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# CORE Insights A world of differences:an introduction to inequality

The authors of this Insight are:
Suresh Naidu: Columbia University
Rajiv Sethi: Barnard College, Columbia University and Santa Fe Institute
Sarah Thomas: Barnard College, Columbia University

1 June 2021

Concepts in this Insight are related to material in:

Unit 1, Unit 5, Unit 10, and Unit 19 of The Economy.

Unit 1 in Economy, Society, and Public Policy.

Highlights

• Inequality among people, households, social groups, and countries can arise along a number of dimensions, such as income, wealth, education, legal and social status, and exposure to crime or police abuse.
• Economists tend to focus on inequality in income and wealth.
• Some inequality arises because of differences in talent and effort, and some because of differences in opportunity, for example, due to differences in family income or education, neighbourhood safety, school quality, race-ethnicity, gender, and nation of birth.
• Some degree of inequality arising from individual talent or effort is often considered acceptable—and indeed necessary—in order to provide incentives for productivity and performance.
• However, inequalities can also thwart the development of talents and blunt the rewards for effort, resulting in outcomes that are unfair and deprive the economy of the talents and creativity of the excluded.
• Two important tools for the measurement of inequality are the Lorenz curve and the Gini coefficient.
• Policies to address inequality come in two forms: pre-distribution of market income, which focuses directly on rights and opportunities, and redistribution of market income, which focuses on taxes and transfers.

## 1 Introduction

Camden and Cherry Hill are adjacent municipalities of similar population size in southern New Jersey in the United States (US), just six miles apart. As far as lived experience is concerned, however, they might as well be in different worlds.

In 2019, the median household income in Cherry Hill was $105,022. The high school graduation rate was above 94%, and the overwhelming majority of high school graduates went on to college. Just 1.5% of the adult population was unemployed, and less than 5% had no health insurance. Among those aged 25 and older, 54% had a bachelor’s degree or higher. And over the six-year period 2013–2018, there were two murders in this community. In the same year, in neighbouring Camden, median household income was$27,015. The high school graduation rate was below 70%, and just a third of high school graduates went on to college. More than 8% of the adult population was unemployed, and 12% had no health insurance. Among those aged 25 and older, less than 10% had a bachelor’s degree or higher. And over the six-year period 2013–2018, there were 214 murders in this community.

Now consider two children born on the same day, one in Camden and the other in Cherry Hill. Over the course of their lives, they will likely face very different conditions at home, at school, and in their neighbourhoods. To some degree their own talents and efforts will shape the course of their lives, but the flourishing of these talents and the rewards for their efforts will depend a great deal on circumstances outside their control. The degree to which their family and social networks will enrich their development will vary substantially, and even their likelihood of survival into adulthood will differ. And if they both make it through high school, their prospects for higher education and later employment are unlikely to be the same.

accidents of birth
Differences in life prospects that arise from factors beyond your control, such as the wealth or educational attainment of your parents.

Differences in life prospects that arise from such factors as the wealth or educational attainment of your parents are called accidents of birth—accidents because you have no control over them. Where you were born is another accident of birth. You have no control over the country in which you were born, and yet, it is an important determinant of the type of life you will lead. Today, the country in which you are born is one of the strongest predictors of your future economic well-being. And within countries, as the example of Camden and Cherry Hill illustrates, the neighbourhood in which you were born can play a major role in determining the opportunities that become available to you over the course of your life.

For more details on how income inequality within and between countries has increased over time, see Section 1.1 of The Economy.

Other accidents of birth include the ethnicity and religion of the family into which you were born, your assigned sex at birth, your height, and the primary language spoken at home, all of which can shape your experiences and outcomes. Being born at a time and a place that values certain innate abilities over others is another way an accident of birth can translate into economic inequality: being a natural at moviemaking doesn’t help if you’re in a society without movies.

Section 19.2 of The Economy gives further examples of inequality related to accidents of birth.

In this Insight, we start with a set of basic questions about economic inequality: What is inequality? What are the reasons to be concerned about it? And how do economists measure inequality?

## 2 The meaning and evaluation of economic inequality

Inequality can arise along many dimensions. Economic inequality typically refers to inequality in the distribution of income and wealth across individuals, families, households, or groups in a society. Other forms of inequality include differences across people in status, rights, and opportunities. The right to vote in the US was originally restricted to white, male property owners in most states. This right was formally extended to African American men in 1870 and to women in 1920, but many barriers to voting were subsequently erected, including poll taxes, literacy tests, and felon disenfranchisement. Some of these remain in place to this day.

inequality of opportunity
Differences across people that arise because of barriers to access, such as school and neighbourhood quality, or discrimination based on race or gender.
inequality of outcomes
Differences across people in the material dimensions of wellbeing arising from any source, including family background and individual talent and effort.

As far as economic inequality is concerned, scholars distinguish between inequality of opportunity and inequality of outcomes. Inequality of opportunity refers to differences across people that arise because of barriers to access, such as school and neighbourhood quality, or discrimination based on race or gender. Such differences imply that some are less able to profit from their talents and efforts than others. Inequality in outcomes refers to differences across people in the material dimensions of well-being arising from any source, including family background and individual talent and effort. This view takes an outcome-oriented perspective, hence the name.

Some people think that society should primarily focus on equality of opportunity: inequality arising from individual differences in talent or effort is acceptable, but inequality arising from ‘accidents of birth’ such as gender, ethnicity, and family background is not acceptable. Others believe that extreme inequalities of outcome, and the material and social deprivation associated with them, ought to be reduced regardless of their source.

### Question 1 Choose the correct answer(s)

Which of the following are examples of inequality of opportunity?

• Antonio earns more money working in finance than his college roommate Lorenzo does as a prosecutor for the federal government.
• In many countries, girls still lack the same access to education that boys have.
• Anita has an easy time finding a good-paying job after college because her parents have many connections and can help her land her first job. Anita’s roommate, Sonia, has no such family connections and has to work a part-time job after graduating until she finds something better.
• In a company, employees that work together on a team project and have the same position in the firm are paid a bonus according to their individual performance in that project.
• This example illustrates inequality of outcomes. Antonio and Lorenzo have different incomes because they chose to work in different occupations.
• Here, gender affects an individual’s ability to profit from their talent and efforts.
• Family connections give Anita access to a wider range of opportunities, which in turn increases her ability to profit from her talents and effort.
• This example illustrates inequality of outcomes, because the employees have the same position in the firm and the same opportunity (the team project), so any differences in outcomes (the bonus) are largely due to differences in talent, effort, and luck.

### Exercise 1 Inequality of opportunity or inequality of outcomes

Jasmine grows up in an upper middle-class family. She enjoys science, works hard, and develops an interest in physics during high school. After attending an elite college, she gets accepted into a PhD program with a leading research lab. Later, she is hired at a tenure-track university position as a physicist in one of the top physics departments in the country.

Omar is not related to Jasmine. He also develops an interest in physics during high school. His interest and talents in the subject match those of Jasmine’s. Omar is unable to attend an elite college due to financial constraints and so he attends a lower-ranked university while working a part-time job. Omar does not benefit from the same level of education and associations that Jasmine has access to, and, therefore, is not accepted into a top PhD program. Even though he wanted to become a physicist, he becomes a wind turbine technician instead, making a lower income than Jasmine. If his family’s economic circumstances had been different, Omar could have ended up where Jasmine has.

Isaac is Omar’s brother. Isaac has had a similar upbringing to Omar, but his talents and interests are different. He does not go to college. Instead, he finds work as a cab driver making less than Omar.

1. Which of the differences between Jasmine, Omar, and Isaac reflect inequality of opportunity?
2. Which differences reflect inequality of outcomes?
3. Thinking about the country and society you live in, write two scenarios similar to those given in this exercise, with one scenario illustrating inequality of opportunity and the other scenario illustrating inequality of outcomes.

Certain inequalities that arise from accidents of birth seem arbitrary and unfair to most people, especially when such inequality is associated with mistreatment and discrimination targeted at specific groups, or lack of access to adequate nutrition, quality schooling, or a healthy environment. Yet certain accidents of birth—such as athletic, academic, or musical talent—when combined with discipline and effort, can give rise to income inequality that may be considered reasonable or fair when not too extreme.

Consider, for example, the question of whether all students in a class should receive the same grade. This would achieve equality of outcomes in a manner that some would consider unfair. It may also give rise to smaller investments of time and effort in learning. Similarly, consider the question of whether all workers in a firm should receive the same compensation, regardless of their productivity. This too would achieve equality of outcomes, possibly at the expense of overall productivity in the firm.

If some inequality is necessary and acceptable, then how much of it should there be? On what basis should we decide? Reasonable people can differ in what they believe are the right answers to such questions.

### Evaluating inequality

Three hypothetical economies are listed below. Each consists of five quintiles, and the numbers represent the average income in each quintile (a quintile represents 20% of the population). For simplicity, suppose that all individuals within a quintile have the same income. Think of each number as corresponding to a hundred dollars of annual income, averaged over the course of one’s life, for each of five income quintiles.

• Economy A: 10, 18, 25, 34, 59
• Economy B: 6, 11, 17, 28, 89
• Economy C: 2, 6, 12, 23, 106

These economies correspond, roughly and respectively, to Bulgaria, Colombia, and South Africa as of 2005 (with income measured in hundreds of dollars).

For more details on how GDP per capita is calculated and used as a measure of income and living standards, see Section 1.2 of The Economy. You can find data on income distributions by country here.

Each of these economies has approximately the same GDP per capita. But life in these economies would be quite different. GDP per capita is a better representation of how people are doing in Economy A, which has relatively low levels of inequality, than in Economy C, which is much more unequal.

Which of the economies (A, B, or C) would you choose to live in if you knew you would be in the top quintile of earners? If you were entirely self-interested (that is, only concerned about maximizing your own income), then you would choose Economy C. But you may also be concerned about inequality, and prefer to live in one of the other economies, where your own income is smaller but total income is more equally distributed.

Now consider a different question: which of the economies do you consider to be the most just? To answer this question, you would probably want more information about whether basic human rights are protected, whether the government is representative or autocratic, whether people can exercise their religion freely, and so on. But even with all this information, people may disagree about what kind of society would be perfectly just.

The philosopher John Rawls argued that disagreement about what constitutes a just society arises because the positions we occupy affect our judgements and perspectives. He considered an interesting thought experiment: what if we had to decide on the kind of world we would want to live in if we did not know what our position in it would turn out to be?

From this “original position” he believed that we would agree on a set of principles that a just society would satisfy. First and foremost, each person would have an equal claim to certain basic liberties. Second, people would come to occupy positions in society based on fair equality of opportunity, and the resulting social and economic inequalities would be “to the greatest benefit of the least advantaged members of society.” This last criterion is known as the difference principle.

These principles allow for inequalities in income and wealth, provided that in “all parts of society there are… roughly the same prospects of culture and achievement for those similarly motivated and endowed.”

To illustrate, consider which of the following two income distributions would be chosen under Rawls’ principles of justice:

• Economy D: 6, 12, 21, 34, 112
• Economy E: 5, 11, 17, 29, 85

As before, think of each number as corresponding to a hundred dollars of annual income, averaged over the course of one’s life, for each of five income quintiles. These economies correspond roughly to Brazil and Ecuador, as of 2005.

Economy D has more inequality than Economy E, but the least advantaged person in D is better off materially than the least advantaged in E. In fact, income is higher in D at every quintile.

Does this mean that D is more just according to Rawls’ principles? Possibly, but not necessarily. If those in the most affluent quintile in Economy D were able to use their income to constrain the liberties of the remainder of the population, or to deny them fair equality of opportunity, the principles of justice may come to be violated over time. Only if basic liberties can be ensured and equality of opportunity sustained does the difference principle become decisive.

### Exercise 2 Apply the principles of justice

Consider the following two societies, where the numbers represent mean income at each quintile:

• Economy F: 6, 10, 13, 17, 31
• Economy G: 5, 11, 16, 23, 47

Interpret each number as thousands of dollars of lifetime income, annualized. Given a choice between these two societies:

1. Which society do you think would be most consistent with Rawls’ principles of justice?
2. Suppose you were to choose between these societies without knowing which position you would come to occupy. Which one would you choose and why?
3. Now suppose that the income of the lowest quintile in Economy G were changed to some other number x, where 0 < x < 6. Is there any value of x such that you would make a different choice? Explain your answer.

### Actual and perceived inequality

Research shows that most people do not have an accurate understanding of the disparities within their own country and across the world, nor do they have a good sense of their position in life relative to others. This could bias their attitudes and beliefs about what is fair and reasonable and about what policies they want to support.

You can read more about Perceived, Ideal, and Actual Inequality in Section 19.3 of CORE’s The Economy.

Michael Norton, a professor of business administration, and Dan Ariely, a psychologist and behavioural economist, asked a large sample of Americans how they thought the wealth of the US should be distributed: what fraction of it, for example, should go to the wealthiest 20%? They also asked them to estimate what they thought the distribution of wealth actually was.

Let’s try a version of that here, but with income rather than wealth.

### Exercise 3 Perceptions of inequality

1. In the country you live in, what share (%) of total income do you think goes to the richest quintile of the population?
2. In your opinion, what share (%) of total income in your country should go to the richest quintile? Explain the reasoning behind your answer.
3. Go to Our World in Data’s webpage for income inequality. Find the answer to Question 1 in the ‘Income shares’ chart, for the latest year available (use the ‘Change country’ option to display data for the country you live in). Discuss any differences between your answers to Questions 1 (perceived income share), 2 (ideal income share), and 3 (actual income share).

### Instrumental factors

A final reason to care about inequality is because high levels of income or wealth inequality can make it harder to achieve other desired objectives. By the same token, attempts at redistribution can interfere with other goals. Here are some examples:

• Economic inequality contributes to political inequality, which can, in turn, exacerbate economic inequality. For instance, high income individuals can contribute to political campaigns, and be rewarded for this by tax cuts that leave them even better off.
• Very high levels of redistribution could lower the returns for effort and innovation, or the returns for investment in the development of skills, and could lower total output (we considered this earlier with the example of a class where all students receive the same grade regardless of effort and performance). On the other hand, high levels of inequality could stand in the way of economic growth by keeping people from economic opportunities and success. For an example of this, see CORE’s Economist in Action video ‘What promotes or kills innovation?’ featuring University of Michigan economist, Lisa Cook. Extreme inequality can further result in the misallocation of investment, where people can’t get financing for promising projects, and it can also lower macroeconomic aggregate demand, making business cycles worse.

Section 19.5 of The Economy explains how differences in endowments, together with institutions and policies, transmit economic inequality from one generation to the next.

• Levels of inequality can be amplified from one generation to the next, as accidents of birth accumulate and are transmitted within families and neighbourhoods. Even complete equality of opportunity in one generation must give way to unequal opportunity in the next, as those with greater talent or effort in the first provide advantages to their children in the next.

## 3 Measuring economic inequality

### Income, wealth, consumption, and opportunity

As we have seen, economic inequality is closely linked to, but distinct from, other forms of inequality: equality before the law, political equality, and basic dignity and respect.

income
The amount of profit, interest, rent, labour earnings, and other payments (including transfers from the government) received, net of taxes paid, measured over a period of time such as a year. The maximum amount that you could consume and leave your wealth unchanged. Also known as: disposable income.
wealth
Stock of things owned or value of that stock. It includes the market value of a home, car, any land, buildings, machinery or other capital goods that a person may own, and any financial assets such as shares or bonds. Debts are subtracted—for example, the mortgage owed to the bank. Debts owed to the person are added.
consumption (C)
Expenditure on consumer goods including both short-lived goods and services and long-lived goods, which are called consumer durables.

Now, we must further differentiate between different types of economic inequality: income, wealth, consumption, and economic opportunity. Our focus through most of this Insight will be on income, but let’s quickly distinguish between these different dimensions.

flow
A quantity measured per unit of time, such as annual income or hourly wage.

Income inequality refers to differences across people in the flow of payments they receive over a given period of time, such as a year. An annual salary is part of an individual’s income, as are social security or alimony payments.

stock
A quantity measured at a point in time. Its units do not depend on time. See also: flow.
asset
Anything of value that is owned.

Wealth inequality refers to differences across people in the value of the stock of resources that they own, minus any debts that they owe such as student loans, credit card debt, or an outstanding mortgage. The stock of resources owned can consist of the accumulation of past income and the value of other material assets such as homes and cars. A broader definition of wealth can also include the value of intangible assets such as a college degree that can be used to generate an increased flow of earnings over the course of one’s life. Wealth inequality is significantly higher than income inequality in the US and around the world.

credit-constrained
A description of individuals who are able to borrow only on unfavourable terms.

Consumption inequality refers to differences across people in the goods and services they purchase for consumption over a given period of time, such as a year. Consumption inequality is typically less extreme than income inequality since people try to keep their consumption relatively constant over time when possible, so volatility in income is not reflected in differences in consumption. However, in an economy with credit constraints, those with low incomes cannot obtain loans, and so tend to consume most of what they receive, while those with high incomes don’t need to borrow, and instead can save and invest a greater proportion of what they earn. Both of these forces result in consumption differences that are less extreme than income differences.

To understand the relationship between income, wealth, and consumption, it is useful to use the analogy of a bathtub. You can think of income as the flow of water being poured into the tub and wealth as the amount (or stock) of water that sits in the tub at any given time. Your flow of income contributes to your stock of wealth. The water that drains out of the tub can be compared to consumption. All else being equal, your consumption of goods and services reduces your stock of wealth. For a more detailed discussion of this relationship, see Unit 10.1 in The Economy.

Inequality of opportunity, as we have already seen, refers to differences across people in their ability to convert their talent and effort into income and wealth. A child deprived of adequate nutrition is unlikely to become a world-class athlete, and a potential musical prodigy may never reach her potential without access to instruments or lessons at an early age.

human capital
The stock of knowledge, skills, behavioural attributes, and personal characteristics that determine the labour productivity or labour earnings of an individual. Investment in this through education, training, and socialization can increase the stock, and such investment is one of the sources of economic growth. Part of an individual’s endowments.

Although it may seem that wealth, income, consumption, and economic opportunity are highly correlated, this need not be the case. Someone just finishing a college degree may have a lot of skills and credentials (known as human capital, which contributes to future earnings) but little income as yet, and rather than a lot of financial wealth, a large amount of debt. And a retiree with great wealth may be receiving a relatively small income from social security disbursements but can sell assets to finance consumption.

### Question 2 Choose the correct answer(s)

Which of the following factors are considered when measuring income inequality?

• accidents of birth and good fortune
• the amount of money held in individual retirement accounts
• the amount of money owed on student loans
• none of the preceding options
• While accidents of birth and good fortune may affect one’s ability to profit from talent and efforts, measures of income inequality do not directly incorporate these factors.
• Retirement account savings do not count as income as they are not an inflow of money. Instead, they would be considered under wealth. (Note that the interest on these savings would be counted as income.)
• Debts do not count as income, rather they are considered when calculating wealth. Debt is subtracted from the total assets to calculate a person’s wealth.
• All of the factors listed above do not constitute income, so are not included in a measure of income inequality.

### Measuring the distribution of household income in the US

To measure income inequality, we can start by looking at the income of households. If you are wondering why economists start with households rather than individuals, it’s because people earn incomes individually, but tend to share and consume their income with household members.

Take a look at the five households below and put yourself in the shoes of an economist trying to measure inequality. How would you rank the economic well-being of these households in terms of their income?

Household A Household B Household C Household D Household E
Annual household income $18,000$35,000 $70,000$150,000 $400,000 Ranking You may have ranked them in the order presented from worst-off to best-off as follows: A, B, C, D, E. This is a perfectly reasonable guess given the information you had, but how does your ranking change with the following information? Household A Household B Household C Household D Household E Annual household income$18,000 $35,000$70,000 $150,000$400,000
Household size and characteristics Household size: 1
Retiree
Household size: 2
Single-parent household with one dependant
Household size: 3
Married couple, one earner, one stay-at-home parent, and an infant child
Household size: 1
Single-person household
Household size: 6
Two earners with four dependants
Ranking

There are roughly 130 million households in the US and they vary in size and characteristics. A household might consist of a single individual, or it might consist of two earners supporting several dependants, such as a child, spouse, grandparent, or other person who relies on someone else for financial support. These types of differences are relevant if we want to draw meaningful comparisons.

economies of scale
These occur when doubling all of the inputs to a production process more than doubles the output. The shape of a firm’s long-run average cost curve depends both on returns to scale in production and the effect of scale on the prices it pays for its inputs. Also known as: increasing returns to scale. See also: diseconomies of scale.

While it is impossible to consider all relevant household characteristics, economists do regularly adjust for household size and try to account for the difference between working-age adults and dependants. In doing so, they sometimes adjust for economies of scale within households as well. Usually, a larger family can use income more efficiently than a smaller one (a single kitchen, for example, can serve multiple family members almost as well as it serves a single individual).

market income
Income before paying taxes and receiving transfers from the government.
disposable income
Income available after paying taxes and receiving transfers from the government.

Before moving on, let us also make a distinction between market income, the sum total of the income you make in a year, and disposable income, the annual income you have after taxes and transfers.

### Exercise 4 Comparing market income and disposable income

Let’s compare two households each containing one individual.

Maria, in Household A, has a market income of $200,000 a year. After taxes and transfers, she has a disposable income of$130,000 a year.

Vanessa, in Household B, has a market income of $40,000 a year. She qualifies for certain government transfers, so her disposable income is higher than her market income. Vanessa’s disposable income is$50,000 a year.

Explain whether you would choose market income or disposable income to compare inequality of well-being between Maria and Vanessa. Discuss some other factors (besides income) that would be relevant for your comparison.

Disposable income is more commonly used in measuring income inequality. The rationale is that it gives a better sense of the level of well-being that households can afford. In the US and other countries, inequality measured in terms of market income is higher than inequality of disposable income. This is not surprising, since taxes and transfers tend to redistribute income from the top of the income distribution towards the bottom. In the US, disposable income is lower than market income for the top quintile of the distribution, and higher for the lowest three quintiles.

### Data interpretation skills

#### Where does data on household income come from?

Data on household income comes from household surveys and tax filings. In the US, the US Census Bureau collects data on household incomes using two surveys: the Current Population Survey (CPS), a monthly survey of roughly 60,000 households, and the American Community Survey (ACS). Some researchers are also able to use anonymized tax data from the IRS, and there are organizations such as the Luxembourg Income Study (LIS) that have pulled together and integrated surveys and income data from around the world.

#### Interpreting data

When you see inequality data presented in the news or elsewhere, these are some of the questions you can ask yourself: Are you looking at wealth inequality, income inequality, or something else? If you’re looking at income inequality, is market or disposable income being used? Are the figures being reported at the household level or have they been brought back down to the level of the individual?

Make sure you read the labels and charts carefully to understand what it is that is being measured.

#### Challenges with measuring inequality

Before moving on to statistical measures of inequality, it is worth noting some limitations and challenges involved with measuring inequality. Some of these have to do with where the data come from, and others have to do with the household characteristics we alluded to earlier.

• Surveys and tax data tend to underestimate top incomes. Richer families are less likely to participate in surveys and tax data is top-coded (censored) for the highest earners to protect their privacy.
• Unpaid household production, such as work done caring for your own children or cleaning your house, is not accounted for in household income. Relatedly, differences between the number of earners within a household are also not considered. These omissions can obscure meaningful differences between households. As an example, imagine two families each with a household income of $60,000. In both families, there are two adults and one child. In one of the households, both adults work full-time earning$30,000 each. In the other household, one of the adults earns the entire $60,000 in income, while the other makes no income but works full-time taking care of the house and caring for the child. Current income inequality measures would say that these two households are equally well off, but clearly, they are not. • Life-cycle differences are not typically considered, even though most people would find it acceptable if young adults and retirees don’t earn as much income as adults at the height of their career. • Comparing income distributions across time is challenging because of changes in population demographics and because individual households can change position in the income distribution as well. Think about your own life. Do you expect to occupy the same spot in the income distribution throughout your entire lifetime? Probably not. However, when levels of inequality are compared over time, we tend to neglect such factors as the age distribution of the population. Section 1.2 of The Economy explains how GDP is adjusted to be comparable across time and across countries. • Comparing household incomes across space is challenging because the purchasing power of incomes is different across geographic locations, and the characteristics of the populations being compared may also be quite different. ### Statistical measures of inequality From data on household incomes, we can approximate the distribution of income for a country or for any other group for which we have data. An income distribution lines up all households or individuals from poorest to richest and tells us how total income in the economy is divided (or distributed) among them. There are a number of different ways that income inequality can then be measured, each designed to capture specific details about the distribution. These measures can be applied to wealth inequality as well, which is far greater than income inequality, but more difficult to estimate. income ratios A measure of inequality that compares income at a given percentile of the income distribution to that of another by taking a ratio. For example, the 90:10 ratio compares income at the 90th percentile to income at the 10th percentile. Income ratios are used to compare different parts of the distribution depending on the type of disparities you are concerned about. For example, you could compare the middle of the distribution to the bottom of the distribution by calculating a 50:10 ratio. To do this, you would divide the income of a household at the 50th percentile by the income of a household at the 10th percentile. Similarly, you could compare the top of the distribution to the middle by calculating a 95:50 ratio, or you might compare the top of the distribution to the bottom by calculating a 90:10 ratio. income shares A measure of the share of income going to some portion of the income distribution. For example, the share going to the top 10% or the top 1%. Income shares measure the share going to any portion of the income distribution, for example, the share going to the bottom decile or the top decile (a decile represents one-tenth of the population). The most commonly used are shares going to the top 10%, 5%, 1%, and 0.01%. ### Exercise 5 Working with data 1. Go to Our World in Data’s Income Inequality webpage and find the section ‘How are the incomes of the rich changing relative to the incomes of the poor?’ Use the ‘Change country’ option to select the country you live in (or a similar country). Discuss how median household income in that country has changed over time. 2. Find the chart on income shares by quintile and use the ‘Change country’ option to select the country you live in (or a similar country). Describe how the share of total income held by the top quintile of people in your chosen country has changed over time. Lorenz curve A graphical representation of inequality of some quantity such as wealth or income. Individuals are arranged in ascending order by how much of this quantity they have, and the cumulative share of the total is then plotted against the cumulative share of the population. For complete equality of income, for example, it would be a straight line with a slope of one. The extent to which the curve falls below this perfect equality line is a measure of inequality. See also: Gini coefficient. The Lorenz curve is a way of visualizing the distribution of income to show cumulative incomes shares. It was developed by the American economist Max Lorenz (1876–1959), while he was still a graduate student at the University of Wisconsin-Madison. To draw a Lorenz curve, we plot the cumulative share of the population, poorest to richest, along the horizontal axis, and on the vertical axis, we plot the cumulative percentage of income going to each cumulative share of the population. For a simple example, think of a population consisting of five people where one person has an income of$100 and the remaining four people have zero income. Each person represents 20% of the population, which means the bottom 80% of this population has 0% of the income and the top 20% of the population has 100% of the income. The Lorenz curve for this population is the red line in Figure 1. The blue line in the figure is called the line of perfect equality. It represents a perfectly equal distribution of income, which in this case, is a distribution where each person has $20 or 20% of the total income. The Lorenz curve helps demonstrate how far a distribution deviates from a perfectly equal distribution. Figure 1 Lorenz curve ### Exercise 6 Construct a Lorenz curve In this exercise, we’ll construct a Lorenz curve for ten households whose annual incomes are represented below, in thousands of dollars. The households are already lined up from poorest to richest. There are ten households in the population, so each household represents a decile (or 10%) of the overall population. A B C D E F G H I J 15 20 35 40 65 115 135 200 375 1,000 0.75% 1.75% 1. In the third row of the table, fill in the cumulative share of income going to each successive decile of the population. The first two cells have already been filled in. 2. Draw the Lorenz curve for this population. 3. If income were equally distributed for this population, how much income would each household have? 4. Draw the line of perfect equality. Gini coefficient A measure of inequality of any quantity such as income or wealth, varying from a value of zero (if there is no inequality) to one (if a single individual receives all of it). In 1912, roughly seven years after Max Lorenz developed the Lorenz curve, an Italian sociologist and statistician by the name of Corrado Gini came up with a measure of inequality, which we now call the Gini coefficient. The Gini coefficient is one of the most commonly used measures of economic inequality; it gives us a way to quantify and compare the degree of inequality between different distributions. The exact Gini coefficient is defined as half the average difference between all the pairs of individuals in the population, divided by the average income of the population. To illustrate, consider Economy H. Economy H: 3, 5, 8, 10, 24 Suppose that each quintile contains just one person. That is, the five incomes are 3, 5, 8, 10, 24 and average income is 10. To see that there are ten possible pairs of individuals, construct all possible pairs while taking care not to double count. This should result in the following pairs: The sum of all ten income differences is: Hence the average difference is 9.4, half of which is 4.7. Dividing by the average income in the population, we get a Gini coefficient of 0.47. We can approximate the Gini coefficient by taking the ratio of the area between the line of perfect equality and the Lorenz curve to the full area that lies beneath the line of perfect equality. In Figure 2, the area under the line of perfect equality is represented by the blue and red shaded areas (A + B). The area underneath the Lorenz curve is represented by area B alone. Notice that the more unequal an income distribution is, the greater area A becomes, and the smaller area B becomes. The approximate formula we can use to calculate the Gini coefficient is, therefore, A/(A + B). To learn more about the Gini coefficient and its approximation, see Section 5.12 of The Economy. If we perform this calculation for Economy H, we get an estimate for the Gini coefficient of 0.376. This is a poor approximation when the population is small, but it becomes increasingly accurate as the population gets larger. Figure 2 Lorenz curve and the Gini coefficient ### Exercise 7 Understanding how population size affects the Gini coefficient 1. Use the Econgraphs Lorenz and Gini tool to plot the curves for Economies A, B, and C, but after multiplying all incomes by 10 (as shown below). In both cases, verify that the share of income going to the top 20% matches your findings. Assuming each quintile contains just one person, compute the Gini coefficients manually for each economy. Verify that these match the values obtained with the tool. • Economy A: 100, 100, 100, 100, 100 • Economy B: 30, 50, 80, 100, 240 • Economy C: 10, 110, 110, 110, 160 2. Using the slider to change the population size, compare the exact and approximate values of the Gini coefficient when there are ten people in each quintile (so the total population is 50). Now do the same for 100 people in each quintile. What do you notice? Does the approximation to the Gini coefficient using the Lorenz curve change as the population in each quintile changes? Using the pairwise distance definition of the Gini, can you explain why the approximation gets better as the population size increases? Note that the quintiles are labelled with letters instead of numbers, so A refers to the bottom quintile and E refers to the top quintile. ### Question 3 Choose the correct answer(s) Consider five individuals, of whom three have zero income and two have$10,000 each. Based on the approximate formula for the Gini coefficient, the measure of income inequality in this group is:

• 0.75
• 0.40
• 0.20
• 0.60
• Using the approximate formula, A = 3,000 and A + B = 5,000, so the Gini coefficient is A/(A + B) = 0.6.
• Using the approximate formula, A = 3,000 and A + B = 5,000, so the Gini coefficient is A/(A + B) = 0.6.
• Using the approximate formula, A = 3,000 and A + B = 5,000, so the Gini coefficient is A/(A + B) = 0.6.
• Using the approximate formula, A = 3,000 and A + B = 5,000, so the Gini coefficient is A/(A + B) = 0.6.

### Question 4 Choose the correct answer(s)

Consider five individuals, of whom three have zero income and two have \$10,000 each. Based on the exact formula for the Gini coefficient, the measure of income inequality in this group is:

• 0.75
• 0.40
• 0.20
• 0.60
• The average difference in income is 6,000 and the average income is 4,000, so the exact Gini coefficient is (0.5 x 6,000)/4,000 = 0.75.
• The average difference in income is 6,000 and the average income is 4,000, so the exact Gini coefficient is (0.5 x 6,000)/4,000 = 0.75.
• The average difference in income is 6,000 and the average income is 4,000, so the exact Gini coefficient is (0.5 x 6,000)/4,000 = 0.75.
• The average difference in income is 6,000 and the average income is 4,000, so the exact Gini coefficient is (0.5 x 6,000)/4,000 = 0.75.

## 4 Global inequality and policy solutions

### Inequality between countries and global inequality

Most people think about inequality within their country’s borders, but we can also calculate inequality between countries and between all individuals on the planet.

Why this is important:

• With globalization, peoples’ lives are increasingly influenced by the lives of people in other countries.
• Through the internet, people have grown increasingly aware of what is going on in other countries and may compare themselves not just to their fellow citizens but to people halfway around the world.

Are there reasons to care more deeply about inequality within your own country than inequality around the world, and vice versa?

inequality between countries
A measure of inequality between countries that relies on national average incomes rather than individual incomes.

Some countries are very affluent on average, while others are much less so. To measure inequality between countries, there are two approaches. First, we can compute a measure of average income for each country (see for example the hockey stick charts in Unit 1 of The Economy). From there, we could calculate the Gini coefficient, or any other statistical measure of inequality, treating each country like an individual having the average income for that country. This may be useful if you are strictly concerned with national comparisons and want to give each country equal representation in your calculation, but it does not account for the incredible variation in population size across countries. Iceland, for example, has fewer than 400,000 people, while the population of India exceeds 1.3 billion. Under the first approach, a rise in average incomes in Iceland will count just as much as an increase in average incomes in India, despite the fact that a billion more people are likely to be impacted by the latter change.

A second approach to measuring inequality between countries is exactly the same as the first, but weights each country according to its population size. Note that the Gini coefficient calculated using the first approach could rise at the very same time that the Gini coefficient calculated using the second approach could fall. This, in fact, happened during the last two decades of the twentieth century as India and China (the two largest countries in the world) experienced accelerated economic growth.

Use CORE’s interactive skyscraper visualization to look at income differences within and across countries from 1980 to 2014.

global inequality
An estimate of income or wealth inequality among all people on the planet.

Finally, what economists refer to as global inequality is inequality measured by comparing the incomes or wealth of all people on the planet. Instead of resorting to average national incomes, global inequality tries to incorporate differences within each country as well. This, of course, is a far harder task, because it is extremely challenging to collect and compare data for households who use different currencies and face very different prices. Incredibly, there have been efforts to do this, and there are reliable estimates of global inequality reaching back to about 1980. Global inequality gives us the fullest picture of income differences around the world and allows us to think not only about differences between rich and poor countries, but also differences between the rich, poor, and middle-class in one country relative to another. To see how global inequality has changed over the last few decades and to learn more about the difference between global inequality and inequality between countries, turn to the section on Inequalities between and within countries in Unit 19 of The Economy.

### Exercise 8 Local and global income distributions

Go to CORE’s global income inequality visualization and select up to 5 countries of your choice, for the year 2014. Use the ‘Skyscraper plot’, ‘Lorenz curves’, and ‘Rich/poor income ratios’ tabs in the visualization to describe some similarities and differences between the income distributions of your chosen countries.

### Policies to address inequality

Taxes and transfers can have unintended consequences, which in turn alters decisions that affect market income. See Section 3.9 of Economy, Society, and Public Policy for a specific example.

predistribution policy
Government actions that affect the endowments people have and their value, including the distribution of market income and the distribution of privately held wealth. Examples include education, minimum wage, and anti-discrimination policies. See also: redistribution policy.
redistribution policy
Taxes, monetary, and in-kind transfers of the government that result in a distribution of final income that differs from the distribution of market income. See also: predistribution policy.

Policies to address inequality can take two forms: pre-distribution of market income and redistribution. Policies that focus on pre-distribution change prices and wages in the market so that people’s incomes are less widely dispersed. This includes policies such as the minimum wage, protection of unions, land reform, and expansion of educational access and quality. Policies that focus on redistribution take the market wages and prices as given, but try to redistribute income using the tax system. A wide variety of taxes are in place in almost every contemporary economy, and they have different effects on inequality.

For a global comparison of inequalities in market and disposable income, see Section 5.12 of The Economy.

In prosperous countries, the primary tools for redistribution are income taxes and government expenditures. In general, more affluent individuals are taxed at higher rates than those who are less affluent, though quirks and loopholes in the tax code exist that individuals of considerable wealth can exploit. Tax revenues, in combination with government borrowing, are used to fund public goods and transfers to the poor and unemployed. The after-tax income distribution is thus more equal than the pre-tax distribution.

To learn more about predistributive policies, see Section 19.8 of The Economy. For more details on redistributive policies, see Section 19.10 of The Economy.

This can be seen in Figure 3, which shows the evolution of inequality in market income and disposable income in the United States and Sweden over the past few decades, as measured by the Gini coefficient. While inequality has been rising according to both measures, disposable income is more equally distributed. Furthermore, while market income inequality has been close in the two countries, disposable income inequality has been consistently greater in the US. This difference reflects Sweden’s far more progressive fiscal system, which taxes higher incomes at a higher rate, and redistributes it to low income citizens as well as supplying public goods.

### Question 5 Choose the correct answer(s)

Access Our World in Data’s chart on inequality of income and examine the Gini coefficient for disposable income from 1918–2014 in the following five countries: Japan, Sweden, Brazil, France, and the US. Which of the following statements are true?

• There was a time when France was more unequal than the US, but this is no longer the case.
• Sweden has had greater inequality than France since 2000.
• Comparing 1984 to 2014, inequality in Brazil fell while inequality in the US rose.
• Sweden has had greater inequality than Japan since 1975.
• In the 1950s and 1960s, France had a higher Gini coefficient than the US, but from 1970 onwards, France had a lower Gini coefficient.
• The opposite is true: since 2000, Sweden had a lower Gini coefficient, so France had greater inequality.
• The Gini coefficient of Brazil has been declining since 1984, whereas the Gini coefficient of the US has been increasing.
• In some years, Sweden had a higher Gini coefficient than Japan, but in other years, Japan had a higher Gini coefficient. We therefore cannot make any general statements comparing inequality in these two countries.

## 5 Conclusion

Inequality arises along multiple dimensions, including income, wealth, access to quality education, environmental quality, and public safety. There is no perfect way to measure it, but even imperfect measures can be very useful in comparing changes in inequality over time or differences across space.

Some degree of inequality may be necessary in order to provide incentives for the utilization of talent and the contribution of effort. Performance bonuses in firms, for instance, are designed to provide such incentives. Inequality arising from differences in talent or effort—for instance the high earnings of star athletes or bestselling authors—are often tolerated. But inequality in access to basic needs, such as good health and quality education, can prevent the flourishing of talent and blunt the rewards for effort. Extreme inequality in income, regardless of source, can further result in extreme political influence by the rich as well as misallocation of resources.

Returning to the example of Camden and Cherry Hill with which we started, there are many in the former community who could achieve the successes in the latter, if given the right opportunity. The constraints under which they operate are harmful to them, and indeed harmful to us all.

Many of these income differences—seen as rewards for hard work, risk-taking, or creativity for example—are considered by most people to be entirely fair, or at least necessary to provide incentives for a well-working economy. Other income differences—the effects of discrimination, coercion, or accidents of birth for example, are regarded by many as unfair.

Economics can help to address the problem of unfair inequality by clarifying its meaning and causes, and guiding policy-makers who seek to foster a more just society.

## 6 Acknowledgements

Olivia Bobrownicki, Sam Bowles, Wendy Carlin, Sam Glendenning, Rohini Somanathan, Eileen Tipoe.

Header image credit: Johnny Miller / Unequal Scenes