## Inequality, Poverty, and Discrimination

### 2. Income Inequality

#### 2.1. A Changing Distribution of Income

We have seen that the income distribution has become more unequal. This section describes a graphical approach to measuring the equality, or inequality, of the distribution of income.

##### Measuring Inequality

The primary evidence of growing inequality is provided by census data. Households are asked to report their income, and they are ranked from the household with the lowest income to the household with the highest income. The Census Bureau then reports the percentage of total income earned by those households ranked among the bottom 20%, the next 20%, and so on, up to the top 20%. Each 20% of households is called a quintile. The bureau also reports the share of income going to the top 5% of households.

Income distribution data can be presented graphically using a Lorenz curve, a curve that shows cumulative shares of income received by individuals or groups. It was developed by economist Max O. Lorenz in 1905. To plot the curve, we begin with the lowest quintile and mark a point to show the percentage of total income those households received. We then add the next quintile and its share and mark a point to show the share of the lowest 40% of households. Then, we add the third quintile, and then the fourth. Since the share of income received by all the quintiles will be 100%, the last point on the curve always shows that 100% of households receive 100% of the income.

If every household in the United States received the same income, the Lorenz curve would coincide with the 45-degree line drawn in Figure 19.1 "The Distribution of U.S. Income, 1968 and 2010". The bottom 20% of households would receive 20% of income; the bottom 40% would receive 40%, and so on. If the distribution of income were completely unequal, with one household receiving all the income and the rest zero, then the Lorenz curve would be shaped like a backward L, with a horizontal line across the bottom of the graph at 0% income and a vertical line up the right-hand side. The vertical line would show, as always, that 100% of families still receive 100% of income. Actual Lorenz curves lie between these extremes. The closer a Lorenz curve lies to the 45-degree line, the more equal the distribution. The more bowed out the curve, the less equal the distribution. We see in Figure 19.1 "The Distribution of U.S. Income, 1968 and 2010" that the Lorenz curve for the United States became more bowed out between 1968 and 2010.

Figure 19.1 The Distribution of U.S. Income, 1968 and 2010

*The distribution of income among households in the United States became more unequal from 1968 to 2010. The shares of income received by each of the first four quintiles fell, while the share received by the top 20% rose sharply. The Lorenz curve for 2010 was more bowed out than was the curve for 1968. (Mean income adjusted for inflation and reported in 2010 dollars; percentages do not sum to 100% due to rounding.)*

The degree of inequality is often measured with a Gini coefficient, the ratio between the Lorenz curve and the 45° line and the total area under the 45° line. The smaller the Gini coefficient, the more equal the income distribution. Larger Gini coefficients mean more unequal distributions. The Census Bureau reported that the Gini coefficient was 0.359 in 1968 and 0.457 in 2010.

##### Mobility and Income Distribution

When we speak of the bottom 20% or the middle 20% of families, we are not speaking of a static group. Some families who are in the bottom quintile one year move up to higher quintiles in subsequent years; some families move down. Because people move up and down the distribution, we get a quite different picture of income change when we look at the incomes of a fixed set of persons over time rather than comparing average incomes for a particular quintile at a particular point in time, as was done in Figure 19.1 "The Distribution of U.S. Income, 1968 and 2010".

Addressing the question of mobility requires that researchers follow a specific group of families over a long period of time. Since 1968, the Panel Survey of Income Dynamics (PSID) at the University of Michigan has followed more than 5,000 families and their descendents. The effort has produced a much deeper understanding of changes in income inequality than it is possible to obtain from census data, which simply take a snapshot of incomes at a particular time.

Based on the University of Michigan's data, Federal Reserve Bank of Boston economist Katharine Bradbury compared mobility over the decades through 2005. She concluded that on most mobility measures, family income mobility was significantly lower in the 1990s and early 2000s than in earlier periods. Moreover, when families move out of a quintile, they move less. Finally, she notes that for the recent decades moving across quintiles has become harder to achieve precisely because of the increased income inequality.