## Measuring Income Inequality

### Learning Objectives

• Explain the distribution of income
• Use the Lorenz Curve to analyze the distribution of income and wealth

In a market economy, your income depends on the resources you own (e.g. labor, land, etc.), and the value the market places on those resources. People who own a lot of resources and people who own resources that are highly valued will tend to earn higher incomes than people who do not. As a consequence, market economies tend to result in inequality of income and wealth. Whether this is good or bad depends at least in part on the degree of inequality. Few Americans believe that Bill Gates doesn’t deserve to be rich, because of the significant value his company, Microsoft, has brought to people. But should he have 100 times the wealth of the average American or 1 million times? That is the question.

Poverty levels can be subjective based on the overall income levels of a country. Typically a government measures poverty based on a percentage of the median income. Income inequality, however, has to do with the distribution of that income, in terms of which group receives the most or the least income. Income inequality involves comparing those with high incomes, middle incomes, and low incomes—not just looking at those below or near the poverty line. In turn, measuring income inequality means dividing the population into various groups and then comparing the groups, a task that we can be carry out in several ways.

### HOW DO YOU SEPARATE POVERTY AND INCOME INEQUALITY?

Poverty levels can be subjective based on the overall income levels of a country; typically poverty is measured based on a percentage of the median income. Income inequality, however, has to do with the distribution of that income, in terms of which group receives the most or the least income. Income inequality involves comparing those with high incomes, middle incomes, and low incomes—not just looking at those below or near the poverty line. In turn, measuring income inequality means dividing up the population into various groups and then comparing the groups, a task that can be carried out in several ways.

Figure 1. Growth of Family Income. Source: Andrea Witte, http://www.connectthedotsusa.com/.

Poverty can change even when inequality does not move at all. Imagine a situation in which income for everyone in the population declines by 10%. Poverty would rise, since a greater share of the population would now fall below the poverty line. However, inequality would be the same, because everyone suffered the same proportional loss. Conversely, a general rise in income levels over time would keep inequality the same, but reduce poverty.

It is also possible for income inequality to change without affecting the poverty rate. Imagine a situation in which a large number of people who already have high incomes increase their incomes by even more. Inequality would rise as a result—but the number of people below the poverty line would remain unchanged.

Why did inequality of household income increase in the United States in recent decades? Indeed, a trend toward greater income inequality has occurred in many countries around the world, although the effect has been more powerful in the U.S. economy. Economists have focused their explanations for the increasing inequality on two factors that changed more or less continually from the 1970s into the 2000s. One set of explanations focuses on the changing shape of American households; the other focuses on greater inequality of wages, what some economists call “winner take all” labor markets. We will begin with how we measure inequality, and then consider the explanations for growing inequality in the United States.

## Measuring Income Distribution by Quintiles

One common way of measuring income inequality is to rank all households by income, from lowest to highest, and then to divide all households into five groups with equal numbers of people, known as quintiles. This calculation allows for measuring the distribution of income among the five groups compared to the total. The first quintile is the lowest fifth or 20%, the second quintile is the next lowest, and so on. We can measure income inequality by comparing what share of the total income each quintile earns.

U.S. income distribution by quintile appears in Table 1. In 2016, for example, the bottom quintile of the income distribution received 3.1% of income; the second quintile received 8.3%; the third quintile, 14.2%; the fourth quintile, 22.9%; and the top quintile, 51.5%. The final column of Figure 1 shows what share of income went to households in the top 5% of the income distribution: 22.6% in 2016. Over time, from the late 1960s to the early 1980s, the top fifth of the income distribution typically received between about 43% to 44% of all income. The share of income that the top fifth received then begins to rise. Census Bureau researchers trace, much of this increase in the share of income going to the top fifth to an increase in the share of income going to the top 5%. The quintile measure shows how income inequality has increased in recent decades.

 Table 1. Share of Aggregate Income Received by Each Fifth and Top 5 Percent of Households, All Races: 1967 to 2016 (Source: U.S. Census Bureau, Table H-2) Year Shares of aggregate income Lowest fifth Second fifth Third fifth Fourth fifth Highest fifth Top 5 percent 1967 4.0 10.8 17.3 24.2 43.6 17.2 1970 4.1 10.8 17.4 24.5 43.3 16.6 1975 4.3 10.4 17.0 24.7 43.6 16.5 1980 4.2 10.2 16.8 24.7 44.1 16.5 1985 3.9 9.8 16.2 24.4 45.6 17.6 1990 3.8 9.6 15.9 24.0 46.6 18.5 1995 3.7 9.1 15.2 23.3 48.7 21.0 2000 3.6 8.9 14.8 23.0 49.8 22.1 2005 3.4 8.6 14.6 23.0 50.4 22.2 2010 3.3 8.5 14.6 23.4 50.3 21.3 2015 3.1 8.2 14.3 23.2 51.1 22.1 2016 3.1 8.3 14.2 22.9 51.5 22.6 Source: U.S. Census Bureau, Current Population Survey, Annual Social and Economic Supplements.   For information on confidentiality protection, sampling error, nonsampling error, and definitions, see //www2.census.gov/programs-surveys/cps/techdocs/cpsmar17.pdf

It can also be useful to divide the income distribution in ways other than quintiles; for example, into tenths or even into percentiles (that is, hundredths). A more detailed breakdown can provide additional insights. For example, the last column of Table 1 shows the income received by the top 5% percent of the income distribution. Between 1980 and 2016, the share of income going to the top 5% increased by 6.1 percentage points (from 16.5% in 1980 to 22.6% in 2016). From 1980 to 2016 the share of income going to the top quintile increased by 7.5 percentage points (from 44.1% in 1980 to 51.5% in 2016). Thus, the top 20% of householders (the fifth quintile) received over half (51.5%) of all the income in the United States in 2016.

## Lorenz Curve

The data on income inequality can be presented in various ways. For example, you could draw a bar graph that showed the share of income going to each fifth of the income distribution. Figure 2 presents an alternative way of showing inequality data in what is called a Lorenz curve. The Lorenz curve shows the cumulative share of population on the horizontal axis and the cumulative percentage of total income received on the vertical axis.

Figure 2. The Lorenz Curve. A Lorenz curve graphs the cumulative shares of income received by everyone up to a certain quintile. The income distribution in 1980 was closer to the perfect equality line than the income distribution in 2016—that is, the U.S. income distribution became more unequal over time.

Every Lorenz curve diagram begins with a line sloping up at a 45-degree angle. We show it as a dashed line in Figure 2. The points along this line show what perfect equality of the income distribution looks like. It would mean, for example, that the bottom 20% of the income distribution receives 20% of the total income, the bottom 40% gets 40% of total income, and so on. The other lines reflect actual U.S. data on inequality for 1980 and 2016.

The trick in graphing a Lorenz curve is that you must change the shares of income for each specific quintile, which we show in the first column of numbers in Table 2, into cumulative income, which we show in the second column of numbers. For example, the bottom 40% of the cumulative income distribution will be the sum of the first and second quintiles; the bottom 60% of the cumulative income distribution will be the sum of the first, second, and third quintiles, and so on. The final entry in the cumulative income column needs to be 100%, because by definition, 100% of the population receives 100% of the income.

 Table 2. Calculating the Lorenz Curve Income Category Share of Income in 1980 (%) Cumulative Share of Income in 1980 (%) Share of Income in 2016 (%) Cumulative Share of Income in 2016 (%) First quintile 4.2 4.2 3.1 3.1 Second quintile 10.2 14.4 8.3 11.4 Third quintile 16.8 31.2 14.2 25.6 Fourth quintile 24.7 55.9 22.9 48.5 Fifth quintile 44.1 100 51.5 100

In a Lorenz curve diagram, a more unequal distribution of income will loop farther down and away from the 45-degree line, while a more equal distribution of income will move the line closer to the 45-degree line. Figure 2 illustrates the greater inequality of the U.S. income distribution between 1980 and 2016 because the Lorenz curve for 2016 is farther from the 45-degree line than for 1980. The Lorenz curve is a useful way of presenting the quintile data that provides an image of all the quintile data at once.

### Measuring Income Inequality

The U.S. economy has a relatively high degree of income inequality by global standards. As Table 3 shows, based on a variety of national surveys done for a selection of years in the last five years of the 2000s (with the exception of Germany, and adjusted to make the measures more comparable), the U.S. economy has greater inequality than Germany (along with most Western European countries). The region of the world with the highest level of income inequality is Latin America, illustrated in the numbers for Brazil and Mexico. The level of inequality in the United States is lower than in some of the low-income countries of the world, like China and Nigeria, or some middle-income countries like the Russian Federation. However, not all poor countries have highly unequal income distributions; India provides a counterexample.

Table 3. Income Distribution in Select Countries (Source: U.S. data from U.S. Census Bureau Table H-2. Other data from The World Bank Poverty and Inequality Data Base, http://databank.worldbank.org/data/views/reports/tableview.aspx#)
Country Survey Year First Quintile Second Quintile Third Quintile Fourth Quintile Fifth Quintile
United States 2011 3.2% 8.4% 14.3% 23.0% 51.1%
Germany 2000 8.5% 13.7% 17.8% 23.1% 36.9%
Brazil 2009 2.9% 7.1% 12.4% 19.0% 58.6%
Mexico 2010 4.9% 8.8% 13.3% 20.2% 52.8%
China 2009 4.7% 9.7% 15.3% 23.2% 47.1%
India 2010 8.5% 12.1% 15.7% 20.8% 42.8%
Russia 2009 6.1% 10.4% 14.8% 21.3% 47.1%
Nigeria 2010 4.4% 8.3% 13.0% 20.3% 54.0%

### Watch IT

This video explains income inequality and discusses some potential causes and fixes for reducing the large disparity between incomes in America.

### Try It

These questions allow you to get as much practice as you need, as you can click the link at the top of the first question (“Try another version of these questions”) to get a new set of questions. Practice until you feel comfortable doing the questions.

### Glossary

Lorenz curve:
a graph that compares the cumulative income actually received to a perfectly equal distribution of income; it shows the share of population on the horizontal axis and the cumulative percentage of total income received on the vertical axis
quintile:
dividing a group into fifths, a method economists often use to look at distribution of income