Trends in the Distribution of Household Income:  A Fairly Technical Appendix

Introduction

The Distribution of Household Income

Equivalised Household Income

Definitions of Income and the Distribution of Income

The Distribution of Income in Great Britain [from DWP data]

The Effects of Taxation and Benefits on the Distribution of Income

Measuring the overall Distribution of Income: Lorenz Curves and Gini Coefficients

Income Growth, Income Shares and Income Ratios

Document Summary

 

Introduction

I am currently in the process of writing two documents on trends in economic inequality under Conservative governments  1979 and 1997 and Labour governments 1997-2010 respectively. I focus in these documents primarily on the likely relationships between political ideologies and trends in economic inequality and describe the main features of the trends themselves but with relatively limited discussion of the technical details involved in the analysis of the trends in economic inequality. This document might be seen as a technical appendix to the preceding documents in which I do outline in more detail some of the technical issues involved in analysing these trends and links are made from the two other documents to this one which students may use if they require further points of clarification.

However ultimately students will require only summaries  of the statistical information provided in these three documents and in the two other documents on Conservative and Labour governments respectively I provide exercises which should enable students to create their own short summaries which should suffice for examination purposes.

[The trends are analysed in much greater  detail on several internet sites and I shall rely especially on several reports from the Department of Work and Pensions, from the Office of National Statistics, from the Institute of Fiscal Studies and from  Poverty.Org . The articles and reports listed below are grouped in subtopics and asterisked according to the length and complexity. Advanced Level students  might wish to concentrate primarily on  One asterisk [meaning relatively short and sweet !] sources since some of the information provided in the more complex sources is ,in my opinion, pitched at University level although there is no reason why interested students should not pursue their interests further…if there is time!]. Your teachers will be able to advise you how to use these following sources.

Gini Coefficient Trends
Click here for article from IFS on inequality to 2005..**

Click here  for IFS PPT on Inequality and poverty to 2007/8?** . This PPT covers the topic very clearly and concisely and is designed for Advanced Level students.

 

More Detailed Reports
Link to Institute of Fiscal Studies Paper : Racing Away: The Evolution of High Incomes***

Link to Institute of Fiscal Studies Paper: Income Inequality under a Labour Government***

Click here for IFS Report on Poverty and Inequality 2010 ***

Households below Average Income 1994/5-2008/9 [Department of Work and Pensions**

An Anatomy of Economic Inequality in the UK : especially Chapter 2: Section 5: Pages 34-40** Especially useful

 

Comments

Click here for BBC coverage of IFS research on Income Inequality Trends under Labour Governments 1997-2008/09. Especially useful

Click here for Polly Toynbee’s Guardian Article on possible effects of recession on income inequality*

Click here for Guardian article on Danny Dorling’s new book “Injustice”*

Click here for a useful recent graphic from the Guardian [March 2009]*

 

 

The Distribution of Household Income

Since the end of the 2nd World War, on average, people in Britain have become better off and nowadays enjoy higher real incomes and better standards of living. More people have a range of consumer durables such as cars , washing machines and  personal computers and can afford foreign holidays which would have been considered luxuries immediately after the Second World War. However despite this general rise in affluence it is also the case that the actual distribution of  national income even in the early 21st Century is still quite unequal and in this document we shall investigate the extent of income inequality in the UK and /or Great Britain.

The analysis of trends in the distribution of  income presents several technicalities.

1. We must recognise the importance of the various definitions of income which are used in connection with the analysis of the distribution of income. Thus , for example, the overall distribution of income varies considerably depending upon whether we measure it before or after the subtraction of taxation and addition of state benefits.
2. We must recognise the importance of the use of equivalised household income as  a means of placing different types of household within the overall distribution of household income. Thus for example a family with three children receiving a total income of £ 30,000 p.a. will clearly be located at a lower position within the overall distribution of income than a single individual receiving £ 25, 000 p.a.
3. We must understand the construction and calculation of Lorenz Curves and Gini Coefficients which are used to provide summary measures of trends in the distribution of income. If the Gini Coefficient for the distribution falls this means that overall income inequality has fallen and vice versa but how are these conclusions arrived at?
4. Trends in the distribution of income are also sometimes presented in terms of the shares of national income received by various quintile and decile shares and in terms of the ratios between the shares received by highest and lowest deciles and/or quintiles. We shall look at these statistics.
5. However trends in decile and/or quintile shares distract attention from the shares of national income received  by percentiles at the highest and lowest extremes of the income distribution. We shall look at these statistics too.

 

Equivalised Household  Income

Data on the  distribution of household income in Great Britain and the UK  are constructed so as to provide an approximate estimate of differences in living standards  and are therefore based upon the assumption that household incomes are a very important determinant of living standards [although it is ,of course, recognised that they are not the only determinant.] As we shall see, however, if household income are to provide a useful approximation of living standards, it is essential that the incomes of households of differing compositions must first be “equivalised” : that is: the incomes of households of different compositions must be weighted to take account of the fact that larger households require higher incomes than smaller households to achieve a given standard of living and vice versa.

Further explanation of the concept of Equivalised Disposable Household Income can be found in Chapter 5 of Social Trends 2010 and further information on the OECD weighting system used to calculate Equivalised Household Income  can be found in Appendix 5 [page 224]  of Social Trends 2010 . Thus the , for example, the household disposable income before  housing costs of a childless couple is given a weighting of ONE, a single adult household is given a weighting of 0.67, subsequent adults are given a weighting of 0.33 and subsequent children are given weightings of between 0.09 and 0.36 depending upon age.

To calculate equivalised disposable household income divide actual disposable household income by the relevant weights.

Thus for childless couples an actual  disposable weekly household income of £300 = an equivalised disposable weekly household income of £300.[ Actual disposable weekly  household income divided by 1]

For a single adult an actual disposable weekly household income of £300 = an equivalised  disposable weekly  household income of £447.7. [Actual disposable weekly household income divided by 0.67.

And so on. Can you work out the equivalised disposable weekly household income of a household containing a couple and  two children with weightings of 0.36 and 0.14 respectively  if their actual disposable weekly household income is £300?

Households with differing membership but the same equivalised household disposable incomes are placed at the same point within the distribution of  income  data based upon household equivalised income   and it follows therefore that income distribution data based upon equivalised household income  do provide an approximation for the distribution of living standards. Contrastingly if households were positioned within the distribution on the basis of the actual and unequivalised incomes the data constructed in this way would provide a very inaccurate approximation of the distribution of living standards within the population since for example a single person household with an income of £300 per week would obviously have a better standard of living than a couple with one child with an income of £ 300 per week..

Further information on the distribution of equivalised household disposable income is provided below.

Definitions of Income and the Distribution of Income    

In order to describe the distribution of  income   it is first important to distinguish between 5 distinct definitions of “Income” and to note that the distribution of Original Income is much more unequal than the distribution of income after taking account of the impact of taxation and government spending. The impact of taxation and government spending on the distribution of income is analysed in several stages as outlined in the schema below which distinguishes the relevant 5 different kinds of “income” used in the analysis of the distribution of income : original income, gross income, disposable income, post-tax income and final income

1. Original income is income received from employment, savings and investment before government intervention of any kind such as through payment of social security benefits and the imposition of taxation.
2. Gross income =  Original income + social security cash benefits.
3. Disposable income= Gross income – direct taxes and National Insurance contributions.
4. Post-tax income = Disposable income- indirect taxes.
5. Final income = Post-tax income + benefits in kind such as health and education.

 The Department of Work and Pensions. [These data have been collected for Great Britain rather than the UK]

Bearing in mind the above information on the meaning of equivalised household income and the various possible measures of income used to analyse the distribution of income let us consider the following data from the Department of Work and Pensions on the distribution of income in Great Britain.

 

 

In relation to the diagram we may note the following main points.

1. The definition of income adopted in this diagram is disposable income before the subtraction of housing costs: [i.e. BHC]
2. You will notice that households are allocated to £ 10 bands within the income distribution on the basis of equivalised weekly household income [which has at least made it worthwhile for you to take the trouble to understand the meaning of this term.] My following references to “income” in the following 9 points refer to “weekly equivalised household income.”
3. The diagram illustrates the number of individuals in   households receiving varying levels of equivalised income grouped into £10 bands. For example almost 600,000 individuals were living in households with equivalised incomes of between £0-£10 per week. [This may have been a very temporary situation for them occurring at the time when these survey data were collected.]
4. The alternating dark blue and light  blue blocks refer to deciles of the households within the population. Thus ,for example, the diagram illustrates that the lowest decile [i.e. the lowest 10%] of income recipients received incomes varying between £0-£180 per week. and that the next lowest decile received incomes of between £180-£ 260[approx] per week and so on. Each decile contains approximately 5.7million individuals.
5. In any analysis of the distribution of income it is important to distinguish between the mean and median incomes of the population. We may use the following hypothetical example to illustrate the difference between mean and median income. Imagine 5 households with the following weekly income levels: £940 p w;  £620 per w ; £ 350 per w;  £130 per w; and £60 per w. To calculate the mean weekly household income we add the 5 weekly household incomes and divide by the number of households= £2100/5 = £420. per week  The median household weekly income is that which is the middle value of our 5 household incomes and in this example it is £350 per week .
6. The overall distribution of income shown in the diagram is said to be skewed in the sense that a large proportion of households are positioned fairly close the median income while a minority are positioned at  the higher end of the distribution. The high incomes of the minority of individuals at the top end of the income scale have the effects of raising the mean  income so that in fact 2/3 of individuals in Great Britain receive the incomes below the mean income. and this means that it is  also important, therefore to consider the value of the median income when analysing the distribution of income.
7. The mean weekly household disposable income is £463 per week and the median weekly household disposable income is £ 377 per week . These are the mean and median incomes for childless couple households . The mean and median weekly incomes of households of different compositions are different from these figures and are calculated via the use of the weighting system which is explained earlier in this document.
8. A weekly income of £226 per week for a childless couple represents an income equal to 60% of the median income. This figure is highlighted because individuals with incomes below this figure are defined by the UK government to be living in poverty. I shall provide information on poverty in subsequent documents.
9. Note that  around 80,000 individuals live in households receiving between £990 and £1,000 per week.
10. However there are also about 2.1Million individuals who live in households receiving   weekly incomes above £1000  per week and if we were to subdivide these individuals into £10 income bands  there would have to be a vast extension of the horizontal axis to represent them on the diagram. For example some top professional soccer players earn £100,000 + per week and to incorporate them the horizontal axis would need to extend for about 1.5 metres. Furthermore the Chelsea Football club owner Roman Abramovich has an estimated fortune of £7.5 Billion. If these moneys are invested to yield 5% interest per year after tax how long would the horizontal axis of the diagram need to be to incorporate this individual? Miles?

Activity:  The following activity is based upon the above diagram. 1. The definition of income adopted in the diagram is   “disposable income before housing costs”. Define “disposable income.”2. .Use the diagram to estimate approximately how many individuals live in households receiving  between £0 and £100 per week. {You will need to estimate by eye how many individuals receive between £0 and £10, how many receive between £10 and £20 and so on…] 3 .Use the diagram to estimate how many individuals live in households receiving between £300 and £400 per week. 4. Use the diagram to estimate how many individuals live in households receiving between £900 and £ 1000 per week. 5. How would you have to modify this diagram if you wanted to include  the incomes of very high income recipients in the diagram?

 

 The Effects of  Taxation and Benefits on the Distribution of Income

You may click here to access information from the ONS website which provides a very helpful introduction to some of the issues surrounding the description and analysis of the effects of taxation and benefits on the distribution of income in the UK. The information will appear in a new window

You may note the following points in relation to these data.

1. The data compare the incomes received by five  quintiles [i.e. sections containing 20% of household units] receiving income ranging from the lowest to the highest income recipients.
2. All households are ranked on the basis of their household equivalent incomes so that for example a family couple with two children receiving say £20,000 per year would be allocated to a lower quintile than a single person receiving £20,000 per year.
3. Comparisons are made between  two of the  5 possible types of income described above: that is: comparisons are made between  the distributions of Original Income and Final Income. Later in the document information on the distributions of all 5 types of income will be provided
4. The data show very clearly that , in terms of the five categories of income listed above, original income is distributed more unequally than final income which in turn means  that the overall effects of taxation and social security benefit policies are to redistribute income from the highest to the lowest income recipients
5. However even after the effects of such redistribution, the highest 20%[i.e. the highest quintile] of income recipients receive incomes which are on average 4 times higher than the incomes  received by the lowest 20% [i.e. the lowest quintile] of income recipients. This is the key conclusion of the data on the distribution of income which I wish to emphasise at this point in this document.
6. Notice also that there are no comparisons between the incomes the top 1% and top 10% of income recipients and the bottom 1% and 10% of income recipients and income differences between these groupings would obviously be far greater than those between the top and bottom quartiles of income recipients.
7. Information on the incomes of the top 1% of income recipients can be found by following the  Link to Institute of Fiscal Studies Paper : Racing Away: The Evolution of High Incomes..

{This section related to Source 3  is a little complicated and you may choose to disregard it when you read through the document for the first time.]

Whereas the above ONS data summarise the main overall effects of taxation and benefits on the distribution of income in the UK, we can use information from Economic Trends to  analyse the effects of government policy in more detail . That is: we can use this information  to separate the effects on the distribution of income of the following individual elements of government policy:

1. the effects of income taxation and national insurance contributions which are shown in the Gross Income statistics;
2. the effects of  social security cash benefits which are shown in the Disposable Income statistics;
3. the effects of  indirect taxation such as VAT which are shown in the Post-Tax Income statistics;
4. the effects of  benefits in kind such as those provided via government health and education services which are shown in the Final Income statistics..

Putting this point another way whereas the above summary linked data from ONS provide  comparisons of  the distribution of original income and the distribution of final income, we should need to compare the distributions of all 5 types of income listed above to provide a fuller description of the effects on government policy on the distribution of income.

In order to make these more detailed comparisons I have extracted some additional information on 2007/08  from the excellent article published for ONS by Andrew Barnard.

Table 1: The Distribution of Income among Households in 2007- 08 [using Household Equivalised Income][ Andrew Barnard  Economic Trends May 2009]

 

 

From Table 1 we may derive some further important conclusions. [Notice in relation to the following points that the figures in the last column of Table 1 are especially significant since they summarise the income ratios of the highest and lowest quintiles of income recipients for the 5 different kinds of income. Thus , for example, in relation to Original income, income recipients in the lowest quintile  receive an average £4651 and income recipients in the highest quintile receive an average £72, 581 giving a Highest quintile/lowest quintile ratio of approximately 16 and so on.]

1 As already shown above in the ONS data, the impact of government taxation and expenditure in 2007-2008  was  to make the distribution of national income more equal as shown  by the statistic that  the ratio of original income received by the highest quintile  to that received by the lowest quintile was16 whereas the ratio of final income received by the highest quintile  to that received by the lowest quintile  was 4.

2. It is very clear that the main mechanism for this increase in equality is provided by social security cash benefits which are paid disproportionately to lower original income recipients and which therefore cause gross income to be distributed far more equally than original income. Note the change in the final column figure from 16 [original income] to 7 [ gross income]

3. In order to analyse the effects of taxation on the distribution of income we must distinguish between proportional, progressive and regressive taxes. Individual taxes may be classified as proportional where as income increases the proportion of income paid in taxation remains constant;  as progressive where as income increases the proportion of income paid in taxation increases; or as regressive where as income increases the proportion of income paid in taxation falls.

Income taxes, employees national insurance contributions and the council tax are defined as direct taxes and these combined direct taxes are progressive and cause income inequality to be reduced such that whereas the highest quintile of gross income recipients receive 7 times higher gross incomes than the lowest quintile of income recipients  the highest quintile of disposable income recipients receive 6 times higher disposable income than  the lowest quintile of disposable income recipients. Direct taxation therefore increases income equality but it does not do so by much .

4.The redistributive effects of direct taxes  on the distribution of income are  more than offset by the effects of regressive indirect taxation [mainly VAT and duties on alcohol and tobacco] which cause the  Highest quintile : Lowest quintile ratio to rise back to 7. The following data illustrate the regressivity of various kinds of indirect taxes.

 

5. Finally benefits in kind serve to increase income equality as is indicated by the fact that  for final income the ratio of highest quintile income recipients to lowest quintile income recipients has fallen to 4.We might for example envisage that many pensioners are relatively poor and also disproportionately likely to use the health services; that large families are disproportionately likely to be poor and also have children likely to be using state  education services and also that households in the highest quintile are more likely to use Private Education [and Private Health Care] which reduces the average benefits in kind gained via the use of state education and health Services. However upper quintile families who do use the state services are likely to benefit disproportionately from them in that, for example, they may use the services of their GP more effectively and the children of middle and upper class parents are more likely than the children of working class parents to achieve educational success.

Analysing Trends in The Distribution of Income Over Time: Lorenz Curves and Gini Coefficients.

1. Lorenz Curves and Gini Coefficients

In order to illustrate the trends in the UK distribution of income over time I shall rely on one source of data from ONS. However before consideration of the ONS Data  I need to provide an explanation of the uses of the Lorenz Curve and the Gini Coefficient as tools for the description and analysis of the distribution of income because the ONS source that we are about to consider makes use of the Gini Coefficient which as you will see is related to the Lorenz Curve.

Diagram 2: Lorenz Curve and Gini Coefficient [I am unable to cite the Internet Source for this diagram.  With apologies!]

% Share of Income

With regard to the above diagram you should note the following points.

1. The diagonal illustrates the line of perfect income equality because it implies that every single member of the population receives an identical income such that the lowest 10% of income recipients receive 10% of national income as do the next lowest 10% of income recipients and so on.
2. If f national income is distributed along the horizontal and then the vertical axis this would imply that national income  distributed perfectly unequally since every member of the population would receive zero income apart from the single highest income recipient who would receive the entire national income for him/herself.
3. The actual degree of income inequality in a society is shown by the area between the diagonal and the Lorenz curve measuring the actual distribution of national income in the society.
4. In the above diagram the lowest 20% of income recipients receive approximately 5% of the national income. If you imagine another Lorenz curve which is further from the diagonal, the distribution of national income shown on this second Lorenz curve would be more unequal than the Lorenz curve actually shown in the diagram
5. In general  the closer the actual Lorenz Curve is to the diagonal the greater the degree of equality in the distribution of national income and vice versa.
6. In terms of the above diagram  the Gini Coefficient= Area A  / Area A+B: that is Area A  divided by Area  A+B.
7. If there is total equality there is no area between the diagonal and the Lorenz curve because the Lorenz curve would be the diagonal.. Therefore A=0 and using the formula A/A+B=0, the value of the Gini coefficient is 0.
   If there is total inequality , B=0 and A/A+B=1 and the value of the Gini coefficient is 1. Thus the value of the Gini Coefficient can vary between 0 and 1 and the smaller the Gini Coefficient, the more equal the distribution of income.
8. Some more technical details are involved in the further analysis of Lorenz curves and Gini coefficients but at least this note gives you a basic explanation of Lorenz Curves and Gini Coefficients which will enable you to follow the ONS data to which we now turn.

 

ONS Data on Trends in the Distribution of Income in the UK

You may Click here for  ONS data trends in the Gini coefficient measured in relation to disposable income . In relation to the ONS data you should note the following points

1. The ONS data begin in 1983 but earlier data indicate that the distribution of income started to become more unequal from 1979 onwards.

2. When you access these data  from ONS you will find that trends in the distribution of income are described in terms of the Gini coefficient which has been explained above.

3. The value of the Gini Coefficient increased significantly in the 1980s which indicates that overall income inequality also increased significantly at this time. Reasons for this increase in income inequality included the relatively fast rate of increase in the original incomes of high income earners, changes in taxation which benefited high income earners disproportionately, the high levels of unemployment which affected the poor adversely and the slow growth of social security benefits.

4. The value of the Gini Coefficient fell slightly between 1990 and 1997 implying a slight reduction in income inequality under the Conservative premiership of John Major.

5. Income inequality subsequently increased under the first Labour Government of Tony Blair. but then fell between 2001/02 and 2005/06.

6. Since 2005/06 and 2008/09 there has been little change in the Gini coefficient measured in relation to disposable income although the latest figures do show a slight increase, a factor which was much emphasised by the Conservatives especially in the 2010 General Election Campaign.

7. These  data illustrate that overall  income inequality has changed little under Labour governments indicating that they have failed to reverse the substantial increases in income inequality which occurred under Mrs Thatcher’s Conservative administration of 1979-90 and indeed that income inequality has actually increased since Labour came to power in 1997.

8. Further comparisons between the Conservative and Labour records on income inequality is provided in the two other documents in this series.

Income Growth , Income Shares and Income Ratios

Further more recent information can be found by following the link to  An Anatomy of Economic Inequality in the UK : especially Chapter 2: Section 5: Pages 34-40** . Charts presented there illustrate that income growth has continued to be more rapid for high income recipients than for low income recipients and Gini Coefficient trend information is presented which suggests that although income inequality increased especially in the 1980s overall income inequality was even greater in the latter years of Labour Governments.

However it is also pointed out that another measure of income inequality is the ratio of the incomes of the highest decile of income recipients to the incomes of the lowest decile of income recipients and that on this basis income inequality reached a maximum in 1991, that it declined slightly during John Major’s leadership of the Conservative Government [1990-1997] and declined further , although with some fluctuations, under subsequent Labour Governments.

This means that precise trends in income inequality vary depending upon how income inequality is actually measured and I shall return to this point in the 3rd and final  document in this series.

Anatomy of Economic Inequality in the UK - Click Here

 

Summary

The description and analysis of the distribution of income in the UK does present some tricky problems but the conclusions of the unit may be summarised as follows.

1. We must recognise that the coverage of the relevant statistics relates sometimes to Great Britain and sometimes to the UK.

2. In order to interpret the statistics we must be familiar with the concept of equivalised household income and be aware that several differing definitions of income are used in the analysis of the distribution of income.

3. The first diagram of the document  [from the Department of Work and Pensions] shows that disposable incomes are distributed quite unevenly in Great Britain.

4. Data from the ONS show  that original incomes are distributed more unequally than final incomes  which indicates that the net effects of taxation and social benefits are to redistribute income form high to low income recipients.

5. In order to analyse trends in the distribution of income over time economists and sociologists make use of Lorenz Curves and Gini Coefficients.

6. Gini Coefficient data from the DWP indicate that household income inequality is greater now than it was in 1997 and has reached a maximum in 2008/09.

7. However trends in the ratio of household incomes of highest decile to lowest decile income recipients suggest that income inequality reached a maximum in 1991 and has declined thereafter under both Conservative and Labour Governments.

8. These trends in income inequality are analysed in the two documents on Income Inequality under Conservative and Labour Governments respectively.

Activity:  1. Using a scale from 1-10 where 1 implies very limited understanding and 10 implies full understanding write down a number which describes your understanding of the Lorenz curve.2. Using the same scale write  down a number which describes your understanding of the Gini Coefficient. [I hope you will be able to write down high numbers. If not, it will mean only that I need to improve my explanation of the terms. No blame attaches to you!] 3. The Gini Coefficient for the distribution of income in the UK rose in the 1980s . Does this suggest  that income inequality increased or that income inequality decreased?  4. What has happened to income inequality in the UK since 1979?