability of randomly se- lecting a pair of identical units for equality polar-
ity or different units for inequality polarity from a pool of units divided among two or more
components’ Coulter, 1989. The second type of index, using the entropy model, is ‘generally based
on an interpretation involving the number of bits of information that are necessary to identify the
location of any unit in its component’ Coulter, 1989.
Measures based on the deviation model aim to illustrate to what extent a value deviates from a
set standard. Measures belonging to this group are mainly based on the absolute, relative and
squared deviations from the mean or mode. These are all frequently used measures for assessments
of intra-generational and inter-generational eq- uity. The most commonly used deviation index is
probably the Gini coefficient. The final type of measure, based on the social
welfare model, attempts to measure the social welfare implications associated with particular
levels of inequality. In this context, social welfare is taken to mean the well-being or happiness of a
society. However, since it is difficult to actually measure well-being or happiness, the utility from
income is often used as a proxy for welfare. For example, Dalton 1920 proposed measuring so-
cial welfare W as the aggregate of the utilities Uy
i
associated with each income y
i
. Thus: W =
i
Uy
i
1 Dalton is also often referenced as the first to
argue that a measure of income inequality could be based on this social welfare model. In practice,
of course, what is required to carry out this measurement is a way of relating different in-
comes to the utility associated with them.
In this paper, we focus on two specific types of welfare measure, namely, a deviation-type mea-
sure based on the Gini coefficient, and a method first proposed by Atkinson 1970 based on the
social welfare model. These two measures are examples of what Sen 1997 classifies as objective
and normative measures, respectively. Where the Gini coefficient is used only to rank different
levels of inequality in an objective fashion, the Atkinson index is normative in the sense that it
incorporates specific value perspectives by relating income inequality to social welfare. In the follow-
ing subsections, we present time series data on the distribution of incomes in Sweden and the UK for
each of these different types of measures.
3
.
1
. Gini coefficient for Sweden and the UK The Gini coefficient is measured as one-half of
the average of the absolute difference between all pairs of relative incomes. The Gini coefficient is
often explained graphically as the ratio of the area difference between the curve of actual income
distribution and the line of equal distribution. The coefficient takes a value between 0 and 1, where 0
represents total equality. The higher the value of the Gini coefficient, the greater the level of in-
equality. Fig. 1 shows the value of the Gini coeffi- cient in the UK and Sweden between 1950 and
1996.
It is clear from the figure that prior to 1980, income inequality declined consistently in Sweden,
mainly as a result of a number of specific social welfare policies. In the UK, by contrast, the dis-
tribution of income remained more or less con- stant until about the mid-1960s. From then, until
the mid-1970s inequality in the UK fell slightly. In both countries, however, income inequality in-
creased during the later years of the period, al- though this trend is considerably more noticeable
in the UK than it is in Sweden.
3
3
.
2
. Atkinson index in Sweden and the UK The Atkinson index can be interpreted as ‘the
proportion of the present total income that would be required to achieve the same level of social
welfare as at present if incomes were equally distributed’ Atkinson, 1983. Atkinson suggested
that it is possible to derive the total welfare corresponding to a particular distribution of in-
come according to the following formula:
W = Y
i
y
i
y
1 − o
·p
i
n
11 − o
2 where Y is the total income; y
i
is the mean income of the i
th
group; y is the mean income of the total income population; p
i
is the proportion of the
3
The Swedish index is based on several different studies, as no single study covers the whole time period in a consistent
fashion. The three main sources were a preliminary study by Bjo¨rklund 1995 on individual income distribution for the
years 1951 – 1958, 1960 – 1976, and on disposable household income distribution for years between 1975 – 1996 from the
income distribution study 1995 SCB, 1997 and Jansson, 1994, 1994a. For a discussion of the data set used, see
Jackson and Stymne 1996. The UK index is calculated for the period 1954 – 1984 from income distribution data compiled
on a tax unit basis and published in Economic Trends ET, various years. A second data set for 1977 – 1996 is based on
income distribution data by household units compiled in the Family Expenditure Surveys FES, various years. For a dis-
cussion of the data set used, see Jackson and Marks 1994 and Jackson et al. 1997.
Fig. 1. The Gini coefficient in Sweden and the UK, 1950 – 1996.
total income population in the i
th
group; and o is a factor which represents the weight attached by
society to inequality in the distribution of income. The Atkinson index is then defined by:
I = 1 − W
Y 3
Since welfare falls as the inequality of income distribution rises, the Atkinson index provides an
increasing function of inequality in the economy, defined by the difference normalised with respect
to total income between the total income and the welfare which it delivers. In a perfectly distributed
economy, y
i
= y for each income group, and so
the welfare level is given by: W = Y
i
p
i
n
1 1 − o
= Y
4 In this case, the inequality measure I reduces to 0,
as would be expected. The factor o is an important parameter in the
measure. It represents society’s preference for equality of distribution of incomes. Since it is
possible to conceive of societies which have a positive preference for an unequal distribution of
income, it is clear that o can take both negative and positive values. When o = 0, society is indif-
ferent to the distribution of income, and welfare again reduces to the total income in the economy:
W = Y
i
yi y
·p
i
n
= Y
5 and welfare is considered equal to the total in-
come.
4
The parameter o therefore allows explicitly for the possibility of attributing different welfare
levels according to different attitudes towards in- equality in society. A value of 0 would mean that
society is indifferent to the distribution of income. As the value of o rises, more weight is placed by
society on the lower income groups. When o reaches , society will accept nothing less
4
To see this, note that y = YP where P is the total income population and Yi = y
i
·p
i
·P is the total income in the ith group. W then reduces to S
i
Y
i
= Y
Fig. 2. The Atkinson index for Sweden and the UK, 1950 – 1996.
than total equality for all sectors of the popula- tion. By contrast, a value below 0 would mean
that society is prepared to lose some income in order to achieve greater income inequality.
The value of o can be determined, in theory, in terms of transfer efficiency. The method is ex-
plained by Atkinson 1983 through a ‘thought experiment’ in which he looked at how much a
rich person would be prepared to lose in transfer costs from administration or inefficiency for ex-
ample when distributing income from the rich to the poor. According to Atkinson, a transfer will
only take place if the net benefit including trans- fer losses is positive. This thought experiment
provides a formula for determining o given by:
1 x
= d
o
6 where x is the proportion of income that is to be
transferred to the poorer person for the rich per- son to accept the transfer and d is the propor-
tional distance between the rich and the poor person. As an example, suppose that a richer
person has twice the income of a poorer one i.e. d = 2 and that she is prepared to lose 40 pence
in transfer costs i.e. x = 0.4. Then o is given by 10.6 = 2
o
i.e. o = 0.74. Fig. 2 illustrates the value of the Atkinson
index for Sweden and the UK between 1950 and 1996, using an o value of 0.8.
5
The basic trends illustrated in Fig. 1 are also apparent in Fig. 2: improvements in income distri-
5
The income distribution data for the UK has been taken mainly from a report prepared by the Institute of Fiscal
Studies providing decile shares of post tax income for the years 1961 – 1991 See Table 2.3 in Goodman and Webb 1994. For
the years not covered by this study, we have used an index based on Gini coefficient data to extrapolate the Atkinson
index. For Sweden we have used disposable income per con- sumption unit for family units in decile groups published by
Statistics Sweden Statistiska meddelanden: Be21SM various years. For those years where income per consumption unit
was not available, income per family unit was used and linked to the years where income per consumption unit was available.
For those years where no decile data on disposable income could be found, we used an index based on Gini coefficient
data to extrapolate the Atkinson index.
bution during earlier years of the period are offset by greater inequality in the later years. Again, the
trend towards increased inequality since about 1975 is more marked in the UK. In this case,
however, Fig. 2 provides an interpretation of this increase in terms of social welfare. The Atkinson
index I can be interpreted as the loss of welfare associated with a given level of inequality in the
distribution of incomes. Fig. 2 reveals that in 1978 this loss of welfare for the UK was around 6.5,
a slight improvement over the 9 loss associated with income inequality in 1950. By 1996, on the
other hand, the welfare loss had more than dou- bled to over 14.
4. Incorporating income inequality into a welfare index
