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Income distribution in Scotland
Sara Grainger & Sandy Stewart, Scottish Executive
Lorenz Curves
Lorenz curves are a useful way of showing graphically the degree of income inequality in a country or region. They can be used to describe and evaluate dispersion of incomes. As they are derived from the entire income distribution rather than just those below a certain threshold, they provide additional context to the more conventional measures of income poverty. Poverty measures generally relate to the number of people whose income falls below a defined amount, usually based on the median of the income distribution rather than the distribution as a whole.
Lorenz curves are easy to construct. The first step is to rank the income of households in ascending order, and then to plot the cumulative share of household income against the cumulative share of corresponding household population. The income measure used for this purpose is the equivalised 1 disposable household income from the Department for Work and Pensions Family Resources Survey (Households Below Average Income datasets).
Chart A1.1 shows the Lorenz curves for Scotland for 2000/01 and 2005/06.
Chart A1.1: Lorenz Curve: Scotland 2000/01 and 2005/06
Source: DWP Family Resources Survey, Households Below Average Income datasets.
Note: Income data are all equivalised and before housing costs.
If all incomes are equal, the Lorenz curve follows the diagonal 'line of income equality', where 50 per cent of the population receives 50 per cent of the income, 60 per cent of the population receives 60 per cent of the income, and so on. As incomes are never equally distributed within a society, Lorenz curves lie below the diagonal. Chart A1.2 shows that the poorer 50 per cent of the Scottish population in 2005/06 received only 28 per cent of the total income, with the richer 50 per cent receiving 72 per cent of total income. The closeness of the Lorenz curve to the diagonal therefore provides a means of assessing the equality of the income distribution. Note from the chart, that the Lorenz curve for 2005/06 for Scotland lies marginally nearer the diagonal that the curve for 2000/01. This demonstrates that the income distribution for Scotland in 2005-06 has moved very slightly nearer to a state of equality.
Lorenz curves may also be used to compare income distributions between regions provided the source data are available on the same basis. Chart A1.2 shows Lorenz curves for 2005/06 for both Scotland and the UK.
Chart A1.2: Lorenz Curve: Scotland and UK, 2005/06
Source: DWP Family Resources Survey, Households Below Average Income datasets.
Notes: UK is inclusive of Scotland.
Income data are all equivalised and before housing costs.
The curve for Scotland lies nearer the diagonal 'line of equality' demonstrating marginally greater equality in Scotland. This has been true for the past 10 years. It can be seen in Chart A1.3 exactly where the differences between the UK as a whole and Scotland lie: in the UK there are proportionately more people with an equivalised net income of less than £60 per week and more than £820 per week, than there are in Scotland.
Chart A1.3: Equivalised household income distribution: UK and Scotland, 2005/06
Source: DWP Family Resources Survey, Households Below Average Income datasets.
Notes: UK is inclusive of Scotland.
Income data are all equivalised and before housing costs.
Gini coefficient
The most widely used summary measure of the degree of inequality in a household income distribution is the Gini coefficient. It represents an overall measure of the cumulative income share against the share of households in the population. The lower the value of the Gini coefficient, the more equally household income is distributed.
The derivation of the Gini coefficient is most easily understood by considering a Lorenz curve of the household income distribution. The area between the Lorenz curve of the income distribution and the diagonal line of equality, as a proportion of the triangular area between the curves of complete equality and inequality, gives the value of the Gini coefficient. The coefficient takes values from 0 to 1 where 0 is total equality, and 1 is total inequality.
The Gini co-efficient for Scotland in 2005/06 is 0.31, equal to that of the OECD average in 2000 2. The UK as a whole is slightly higher at 0.35 in 2005/06. Across 27 OECD countries with data available, Gini coefficients range from 0.23 in Denmark and 0.48 in Mexico.
Chart A1.5 shows how the Gini coefficient in Scotland has changed between 1996/1997 and 2005/06.
Chart A1.4: Relationship between the Lorenz Curve and Gini Coefficient
Chart A1.5: Gini coefficient, Scotland 1996/97 - 2005/06
Source: DWP Family Resources Survey, Households Below Average Income datasets.
Notes: Income data are all equivalised and before housing costs.
The dotted lines show the 95% confidence intervals. Note that the confidence intervals reduce in 2002/03 when the Scottish sample was boosted.
Chart A1.5 provides further context in which to interpret the Lorenz curves shown in Chart A.1. By looking at a full decade's data it can be seen that there has been little change in inequality in Scotland over the past 10 years: inequality rose slightly between 1996/97 and 2000/01 and then fell again until 2004/05. Comparing 2000/01 to 2005/06 suggests that inequality has fallen very slightly, but comparing 2005/06 to 2004/05 suggests that inequality is rising very slightly. However, care should be taken when interpreting the meaning of changes in the Gini coefficients over time as these may mask some structural change which could be identified by comparing Lorenz curves or considering the income of the population in more depth.
Chart A1.6 shows the percentage of total income received by each income decile between 1996/97 and 2005/06. It shows that over the last 10 years the bottom six deciles (60 per cent of the population), and the top two deciles (20 per cent of the population), both consistently received around 40 per cent of the total income, further emphasizing that income inequality has remained largely stable over the past decade.
Chart A1.6: Percentage of total income received by each income decile, 1996/97 - 2005/06
Source: DWP Family Resources Survey, Households Below Average Income datasets.
Note: Income data are all equivalised and before housing costs.
Inequality and poverty
The relationship between inequality and poverty is not straightforward. This is because poverty is usually measured by counting the number of individuals living on an income below a specified threshold, such as 60 per cent of the median. This means that the actual income of the very highest earners, which affects equality measures, has no effect on poverty measures.
It is possible to imagine scenarios in which poverty could decrease but inequality could increase (for example if the income of the lowest four deciles increases, the income of the middle few deciles remains stable, and the income of the top two deciles increases substantially) or where inequality could decrease but poverty remains stable (for example if the incomes of the top two deciles reduced to the same level as the seventh and eighth deciles, but all other deciles remain unchanged).
In Scotland over recent years there has been a very slight move toward equality and also a reduction in the number of people living in poverty. Chapter 5 contains detail of for more detail on poverty estimates and household incomes - see Charts 5.6 and 5.7.
It is households with children who have seen the greatest reduction of low income in the past decade and, as can be seen in the four graphs below, it is children, and working age adults who live in households with children, that have seen the largest move towards equality since 2000/01. In comparison, there has been no change for working age adults who live in households with no children, or pensioners. It is likely that child tax credit, which has had a high take-up rate (82 per cent in 2004/05) has played an important role in this shift. 3 Take-up rates of working tax credit and pension tax credit have been low in comparison (61 per cent and between 61 and 69 per cent respectively in 2004/05) 4 especially amongst the low income groups and this may explain why similar trends have not been observed for these groups.
Chart A1.7: Lorenz Curve: Pensioners, Scotland 2000/01 and 2005/06
Chart A1.8: Lorenz Curve: Children, Scotland 2000/01 and 2005/06
Note: children obviously do not have incomes of their own, by are allocated the equivalised income of the household in which they live: it is the key assumption of equivalisation that all household members benefit equally from the household income, regardless of who earns it.
Chart A1.9: Lorenz Curve: Working age adults living in households with no children, Scotland 2000/01 and 2005/06
Chart A1.10: Lorenz Curve: Working age adults living in households with children, Scotland 2000/01 and 2005/06
Factors influencing the Gini coefficient
At this stage it might be helpful to discuss factors which might influence the value of a Gini coefficient over time.
The Gini coefficient is a dimensionless measure of inequality based on income ratios. It reflects relative incomes without consideration of actual incomes. If an economy grows and the added income is shared across households in proportion to their income, the Gini coefficient would remain unaltered. The Gini coefficient is therefore an important economic measure and should be considered alongside other indicators, such as GDP.
Many factors determine the level of the Gini coefficient. Firstly there are factors which reflect societal change, for example demography and labour market participation.
The long term demographic trends in Scotland show that people are living longer, marrying later, having fewer children and the divorce rate is increasing. These and other factors determine changes in household composition, such as increasing numbers of single and lone-parent households, which are likely to affect the level of inequality. For example, imagine a society in which all individuals have exactly the same disposable income before equivalisation, but in which half the adult population live alone in single person households and the other half of the adult population all live in households with at least one child. The incomes of the adults who live alone will increase after equivalisation while the incomes of the adults who live with children will fall. In this society, inequality of income would be pronounced even though all the adults have the same pre-equivalisation income. Should the two halves of the population decide to form households together income equality would increase markedly. Over the past three decades, the increasing trend for single adult households has probably contributed to growing inequality and therefore rising Gini coefficients. These trends are likely to continue without some form of intervention.
Recent trends in labour market participation show that the number of households in which all adults are working has increased considerably and the number of mixed households, where some adults work but others do not, has been decreasing. This suggests that there has been an increase in labour market participation amongst women with working partners. At the same time, the number of households with no working adults has remained fairly stable. Taken together, this has led to increased polarisation between two-earner and zero- and single-earner households. Again, all other things being equal this would result in growing inequality and a rising Gini coefficient over time.
Secondly, there are factors which can be determined by government policy or controlled by intervention. These include taxation, tax credits, means-tested benefits.
Income tax, for example, is a progressive tax (i.e high earners are taxed at a higher rate than low earners). Varying the parameters of the tax regime, can therefore influence the distribution of disposable income. Taxing high earners more would tend to reduce the Gini coefficient. Universal income tax cuts tend to increase inequality.
There are however, many factors which can effect equality within a society and it is not possible to draw firm conclusions about what has kept the Gini coefficient relatively stable over the past few years in Scotland, or what accounts for the minor variations that we have seen. Similarly, it is not possible to say that the introduction of a single policy will cause equality to rise or fall without full consideration of all other factors and likely future trends.
Scottish Ministers are considering further what to do about both income inequality and poverty as part of its commitment to making Scotland wealthier and fairer.
Any comments on this article can be sent to income.statistics@scotland.gsi.gov.uk or telephone 0131 244 3004.
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