A world of differences
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 1.0.
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?
- 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 1.0 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
- 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.
- 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%
- 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.
- Draw the Lorenz curve for this population.
- If income were equally distributed for this population, how much income would each household have?
- 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.
\[\begin{align*} \text{Gini} = ({\frac{1}{2}}) {\frac{\text{Average difference between pairs}}{\text{Average income}}} \end{align*}\]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:
\[(3,5), (3,8), (3, 10), (3, 24), (5, 8), (5, 10), (5, 24), (8, 10), (8, 24), (10, 24)\]The sum of all ten income differences is:
\[2 + 5 + 7 + 21 + 3 + 5 + 19 + 2 + 16 + 14 = 94\]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 1.0.
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
- 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
- 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:
- 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:
- 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.