Chapter 7 Measuring Economic Inequality

Robert Joyce

What is economic inequality and why do we measure it?

Why are there many measures of inequality?

How do I decide which measure of inequality to use?

What if two measures of inequality show different patterns or trends?

Are all inequality measures reliable?

In 2011, Adbusters—a Canadian magazine that protests against what it believes to be the damaging effects of consumerism—called for a protest against the power of the US financial sector. On 17 September 2011, demonstrators massed in Zuccotti Park, close to Wall Street in New York City and refused to leave.

This was the beginning of the Occupy protest movement. Three weeks later, there were Occupy protests in 951 cities in 82 countries.

economic inequality

This captures how unevenly distributed something is among a population. Economic inequality focuses on how key economic outcomes, such as income or wealth, are spread among the population.

The protestors had many demands (and often disagreed among themselves), but their slogan articulated what they believed to be a fundamental unfairness in society: ‘We are the 99%’. This refers to the belief that the top 1% in society have a disproportionate share of power and influence, and that this power is growing. The explosion of the Occupy movement showed that this is a worry that is widely shared. Economic inequality has rarely been as prominent in public and political debate as it is now.

The British public also perceives inequality and poverty to be growing and we know they find it increasingly unacceptable.

While aggregate measures such as GDP, national income and employment help understand how the overall economy is performing, they do not tell us how resources are distributed between the inhabitants of the country.

There are other statistics that claim to tell us how unequal we are as a society, and how this is changing. But what do these measures of inequality actually mean? How can one number tell you about the relative fortunes of tens of millions of people? These are two of the key questions that this chapter attempts to equip you to answer.

Measuring inequality is only one part of what is needed to make judgements about these questions, or to assess what—if anything—to do about them. For example, most people would want to know how an inequality has arisen in order to assess its fairness, and the inequality statistic itself will not tell you that.

Therefore understanding the measurement of inequality is not a narrow statistical issue:

• Which types of inequality matter? Inequality measures implicitly incorporate many judgements that have nothing to do with statistical theory. The measurement is not (and should not be) divorced from the more fundamental judgements we have to make as a society. Different ways of measuring inequality are more or less appropriate, depending on precisely what it is you care about.
• What is happening that is reflected in the trend? Trends in different measures of economic inequality can tell you a lot more if you view those statistics using some basic insights from economics.
• Inequality is a complex concept. There are many ways of thinking about it and of measuring it. People might define it as the gap between rich and poor or, from a more statistically-minded respondent, the degree of dispersion in how well-off people are. There are at least two important follow-up questions in the context of creating statistics. First, how do we decide how rich, poor or well-off someone is? Inequality with respect to what, exactly? Second, how can we summarise the so-called gaps or degree of dispersion when we are talking about a comparison, not between two people, but very often, between millions? How do we weight what is going on at the bottom, middle and top to arrive at a simple statistic?

7.1 What is inequality, and why do we measure it?

Many of the headline statistics that we are given about societies are based on totals or simple averages: how rich they are, how happy they are, life expectancy in that country, and so on. These are all important statistics, but societies themselves can look very different indeed, even if on average they appear the same. Picture one country where income or wealth is spread evenly throughout its population, and another with the same total resources but where the majority is held by a narrow circle of elites. Most people would think that the difference between these two countries is significant. Measuring inequality is a way of capturing differences of that kind.

7.1.1 Measuring income to measure income inequality

Income is, broadly defined, the flow of financial resources people receive. For people who are working, their main source of income is typically earnings from work. For people who are not working, their income might come from benefits or pensions. In reality, many households have multiple sources of income. In addition, people pay taxes on their income, and this also needs to be taken into account.

Chapter 5 looked at earnings from work, and importantly pointed out that we normally look at wages at the individual level but income on a household or family basis. This implicitly assumes that incomes are shared equally among all members of a household—a simple and transparent assumption, although literature on the topic suggests that there are certainly households where full sharing of income does not take place.¹

disposable income

Disposable income measures the amount of income people have to spend, literally ‘at their disposal’. It is, broadly speaking, their income after deducting direct tax payments (such as income tax) plus any cash benefits they may receive from the state.

When we look at measures of income, we look at earnings plus benefits and pensions less taxes for the household as a whole. This gives as a measure of disposable income—the aim is to capture how much money people have available to spend.

There is one more issue that needs to be dealt with when adding up incomes across all members of a household: how do we take account of the needs of households of different sizes? A single person living on their own might find an income of £500 a week provides them with a good standard of living. But a couple with two children—who have to pay for larger accommodation and additional food and clothing—would tend to find that £500 provides a much more modest living standard.

equivalisation

Equivalisation is the process by which we adjust for the effect of household size and composition on living standards. This reflects the fact that households with more people require a higher level of income to achieve the same standard of living as a household with fewer people in it.

The usual way of adjusting for household size and composition is called equivalisation. This adjusts income based on the number of people in a household, using a standard scale. We will come back to equivalisation later, but it is very important if we are trying to compare the living standards of people who live in different kinds of households.

How it’s done Equivalising household income

When looking at incomes, the usual approach is to consider the incomes of all the people in the household added together. We then compare different households’ income levels in measures for a variety of purposes, including inequality.

One challenge is that households are of different sizes; a household can be a single person living together or a family with children. To maintain the same living standard, a household with more members requires more income. It is therefore common to adjust household income to account for the number of members in the household. This process is called equivalisation.

Equivalisation attaches a weight to each member of the household, according to a common scale. The scale used in the UK, and commonly elsewhere, is the modified OECD scale. This has four main weights:

• The first person in a household is given the weight of 1.
• Second and subsequent adults are given the weight of 0.5.
• Children under 14 are given a weight of 0.3.
• Children aged 14 or over are given a weight of 0.5.

This means that a household of one person living on their own has a weight of 1, while a family comprising a couple with two children under 14 carries a weight of 2.1 (1 + 0.5 + 0.3 + 0.3).

In the UK, it is common for income to be equivalised to a household with two adults, which has a weight of 1.5. The household weights are therefore divided by 1.5 to give an equivalised income.

To calculate the equivalised income, you simply divide the income the household receives by the weighting of the household. So for an income of £500 a week, for a single person that is an equivalised income of £746 (£500 ÷ (1/1.5)). For a couple with two children under 14 it would be £357 (£500 ÷ (2.1/1.5)).

There are obviously many judgements involved in an equivalisation scale around the economies of scale of people living together. It therefore remains an area of active interest and research.

7.1.2 Measuring income inequality using the Gini coefficient

Gini coefficient

A summary of statistics used to capture inequality. The higher the value of the Gini coefficient, the higher the inequality. The Gini coefficient is usually a value between 0 and 1.

income inequality

A measure of how unevenly income is distributed between a population of households.

We will jump straight to the most commonly used statistical measure: the Gini coefficient of income inequality.

The Gini coefficient varies between 0 and 1 (or between 0% and 100% if expressed as a percentage), with a higher figure representing more inequality.

To calculate the Gini coefficient, we arrange the population in ascending order of income. To illustrate this in a very simplified way, we can imagine a population of five people (and we assume that they all live as single-person households).

How it’s done Reporting the Gini coefficient and drawing the Lorenz curve

For each individual in our five-person economy, we calculate their share of total income. We then turn this into a cumulative percentage; in this example, the first two people have 25% of total income between them.

	Person 1	Person 2	Person 3	Person 4	Person 5	Total
Income	£200	£300	£350	£450	£700	£2000
Share of income	10%	15%	17.5%	22.5%	35%
Cumulative income share	10%	25%	42.5%	65%	100%

Figure 7.1a Example data showing income shares of a five-person economy

Example data showing income shares of a five-person economy

Lorenz curve

A curve showing the cumulative proportion of, for example, income that is earned by the households with the lowest incomes. This is plotted by arranging households in order from lowest to highest income; for any share of the population we can read off what share of overall income they earn.

We can illustrate the next stage of the calculation graphically, with the horizontal axis being the share of people, and the vertical axis being the share of income. We can then plot the points shown in the table to form something known as the Lorenz curve. The Gini coefficient is then calculated as the area between the 45-degree line and the Lorenz curve, as a fraction of the total area under the 45-degree line. More precisely, it is calculated as area A divided by the sum of areas A and B.

Figure 7.1b Lorenz curve

Lorenz curve

The area under the Lorenz curve is 0.2 × (5% + 17.5% + 33.75% + 53.75% + 82.5%) = 38.5% or 0.385 as a proportion.

The area under the 45-degree line is 50% or 0.5 as a proportion.

The convention is that the Gini coefficient is between 0 and 1. To calculate the final Gini coefficient, we divide the shaded area A (0.5 – 0.385 = 0.115) by the area under the 45-degree line, which is areas A + B (= 0.5).

We say that the Gini coefficient for this group of households is 0.23, or 23%.

Some extreme examples might help us better understand how the Gini coefficient relates to the Lorenz curve:

• Perfect equality. In this case, everyone would have £400 of income. When you plot the Lorenz curve now, you would find it overlaid the 45-degree line. This means the areas underneath both the Lorenz curve and 45-degree line would be the same, and the Gini coefficient would be zero.
• Perfect inequality. Take the opposite case, where only one person has all the income, so four people have zero income and one person has £2000. In this case, the Lorenz curve will follow the horizontal axis and the Gini coefficient is the whole area under the 45-degree line, and therefore equal to 1 (or 100%).

The Gini coefficient can be generalised to any number of people and to concepts other than income, to measure different dimensions of inequality.

7.1.3 Using the Gini coefficient for comparisons

Figure 7.2 shows how the Gini coefficient varies between different OECD countries. As you can see, the US has higher levels of inequality compared to most European countries. The Nordic countries tend to have some of the lowest levels of inequality.

But we do not only have to measure income, and we do not only have to summarise inequality using the Gini coefficient. Different approaches tell us different things about the underlying reality of economic inequality.

7.2 Inequality of what?

The Gini coefficient is one measure of inequality, but not the only one, and there are many important choices we have to make if we want to report inequality using one measure over another.

We have measured inequality of income thus far, but we could in principle measure inequality in anything that varies across the population. Here we will examine a standard set of metrics commonly used in economic statistics that attempt to provide reasonably comprehensive measures of economic wellbeing: income, consumption and wealth.

Other inequality measures include earnings from employment, food consumption, or pension provision; various causes or consequences of material wellbeing, such as health and education outcomes; and, increasingly, also work at the boundary between economics and other disciplines that try to capture both material and non-material factors, such as happiness or life satisfaction. Kahneman and Deaton (2010), Layard (2006), and Ginn and Arber (1999) are some interesting examples of studies on the topic.

Which to use? When interpreting statistics on different dimensions of economic inequality, it is extremely helpful to keep in mind an economic framework for understanding how these different dimensions are related, why the levels of inequality in each might be different (and might change differently over time), and indeed how these differences can themselves be richly informative about what is actually happening in the world.

7.2.1 The relationship between income, consumption and wealth

Let us start from the definitions of these variables. The basic distinctions are relatively straightforward.

income

The flow of additional economic resources accruing over a given period. For a typical household, this may include earnings and government benefits; for other households, this may include profits from self-employment, dividends or interest on savings.

consumption

The value of the set of goods and services that a household actually enjoys over a given period, for example, spending on food, recreational activities and clothes.

wealth

The stock of economic resources held at a point in time. It can be measured gross—ignoring any debts that need to be repaid—or net—after subtracting debts that will have to be repaid.

• Income: The flow of additional economic resources accruing over a given period. For a typical household, this may include earnings and government benefits; for other households, this may include profits from self-employment, dividends or interest on savings.
• Consumption: The value of the set of goods and services that a household actually enjoys over a given period, for example, spending on food, recreational activities and clothes.
• Wealth: The stock of economic resources held at a point in time. It can be measured gross—ignoring any debts that need to be repaid—or net—after subtracting debts that will have to be repaid.

Some simple economics clarifies the links between these three variables as people move through their lives:

• In each period of life, people have a stock of wealth and they receive an additional flow of income.
• In each period, they consume some amount of goods and services. The resources available to finance this are their gross wealth plus that period’s income, plus any new borrowing they are able to undertake, minus any cost of servicing debt taken out previously. (This abstracts from the possibility of consuming home-produced or publicly-provided goods, which we discuss in Section 7.3).
• If they choose to consume less than their income, the remainder becomes potential consumption in future periods—it adds to their net wealth—and vice versa, if consumption exceeds income.

Let us set this down a bit more formally:

• W_t is the stock of wealth at the beginning of time t
• Y_t is the income received during period t
• C_t is the consumption during period t

Let us also simplify matters by assuming zero interest rates, so that we have the following equation known as the intertemporal budget constraint:

\[\text{W}_{\text{t}} + \text{Y}_{\text{t}} – \text{C}_{\text{t}} = \text{W}_{\text{t}+1}\]

saving during period t is

\[\text{S}_{\text{t}} = \text{W}_{\text{t}+1} – \text{W}_{\text{t}}\]

which gives us the relationship

\[\text{C}_{\text{t}} = \text{Y}_{\text{t}} – \text{S}_{\text{t}}\]

The permanent income hypothesis (PIH), first developed by Milton Friedman, argues that decisions about how much to consume are likely to be related to lifetime income (or more precisely expected future income plus any wealth already accumulated), not simply current income. This means that people smooth their consumption over their life cycle through a combination of borrowing, saving and running down savings.

We can take a stylised case of an individual who spends 20 years in education, 40 years working and 20 years in retirement. We assume further that the individual knows precisely what their income will be at all points in their life, that they begin with no wealth, that they know exactly when they will die, and that they have no desire to leave any wealth behind when they die.

Figure 7.3 shows how income (Y), consumption (C) and wealth (W) vary over the life cycle of this individual. Consumption is equal over the lifetime at c, while income varies between 0 in the first and last 20 years and y in the middle 40 years. Total lifetime income is 40y, which is also 80c as in this example y = 2c. The bottom panel shows how wealth develops, with the first 20 years showing declining negative net wealth as the individual borrows, and peaks just before retirement at age 60.

In this example, the person smooths their consumption completely so it is a constant level of c every year throughout their life. This level of consumption is their ‘permanent income’, and there are fluctuations around it. For some periods, their actual income is below their permanent income, and for other periods, it is above it.

There are many respects in which a pure version of the PIH oversimplifies reality, but these dilute, rather than remove, the key insight for our purposes: someone’s consumption in any one period tends to be related, not simply to their income in that period, but also to income in other periods. The consequences of this for how we measure and understand inequality in these various measures are discussed below.

7.2.2 Income inequality and life stage

Putting the above points together, we note that the ‘permanent’ component of income (or more loosely speaking, lifetime income) will be less unequally distributed than income itself. In our vastly simplified example above, the permanent income is constant at c in every year, but the actual income is zero for half of the person’s life and 2c for the other half. With a population of people just like this—but born at different times—if, at any time we take a year of someone’s life at random, we will see an actual income of either zero or y, but always a level of consumption or permanent income of c.

Again, while reality is obviously far more complex, the same insight applies. At any time, a person’s income is comprised not only of its permanent component, but also of a component that relates systematically to age—for example, career progression tends to mean that income grows systematically through the working-age years, often before falling back during retirement—and a component that reflects all other fluctuations in income over the course of someone’s life—for example, due to job loss). Hence income inequality, as it is usually defined, incorporates inequalities arising from the second two components in addition to inequalities in permanent income.

Analysis of longitudinal data that follow people over significant portions of their lives has confirmed this (Roantree and Shaw 2018). The data points on the left-hand side of Figure 7.4 show two measures of income inequality in Great Britain if you measure them at one point in time, which is the standard approach (see Section 7.3.4 for discussion of these measures). It then shows that these measures of inequality are reduced if we instead repeat the measurement exercise for each person in multiple years, take the total or average of their incomes in each of those observations, and then summarise the inequality across people in that total or average.

The logic of the PIH tells us that inequality in consumption is likely to be lower than inequality in income, since consumption tracks not simply current income, but—to at least some degree—permanent income.

7.2.3 Wealth inequality and life stage

Even more so than with income, it is important to understand the systematic relationship between wealth and age when thinking about inequality across the whole population (i.e. people of different ages).

Again the PIH is important: people tend to build up wealth until around the point of retirement. In our example above, the person saves when they are working and builds up a peak of wealth just before they retire. But look at the scale in our very simple example: this person has wealth of 20c at retirement. This is twenty times their annual consumption or ten times their annual income when working. So the variation in wealth over someone’s lifetime is likely to be much greater than income—which is to say that if, as is very common, we are assessing a population of people of different ages, wealth inequality is likely to appear to be greater than income inequality.

ONS Resource

Read the most recent data on wealth in the UK and supporting commentary, published by the Office for National Statistics.

In summary, one of the reasons why overall measures of wealth inequality can be very high is that the age-related component is especially large. Combining ONS analysis of income and wealth in the UK, Figure 7.5 shows there is a strong age gradient in wealth, and that the differences in wealth between age groups are far bigger than the differences in income. The implication is that wealth inequality is significantly lower within age groups than overall.

7.2.4 The relationship between inequality in income, consumption and wealth

Under additional economic conditions or assumptions, one can derive many other potentially useful implications. But there are some important points to bear in mind when interpreting inequality statistics on income, consumption or wealth.

We should generally expect:

• consumption inequality to be lower than income inequality
• income inequality, and especially wealth inequality, to be lower within age-groups than within a population of varying ages

These two empirical analyses show that consumption inequality is currently significantly lower than income inequality.

Blundell, Pistaferri and Preston (2008) for the US and Brewer and O’Dea (2012) for the UK.

Even if the economic theory is right, the practical data realities can make things a little messier. To give just one example, we often do not observe consumption of goods and services, but just spending. That measured expenditure is often infrequent—not only for classic durable goods like cars, which are the most obvious cases. People might do a weekly food shop, but every few weeks they may spend significantly more by stocking up on tinned food as well as fresh. This ‘lumpiness’ in when people purchase goods can make consumption look artificially more variable than it really is relative to income, if measured by looking at point-in-time spending and income across the population.

We should understand distinctions between different economic concepts—and the patterns in inequality in each of them. But we can be more ambitious than that. A basic economic framework with which to interpret inequality statistics can allow us to combine the rich set of information we have from different inequality measures, in order to learn something deeper about what is happening in the world, than we could get from any one measure in isolation.

A substantial body of research in empirical microeconomics over the past few decades has been doing precisely that. For example, there is now a large body of literature that uses data on income and consumption inequality together—and exploits the conceptual relationship between them—in order to try to identify whether changes in income inequality reflect changes in inequality in the permanent component of income, or more transitory fluctuations (for example, Blundell and Preston, 1998; Blundell, Pistaferri and Preston, 2008). We can also use these relationships to address problems or limitations with some of our data.

For a recent examination of trends in leisure inequality in the US, see Attanasio and Pistaferri (2016).

Attanasio O, Pistaferri L (2016), ‘Consumption Inequality’, Journal of Economic Perspectives, Volume 30(2), pages 1 to 27

None of income, consumption and wealth are actually comprehensive measures of what matter to people. The life satisfaction and happiness measures are potentially much broader in capturing all kinds of other inputs to wellbeing, such as mental health. It is also true when compared to the most basic, stripped-down utility function in first-year economics textbooks, which specifies that people get utility from both material consumption (financed through income and wealth) and leisure. This captures the basic point that people care about the utility they get from the consumption they can afford (net of the disutility from the work they have to do to earn it) and from the things that they are able to do with the rest of their time (whether from ‘leisure’ in the traditional sense, or caring for children or family, and so on).

All else equal, people would rather be able to afford a given level of consumption from fewer hours of work, giving them more time to do other things. It is very rare for inequality statistics to take this point seriously, but it is potentially important, especially when there are large variations or trends in how people spend their time between things like employment, commuting, home chores, childcare and recreation.

7.3 How unequal is a distribution?

There are other inequality measures besides the popular Gini. They reflect implicit judgements about what matters, and different judgements can lead to different conclusions about economic inequality in real-world settings.

We can use the range of different inequality statistics to build up a rich picture of what is going on in the world, rather than simply be confused when they seem to give conflicting messages.

7.3.1 The aggregate measure of inequality does not tell the whole story

As a useful running example, we shall use the changes in inequality in income seen in Great Britain between the financial years 1997 to 1998 and 2004 to 2005. This approximately captures the first two terms of Tony Blair’s Labour government and illustrates some interesting aspects of measuring inequality in a distribution. Using this measure of income, Figure 7.6 shows the average annual growth in income at each percentile point of the income distribution over the near decade in question.

We can conclude:

• Households towards the bottom tended to catch up with households around the middle. For example, income at the 20th percentile grew by 28% while income at the 50th percentile grew by 22% per year. So broadly it seems that inequality within the bottom half of the population narrowed.
• But incomes at the very bottom did not grow as quickly as the incomes of the merely quite low-income group. Although we might question data quality at the very bottom of the distribution.
• Income inequality within the top 20% increased. Those with the highest incomes pulled further away from those in the upper-middle.

So what happened to income inequality overall? It is not clear how we should answer this. The very top clearly pulled further away from the very bottom; but inequality within the middle 60% of the population narrowed.

Statistics such as Gini coefficients are used in public debate as though they are definitive and unambiguous answers to questions about what has happened to inequality. As we can see, these statistics may well be papering over a complex picture of changes in income across the whole distribution.

7.3.2 Ratio and shares measures of inequality

We can simplify Figure 7.6. The figure contains almost 100 data points and these cannot all be communicated every time a policymaker, or a news bulletin, wants to know about inequality and what is happening to it. This is where summary measures of inequality come in.

The inevitable trade-off is that simplification involves losing some information. It may be clear by now that any summary of how overall inequality has changed in Figure 7.6 is going to have to make implicit judgements about how heavily to weight what’s going on in different parts of the distribution. Rather than just showing you the whole picture and letting you decide what weight to attach to different parts of the distribution, a summary measure makes that weighting decision for you and hides the underlying picture.

ratio approach

An approach to measuring inequality that is calculated as the ratio of incomes measured at two points on the income distribution. We might compare the income 90th percentile—which is the income level at which 90% of people have a lower income—and the 10th percentile, which is the income level at which 10% of people have low incomes.

The ratio approach to measuring inequality looks at how incomes at different points of the distribution vary. Continuing with our running example of equivalised household income, we arrange people by order of equivalised household income from the lowest to the highest. We then choose a point on the distribution—such as the 10th percentile, often labelled as P10, which is the income for which 10% of households have a lower level. We then compare the 10th percentile with, say, the 90th percentile by calculating the ratio of the two.

income shares approach

An approach to measuring inequality that looks at what proportion of total income is owned by a particular part of the population.

A variation on the ratio approach is the income shares approach. It has a similarly straightforward interpretation: the top 1% share, for example, is simply the proportion of all income accruing to the highest-income 1%. These share measures depend on the relativity between the incomes of one group—for example, the top 1% or top 10%—and the rest, in contrast to the ratio measures, which depend on the relativity between a specific percentile and another specific percentile.

How it’s done Ratio and shares measures of inequality

Figure 7.7 A hypothetical example showing how the ratio measure of inequality is calculated

A hypothetical example showing how the ratio measure of inequality is calculated

In Figure 7.7, for our hypothetical income distribution, we have flagged the 10th, 50th and 90th percentiles and labelled them as P10, P50 and P90. Note that P50 is also the median.

Perhaps the most common ratio is the 90:10 ratio which is P90/P10. In this example this would be £750/£300 = 2.5. But it is also common to look at the separate 50:10 and 90:50 ratios, as these measure inequality at the bottom and top of the income distribution separately. More generally, this ratio approach can be used to look at any two parts of the income distribution.

For the shares approach (Figure 7.8), we take the shares of income of the highest-income 20%—i.e. those above the 80th percentile, which we call S80. This is then compared to the share of income of the lowest income 20%—i.e. those below the 20th percentile, which we call S20. In Figure 7.8, these are the shaded areas under the curve.

Figure 7.8 A hypothetical example showing how the income shares measure of inequality is calculated

A hypothetical example showing how the income shares measure of inequality is calculated

In this example, the 80:20 share ratio is S80/S20 = 40%/10% = 4. A special version of this measure is something called the Palma ratio, which is the S90:S40 ratio using the notation above. This is the share of the income of the top 10% (above the 90th percentile) divided by the share of the bottom 40%.

Alternatively, we can simply look at the shares of income going to the top or bottom of the income distribution. A common metric in recent discussion is the share of income going to the top 1% of the income distribution.

Let us now apply the ratio approach to understand what happened to income inequality between 1997 to 1998 and 2004 to 2005. We can see that in the decade represented by Figure 7.6, the 90:10 ratio declined: this is because incomes grew by a higher percentage at the 10th percentile than at the 90th. The 90:10 ratio fell from around 4.15 to 3.97, or by around 4.5%, so a fall in inequality.

But this only tells half the story. The fall in the 90:10 ratio is almost entirely due to a decline in the 50:10 ratio from 2.04 to 1.97, a fall of 4%. The 90:50 ratio barely changed, falling by only 1% from 2.04 to 2.02. Loosely speaking, the 50:10 puts all the weight on what has happened within the bottom half and the 90:50 puts all the weight on what has happened within the top half. With that interpretation it was falling inequality at the bottom of the income distribution that most contributed to an overall fall in inequality.

Even that is a somewhat generous characterisation: the 90:50 ratio, for example, is completely insensitive to what happens within the top 10% of the population. Figure 7.5 shows that there were substantial changes in inequality in that part of the distribution. And when we use a measure that captures the very highest income households such as the 99:50 ratio, we see inequality on this measure rise from 4.55 to 4.84, a 6% rise.

As can be seen by this example, these ratio measures are often sensitive to which parts of the income distribution you choose to compare. Each single ratio on its own selects only two pieces of information from a much richer set of information that it has discarded.

Just like the ratio measures, income share ratios are simple, transparent and useful, but they do gloss over a lot of detail. For example, the top 10% share is entirely insensitive to the level of inequality within the top 10% (just like the 90:10 ratio), or indeed the bottom 90%.

In summary, part of the appeal of the ratio and share measures is that they are so transparent about exactly what kind of inequality they are referring to. And by looking at two or three of them together, you will often still get a fairly good sense of how the distribution as a whole has changed. But an unappealing feature is that they ‘throw away’ a lot of information coming from much of the distribution.

A desire for a measure that is sensitive to relative levels of income at every point in the distribution is therefore understandable.

One advantage that the Gini coefficient has over some other summary inequality measures is that it can be calculated including negative values. Sometimes, this is only a minor consideration. In the example of income that we have been using here, this is often the case—although it is not necessarily trivial, due, for example, to self-employment losses. But it can be much more significant when measuring some other inequalities.

ONS Resource

Wealth inequality is a measure of how unequally wealth is distributed across the population. Household total wealth in Great Britain: 2018 to 2020 reports the wealthiest 10% of households held 43% of all the wealth in Great Britain in the period 2018 to 2020; in comparison the bottom 50% held only 9% (ONS 2022).

7.3.3 Comparing measures of inequality

There are several other established inequality indices which, like the Gini, incorporate information about relativities in income throughout the entire income distribution and collapse these into a single summary number. These include:

• mean log deviation (MLD)
• coefficient of variation (CV)
• Atkinson indices

There is one inevitable consequence of having different indices. Each puts different amounts of weight on what is happening in different parts of the distribution.

For example, the Gini is relatively sensitive to what happens around the middle of the distribution when compared to other measures. The MLD and CV tend to be more sensitive to the bottom and top, respectively.

The trade-off with these more complex summary inequality measures (including the Gini) is that, while they incorporate all the available information from the distribution, in doing so they are inevitably more complicated and less transparent about what weight they implicitly assign to different parts of the distribution. If the underlying change in the income distribution is complicated, as in Figure 7.6, the advice is clear. Before making general statements about trends in inequality, check whether they are robust to the choice of summary measure.

When inequalities in some parts of the distribution are falling and inequalities in another part are rising, debates can be had on whether overall inequality is rising or falling. But your choice of summary measures is a highly subjective choice about how to weight different parts of the distribution.

If you want to ensure that you have not missed an important part of the story, there is no substitute for going beyond summary measures and looking comprehensively at how the whole distribution has changed..

7.3.4 Trends in inequality

Figure 7.9 contains ratio and share measures for the UK between 1977 and 2022, as well as the Gini coefficient.

Given the data that we have, there is a striking similarity in how the different measures have moved. In the next section, we will discuss some limitations in the underlying data. This may have increased the estimate of the top 1% share, and hence also the Gini.

Figure 7.10 compares inequality in income and wealth for Great Britain between 2006 and 2020.

7.4 Data limitations and improvements

There are a number of very important practical problems with the data we use.

7.4.1 What kind of data?

micro data

The term used to describe the record-level data from which statistics are compiled. For income data, this means the data about each household— such as their income and composition— that are used to calculate statistics such the Gini coefficient.

The most obvious and basic requirement for the measurement of inequality is micro data, data on the units of analysis (most commonly people or households) between whom we wish to compare economic circumstances. For example, National Accounts data on economic aggregates clearly do not suffice: these tell us nothing about how circumstances vary across the population.

Survey datasets are the most typical basis for the measurement of economic inequality. These are datasets normally collected specifically for research or analytical purposes, in which a sample of people or households is asked directly to report its economic circumstances. Sometimes, respondents are asked to verify their self-reported information using, for example, payslips. The information collected from this sample is then used to estimate the distribution of those circumstances in the population as a whole. From this, measures of inequality can be calculated.

The other type of data that sometimes—and increasingly—contributes to inequality measurement, is administrative data. These are data collected for operational reasons, rather than research or statistical reasons, but they often offer valuable information that can be exploited by analysts or researchers. The administrative data relevant for economic inequality measurement are typically those collected by government—for example, data from the government’s tax records, collected so that the government can calculate and collect tax. These data provide information on the incomes of individuals and can also contribute to the measurement of income inequality.

Survey datasets are most often used in inequality measurement:

• Surveys contain comprehensive measures of our objects of interest. We want to capture income, consumption or wealth, for example, and while administrative data sources provide good measures of specific forms of taxable income or wealth, they typically do not cover other key components. For example, income tax records do not tell us about the incomes households receive from most working-age benefits, or other non-taxable income sources. Similarly, government data on wealth are typically confined to the components that get taxed—for example, wealth that is passed on when people die.
• Surveys can measure households. Administrative data usually collect information on individuals—for example, each individual, rather than each household, who is potentially liable for income tax. But inequality measurement is often more appropriate if it accounts for the circumstances of the whole household. With only administrative data, we usually cannot calculate measures like household income that are used for inequality measurement.
• Surveys track consumption. Consumption inequality is particularly unlikely to be feasibly analysed using administrative data, since governments typically do not have an operational need to collect the kind of data on consumption that would be useful for inequality measurement. VAT, for instance, is collected and handed to the government by firms, not people or households, (even though ultimately they may end up paying for it through higher prices).

Nevertheless, administrative data can also have significant advantages over survey data:

• Administrative data sample sizes are usually large. They are collected by government for operational purposes and so they sometimes cover the entire population of interest. This makes inferences about inequality in the population more robust, and it makes it possible to look in more detail at inequality within, or between, relatively small subgroups.
• Administrative data capture specific subgroups. Surveys struggle to obtain representative samples of groups that—problematically for inequality measurement—are often found at the top and bottom of the distribution.
• There is usually less measurement error in administrative data than in survey data. Surveys rely on self-reports and are therefore prone to reporting biases (for example, due to mistakes in recalling their actual income or spending).

Sometimes, administrative datasets are linked together—so that, for example, benefits data and tax data can be combined—or linked to household surveys if we can be sure that two individuals in the data are in the same household. Some countries have much more advanced infrastructure than others in this respect, due largely to different approaches to data confidentiality.

Reaping the benefits of administrative data for research and statistical purposes is certainly much easier if one is interested in analysing Scandinavia than if one is interested in the UK. For example, the data for Sweden allow data on income to be analysed according to age, gender, location, occupation and educational attainment. That level of detail is not available in the UK, which relies on survey data.

7.4.2 Sources of survey data

As technological—and, in some cases, legal—barriers to the use of large-scale administrative data for statistical purposes are gradually being overcome, their use is becoming more common. There is an increasing tendency to supplement survey data with administrative data in order to get some of the best of both worlds, including in the area of inequality measurement.

There are two main household surveys in the UK that provide information on incomes and are commonly used to measure income inequality, among other things. In addition, there is one household survey that looks at wealth.

The Family Resources Survey is a survey focused primarily on incomes, covering around 19,000 households every year. This is used to produce outputs such as Households Below Average Income, which includes measures of poverty and inequality. This is the strongest source of household income information.

ONS Resource

The Family Resources Survey is used to compile a statistical publication called ‘Households Below Average Income’. This is the primary source of information on income poverty and inequality in the UK.

The Living Cost and Food Survey is a smaller survey of around 5,000 households. The lower sample means that it is less precise than the Family Resources Survey, but has two main advantages. Firstly, it includes expenditure—allowing analysis of both income and spending—which the Family Resource Survey does not. In addition, the Living Cost and Food Survey has data back to 1977, allowing a long time series.

ONS Resource

The Living Cost and Food survey underpins analysis such as the Effect of Taxes and Benefits publications.

The other main household survey that is used to look at inequality is the Wealth and Assets Survey, which can be used to measure household wealth. Measuring wealth can be more challenging than income as, while people may know their income, asking them about the value of their property or pension savings—which are key components of wealth—is more challenging. The challenges with collection mean these data are less timely than for household income.

ONS Resource

Read the main results of the Wealth and Assets Survey.

7.4.3 Alignment with economic concepts: Income and wealth

The data that are feasible and typical to collect do not always align perfectly with the underlying economic concept that they are trying to shed light on. There are differences between income, consumption and wealth in how closely these economic concepts correspond to the data that are typically collected in order to measure them—before we even begin thinking about whether those data are measured with error or are representative.

• Income. If all of a household’s income comes from a salaried job and the interest paid on their bank savings, for example, then a standard household survey designed to measure incomes aims to measure all of this income. There are exceptions, though, which probably impact high-income households more than most. A company owner-manager who retains profits in his or her company, to be taken out at a later date, will be problematic because this is not a stream of income that household surveys even try to capture—there are obvious practical reasons why it would be difficult to do so—even though, economically, it is income in much the same way as income that is put away in a bank account. Capital gains are similarly difficult to measure and are typically ignored.

There is novel work that attempts to include retained corporate profits and capital gains in income measures in a number of countries, and it is typically found to matter.^2 3 4

• Wealth. This can be difficult to quantify accurately, such as rights to occupational pension income in the future. Claims on future state pension entitlements are rarely captured even though, arguably, these are wealth just as surely as are private pension entitlements.

The broadest economic definition of wealth would also include ‘human wealth’ (essentially the present value of the stream of future potential earnings) which is, of course, not directly measurable at all—although there is research that attempts to incorporate it. Abbott and Gallipoli (2019) provide a recent example of this with respect to wealth inequality measurement.

7.4.4 Alignment with economic concepts: Consumption

Consumption is not a concept that directly corresponds to typical data actually collected, so inequality in consumption is both conceptually and practically hard to measure.

non-market goods

Non-market goods and services are those that are not provided through the market. These include some goods provided free of charge or subsidised by Government and own-produced services, such as looking after children.

durable goods

Durable goods are ones that provide an ongoing source of benefits. They are not single-use items. A car, laptop or household furniture are good examples.

consumption lags expenditure

We often buy goods but do not consume them immediately. I may buy a book but not consume (i.e. read) it until later. Likewise, I might consume durable goods, such as a laptop, for a number of years after I have purchased it.

semi-durable goods

A semi-durable good is one that provides some element of ongoing benefit from its use but is not as long-lived as a durable good. For example, clothes may wear out more quickly than a piece of furniture, so are regarded as semi-durable.

• Non-market goods. These include goods or services that are publicly provided (health insurance), publicly subsidised (social housing) or produced within the home. In any of these cases, consumption of these goods exceeds private expenditures on them. It is relatively unusual for consumption measures to account for these. It can be particularly problematic when comparing consumption distributions across countries, given large differences in levels of public provision and—particularly when including developing countries—home production. Within countries, too, it may be important in interpreting trends over time, such as when a good that was formerly home-produced, becomes increasingly bought on the private market (for example, childcare, as maternal employment rates rise).
• Durable goods. These goods can be consumed for longer periods than simply at the point of purchase. The examples that perhaps spring to mind first are things like furniture, cars and large appliances. But the most important case is in fact housing. Those who own their home bought the right to consume their housing in perpetuity at the point of purchase. Ownership of durables means that, in any one period, a household is likely to be consuming things without spending anything on them, meaning that expenditure in that period understates consumption of those things. Conversely, in periods where durables are bought, expenditure will overstate consumption in that period, because the consumer is really paying for the right to consume over many future periods, not simply in the current one. This lumpiness in durable expenditure can mean that, in a cross-section of people where some purchase durables in that period and others do not (but still consume them), inequality in durable expenditures is far higher than inequality in consumption of durable goods.
• Consumption lags expenditure. The last point applies more generally than just to the classic durable goods. Quite a wide array of goods that are bought are not immediately perishable, meaning that the time of their consumption need not correspond especially closely to the time that they are bought (the term semi-durable goods is sometimes used to recognise this point). Food shopping provides a good everyday example. People might buy fresh groceries every week, but every so often they may do a bigger shop, for example if they stock up on things like tinned food. This again creates a disjuncture between expenditure and consumption (at least when measured over relatively short periods), and the lumpiness of spending will tend to make consumption inequality across the population look artificially high.

In principle, an analyst can attempt to convert observed ownership of durables into estimates of the per-period value of the consumption they bring, and add these to non-durable expenditures. But in practice there are significant limitations here. Ownership of durables (and even less, semi-durables) is very rarely comprehensively measured, with housing and cars probably the most common that are included in survey data. Even if ownership is observed, imputing the value of the consumption flow they bring is necessarily an imprecise endeavour because market rental values are not directly revealed (through observed expenditures) but have to be estimated using the limited information available (for example, in the case of housing, the location of a home and the number of bedrooms that it has).

imputed rents

Imputed rents are the costs that homeowners are viewed as incurring for living in their homes. It is based on the idea that, by living in your home, you are foregoing the rent you could charge; as such this is the opportunity cost of owning and living in a home.

Income measures might also try to account for the ‘implicit’ income that households get from durable goods. For example, including imputed rents as part of a broader measure of income. Some more insight into this can be gained from Brewer and O’Dea, 2012.

7.4.5 Lack of representativeness and measurement error

representativeness

Representativeness describes the quality that the sample of data used in constructing statistics is representative of the population as a whole. One simple example is that the gender mix of the sample must be the same or very similar to the population as a whole.

sample weighting

When producing statistics, the achieved sample does not always match the population we are trying to estimate. We can deal with this by putting more weight on the cases that are underrepresented. For example, if the number of men in an achieved sample is lower than the population as a whole, we increase the weight on the men who are sampled to given a more representative picture overall.

By lack of representativeness we mean that the micro data used to construct inequality estimates for a population may not be a perfect microcosm of that population, with certain types of people under- or over-represented. Surveys typically attempt to correct for this through sample weighting—techniques for adjusting upwards the relative weight given to types of household that are known to be under-represented. This is often a very important and worthwhile procedure, but there is never a guarantee that it will truly make the sample perfectly representative with respect to all of the variables that we need. By mismeasurement we mean that a given micro unit (for example, an individual or household) may not have their circumstances (for example, income or wealth) measured accurately.

The details vary, depending on what we are trying to measure and, as discussed above, on the kind of data being used. But in general there is evidence that these concerns can be a particular issue at the tails of the distribution, particularly with commonly used survey data. Overall, it is believed that non-response is highest for the lowest and highest earners.

classical measurement error

This error occurs where there is no bias but just some uncertainty over the true value. The true value is as likely to be higher than the sample estimate as it is to be lower than the sample estimate.

If surveys had classical measurement error, where the mismeasurement is independent of the true value of what is being measured, the impact of the errors would be to bias inequality measures systematically upwards (because they add an additional source of random variation). It is not generally safe to assume that this is the impact of the mismeasurement of economic resources. Evidence suggests that those at the top and bottom are especially likely to have their resources mismeasured, and that this tendency is for them to be systematically under-recorded, at least in survey data.

7.5 Improving flawed measurement

We can safely say that there is scope for controversy when we draw conclusions about inequality. Two particular issues require caution: the top and bottom of the income distribution.

7.5.1 Those on the lowest incomes

Starting at the lowest point of the distribution: household surveys by definition do not attempt to include the homeless, nor those in residential care, nor prison. They are not even in the sampling frame. This means that the survey weights mentioned previously will not address the issue, even if they do a perfect job of correcting for non-random response to the survey. In many cases, administrative data may be little better—if at all better—at capturing the most destitute groups, as these may be precisely those subsections of the poorer population who slip between the cracks of the government’s support networks and hence its administrative systems.

But even if we look at the target group for the household surveys, there are challenges. If we under-record the incomes of the poorest, we might still be overstating the level of inequality in the population.

Figure 7.11 shows the median spending of households when ranked by income.

This looks odd. The lowest level of spending is when income is around £100 a week. But those on incomes less than £100 report median spending that is higher than people earning £100, and sometimes spending is more consistent with those much higher up the income distribution.

There are a number of factors likely to account for this. It could in part be affected by the consumption smoothing suggested by the Permanent Income Hypothesis we explored above. More in-depth analysis suggests that under-reporting of income plays an important role.

Read Brewer, Etheridge and O’Dea’s work on how under-reporting skews the data.

Brewer M, Etheridge B,O’Dea C (2017), ‘Why are Households that Report the Lowest Incomes So Well-off?’, Economic Journal, Volume 127, Issue 605

One may not find this surprising, given that the relative complexity of income sources towards the bottom of the income distribution might bring with it more scope for error. Whereas a typical middle-income household gets a large majority of its income from employment, towards the bottom the array of different state benefits and tax credits become more important.

We have direct evidence that benefits are under-recorded in surveys, from comparing the implied aggregate amount of benefits received in a survey from the amount that the government is actually paying out (Belfield and others (2016)).

In the US too, a series of papers by Bruce Meyer and James Sullivan have argued that incomes at the bottom of the distribution can be poorly measured by surveys and that consumption suffers less from the same problem. See, for example, Meyer and Sullivan (2003).

Administrative data are one promising avenue for improving the measurement of incomes at the bottom. Rather than asking people about their potential myriad sources of income, the government might well hold much of that information already.

7.5.2 Those on the highest incomes

Due to a combination of low response rates and mismeasurement, surveys seem almost invariably to under-estimate the resources of the most well-off. High-end resources are underestimated for income, ^5 6 7 for wealth⁸ and for consumption.⁹

Mismeasurement seems likely to be the larger contributor—at least for incomes—perhaps due to the greater complexity in the affairs of those at the very top.^10 11

Some of these issues are less severe in administrative data sources. There are now estimates of inequality measures, including those very sensitive to the very top of the distribution, for a large number of countries that draw on administrative sources, with efforts made to harmonise measurement across countries to the extent possible

The World Inequality Database is a collaboration between more than 100 researchers covering 70 countries. Although it accepts the data limitations that we have focused on, it has become an authoritative source for data on the wealthy.

You might wonder why we still spend so long worrying about the limitations of surveys to capture the resources of the rich when we could just turn to administrative data. One key problem is the distinction between households and individuals, mentioned earlier in this chapter. To measure inequality in economic resources, we most typically want to measure them for the whole household in which someone lives. On the other hand, most countries’ tax systems are individual-based, so the tax records typically only contain information on the personal income or wealth of the individual.

Hybrid approaches, which try to get the best of both worlds, are possible.. The UK is actually a frontrunner in this. For its headline measure of income inequality, it has for many years used a household survey as the primary basis, while supplementing it with data from administrative tax records to try to improve measurement at the top—a step not taken by any other country in its official measurement of income inequality.

The household survey is the Family Resources Survey, which is used to create a derived dataset of income variables known as the Households Below Average Income dataset (HBAI).

SPI adjustment

The Survey of Personal Incomes (SPI) adjustment corrects for the under-recording of very high incomes in surveys of income. It takes information from income tax data to adjust survey income to provide a more accurate picture of those with the highest incomes.

The administrative data used to correct for under-coverage of top incomes in HBAI is from a sample of tax records called the Survey of Personal Incomes (SPI), and the procedure that uses these data to attempt to correct for under-coverage is known as the SPI adjustment.

Recent research has shown that the SPI adjustment does tend to significantly increase inequality measures such as the Gini coefficient. The same authors have also explored ways of refining the SPI adjustment methodology, and shown that this would likely further increase the measured Gini.^12 13

To deal with under-coverage, two steps are taken as part of the SPI adjustment. The weight given to households containing an adult with a personal income above a certain level is increased in line with the numbers above that level according to administrative data; and the survey measures of the personal incomes of those adults are replaced with values derived from the administrative data, incorporating the knock-on effects on the household incomes of everyone they live with.

Figure 7.12 shows how the SPI adjustment has increased the Gini coefficient for Great Britain.

If you are focused on inequalities that are sensitive to how the very top of the distribution are faring, you should be very cautious about using purely survey-based measures. Despite this, it remains commonplace across the globe for Gini coefficients to be derived from survey data that make no attempt to correct for mismeasurement at the top. Administrative data sources are likely to be significantly more reliable for these purposes, though they, too, have their limitations.

7.6 Summary

In this chapter, we have discussed the main ways of measuring economic inequality. We have particularly emphasised the value of being able to use these statistics in combination with some basic economics and some coherent thinking about what kind of inequality matters to you.

Differences in the impressions given by different prominent inequality measures, with respect to levels or trends in inequality, can often create confusion about what is really going on. Among the key reasons for this are:

1. They sometimes measure inequality in different things, such as income or wealth or consumption, or using slightly different concepts of income or wealth. Here a very basic economic framework for understanding how these variables are related to each other can help clear up a lot of the mess, and indeed can make the differences between measures informative rather than confusing.
2. They sometimes use different statistics to summarise the same distribution, such as the Gini coefficient versus the 90:10 ratio or the top 1% share. Ultimately, the only way to guarantee that you have not missed anything important is to assess the whole of the distribution that these statistics aim to summarise (or the change in the whole distribution), for example via a Lorenz curve. Short of that, the remedy when interpreting different statistics is simply to realise that they are telling you about different parts of the distribution, sometimes very transparently (in the case of ratio or share measures) and sometimes less so (for example,. in the case of the Gini). Again, a good understanding of this can allow you to use the different summary statistics to build up a richer picture of what is going on rather than simply be confused by the differences between them.
3. They can be impacted to differing extents by limitations in the data used to calculate them. One piece of guidance here is to exercise particular caution when dealing with survey-based measures of inequality that are very sensitive to trends at the tails of the distribution, which is where—inconveniently for inequality measurement—measurement issues tend to be most severe.

7.7 Further reading

• Abbott B, Gallipoli G (2019), ‘Permanent-Income Inequality’, Working paper dated March 4th 2019
• Alstadsaeter A, Jacob M, Kopczuk W, Telle K (2016), ‘Accounting for Business Income in Measuring Top Income Shares: Integrated Accrual Approach Using Individual and Firm Data from Norway’, NBER Working Paper No. 22888
• Atkinson A, Piketty T, Saez E (2011), ‘Top incomes in the long run of history’, Journal of Economic Literature, Volume 49, pages 3 to 71
• Attanasio O, Pistaferri L (2016), ‘Consumption Inequality’, Journal of Economic Perspectives, Volume 30(2), pages 1 to 27
• Bee C, Gathright G, Meyer B (2015), ‘Bias from unit non‐response in the measurement of income in household surveys’, unpublished paper, 4 August
• Belfield C, Cribb J, Hood A, Joyce R (2015), ‘Living Standards, Poverty and Inequality in the UK: 2015’, IFS Report 107
• Blundell R, Pistaferri L, Preston I (2008), ‘Consumption Inequality and Partial Insurance’, American Economic Review, Volume 98(5), pages 1887 to 1921
• Blundell R, Preston I (1998), ‘Consumption inequality and income uncertainty’, Quarterly Journal of Economics, Volume 113(2), pages 603 to 640
• Bollinger C, Hirsch B, Hokayem C, Ziliak J (forthcoming), ‘Trouble in the Tails? What We Know about Earnings Nonresponse Thirty Years after Lillard, Smith and Welch’, Journal of Political Economy
• Brewer M, Etheridge B, O’Dea C (2017), ‘Why are Households that Report the Lowest Incomes So Well-off?’, Economic Journal, Volume 127 Issue 605
• Brewer M, O’Dea C (2012), ‘Measuring living standards with income and consumption: evidence from the UK’, IFS Working Paper 12/12
• Burkhauser R, Herault N, Jenkins S, Wilkins R (2017a), ‘Survey Under-Coverage of Top Incomes and Estimation of Inequality: What is the Role of the UK’s SPI Adjustment?’, Fiscal Studies
• Burkhauser R, Hérault N, Jenkins S, Wilkins R (2017b), ‘Top incomes and inequality in the UK: reconciling estimates from household survey and tax return data’, Oxford Economic Papers
• Cowell F (2000), ‘Measurement of Inequality’, Chapter 2 in Atkinson A, Bourguignon F (eds) ‘Handbook of Income Distribution’, pages 87 to 166
• Kahneman D, Deaton A (2010), ‘High income improves evaluation of life but not emotional well-being’, Proceedings of the National Academy of Sciences, Volume 107(38), pages 16489 to 6493
• Kopczuk W (2015), ‘What Do We Know About the Evolution of Top Wealth Shares in the United States?’, Journal of Economic Perspectives, 29(1), pages 47 to 66
• Larrimore J, Burkhauser R, Auten G, Armour P (2017), ‘Recent Trends in U.S. Top Income Shares in Tax Record Data Using More Comprehensive Measures of Income Including Accrued Capital Gains’, NBER Working Paper No. 23007
• Layard R (2006), ‘Happiness and public policy: A challenge to the profession’, Economic Journal, Volume 116, Issue 510, pages. 24 to 33
• Lechene V, Pendukar K, Wolf A (2020), ‘OLS estimation of the intra-household distribution of expenditure’, IFS Working Paper 20/06
• Meyer B, Sullivan J (2003), ‘Measuring the Well-Being of the Poor Using Income and Consumption’, Journal of Human Resources 38
• Office for National Statistics (2018), ‘Wealth in Great Britain Wave 5: 2014 to 2016’
• Piketty T, Saez E (2003), ‘Income Inequality in the United States, 1913–1998’, Quarterly Journal of Economics 118(1), pages 1 to 39
• Roantree B, Shaw J (2018), ‘What a Difference a Day Makes’, Journal of Economic Inequality, Volume 16, pages 23 to 40
• Sabelhaus J, Groen J (2000), ‘Can Permanent-Income Theory Explain Cross Sectional Consumption Patterns?’, Review of Economics and Statistics 82(3) pages 431 to 438
• Silber J, (1999), ‘Handbook of Income Inequality Measurement’, Springer Netherlands

Notes