Income Distribution

Income Distribution in the U.S.
Wealth distribution in the U.S. is a constant point of interest, it examines
The Lorenz Curve Debut

A common tool used for viewing income distribution is the Lorenz curve. The Lorenz curve was originally formulated in an article by Max O. Lorenz in 1905 and published by the American Statistical Association. The original article dealt with methods of measuring the concentration of wealth and can be found here.

Deriving the Lorenz Curve

Begin with census data describing income distribution

Share of Aggregate
Income, US Households

Lowest 20%
Next Lowest 20%
Middle 20%
Second Highest 20%
Highest 20%





This data is from Money Income in the United States: 2001, U.S. Census Bureau. 1968 is the year in recent history during which the income distribution in the U.S. was most equal.
Fin2ding the Lorenz curve:
se the 1968 data and compute the cumulative percentages.

Lowest 20%
Next Lowest 20%
Middle 20%
Second Highest 20%
Highest 20%

0+4.2 =4.2
4.2+11.1 =15.3
15.3+17.5 =32.8

Cumulative Percentage of Aggregate Income, US Households, 1968

Lowest 20%
Lowest 40%
Lowest 60%
Lowest 80%
Lowest 100%


Money Income Of Households--Percent Distribution by Income Level, Race, and Hispanic Origin in Constant from 1980 to 2008.

The Results

We arrive at six points:

(0, 0), (20, 4.2), (40, 15.3), (60, 32.8), (80, 57.2), (100,100).

These coordinates represent percentages and can be changed to decimal numbers:

(0, 0), (0.2, 0.042), (0.4, 0.153), (0.6, 0.328), (0.8, 0.572), (1,1).

The points are plotted in the graph below and are connected by a smooth curve, the Lorenz curve. The diagonal line is where the curve would be if there were absolute equality in the distribution of income. The curve will always begin at point (0,0) and will always end at point (1,1). The points on the curve between these two points are the only points that will change. The greater the distance of the line from (0,0) to (1,1); the greater the inequality.

Read more about the Lorenz Curve on wikipedia article
Additionally, read more about the Lorenz Curve and Gini coefficient on this website

According to the class notes, the diagonal line which represents absolute equality in the distribution of income is also referred to as the "45 degree line". The area underneath the "45 degree line" and the area above the Lorenz curve is known as the "Gini coefficient" or "Gini index".

Gini Coefficient ( or Gini Index)

  • The Gini is the numerical representation of Income distribution

The Gini Coefficient is the area between the Lorenz Curve and "45 degree line" and is measured as a percentage (decimals and fractions work as well).
Range of values for Gini coefficient:

  • If there is perfect equality in the distribution of income, then the Gini coefficient is equal to zero. (minimum value of Gini index) Which will be represented on the graph as a diagonal line.
  • If there is perfect inequality in the distribution of income, then the Gini coefficient is equal to one. (maximum value of Gini index) Which will be represented on the graph as a horizontal line.

external image Economics_Gini_coefficient.png

In Summary

The Lorenz Curve will move away from the "45 degree line" if inequality increases. Things that increase inequality would be an increase in income of skilled workers compared to income of unskilled workers; this will only increase the gap between rich and poor, which in effect increases inequality. In the same way that the Lorenze Curve moves away from the "45 degree line" as inequality increases, the Gini coefficient increases as inequality increases.

Has Income Inequality in the U.S. Really Increased?

There are frequent complaints that U.S. income inequality has increased in recent decades. Estimates of rising inequality that are widely cited in the media are often based on federal income tax return data. Those data appear to show that the share of U.S. income going to the top 1 percent (those people with the highest incomes) has increased substantially since the 1970s.

However, there have been large changes in U.S. tax rules over time that have made a dramatic difference on what is reported as income on individual tax returns. Tax changes induced thousands of businesses to switch from filing under the corporate tax system to filing under the individual tax system. Corporate executives switched from accepting stock options taxed as capital gains to nonqualified stock options taxed as salaries. The huge growth in tax-favored savings plans, such as 401(k)s, has resulted in billions of dollars of investment income disappearing from tax returns. Meanwhile, studies of inequality that are based on tax return data usually exclude transfer payments, which results in exaggerating the shares of income received by those at the top by ignoring growing amounts of income at the bottom.

Measurements of inequality have also been affected by large reductions in income tax rates, particularly in 1986. Estimates by many economists indicate that the reported income of highincome taxpayers is very responsive to tax rates. When top tax rates on wages or capital gains fall, reported incomes rise, and a larger fraction of the incomes of those at the top show up on tax returns. International comparisons show that reported income shares of those at the top have risen the most where top tax rates have been cut the most (the United States, the United Kingdom, and India) and have risen the least where top tax rates have remained very high (France and Japan).

In sum, studies based on tax return data provide highly misleading comparisons of changes to the U.S. income distribution because of dramatic changes in tax rules and tax reporting in recent decades. Aside from stock option windfalls during the late-1990s stock-market boom, there is little evidence of a significant or sustained increase in the inequality of U.S. incomes, wages, consumption, or wealth over the past 20 years.
(Source: Author: Alan Reynolds).

Overview of Income Distribution

In this section, we will address the omissions and shortcomings in the conventional Census income distribution figures and show the actual distribution of income once these corrections are made. The analysis is based on data taken from the Census Bureau's Current Population Survey (CPS) from March 1998 (covering incomes for 1997).5 In order to increase understanding of the corrections made, the adjustments are presented in four separate stages, the first three can be found in Chart 2 below.

Chart 2 (Stages 1-3):


Stage 1: Reporting Conventional Census Data.

Stage 1 presents conventional Census Bureau income distribution statistics based on pre-tax "official money income" and demographically unequal quintiles. Many policymakers and members of the press rely heavily on these income distribution statistics.6 They serve as the basis for comparison to the corrected figures described in Stages 2, 3, and 4.

Stage 2: Adding a More Complete Count of Income and Taxes.

The money figures in Stage 1 exclude many types of income and compensation received by families and individuals, as well as the effects of taxes in reducing income. Stage 2 corrects for these omissions by making the following adjustments.
  • The value of realized capital gains is added to income.7
  • The value of welfare benefits such as food stamps, public housing, the school lunch program, and the earned income tax credit are added,8 as are the value of employee health benefits and the insurance values of Medicaid and Medicare benefits.9
  • Federal income taxes, property taxes, state income taxes, and Social Security payroll taxes are then subtracted from family income.

Stage 3: Adjusting Quintiles to Contain Equal Numbers of Persons.

The largest flaw in the Census income distribution data is that its income "quintiles" do not contain equal fifths of the U.S. population, but are in fact unequal in size.11 Indeed, in reality the top Census "quintile" contains not 20 percent of the population but 24.3 percent, while the bottom quintile contains only 14.8 percent of the population. The top quintile has 65 percent more persons than does the bottom quintile. With conventional Census figures, the bottom "quintile" is hollow, representing far less than one-fifth of society; by contrast, the top "quintile" is overpopulated, containing far more than one-fifth of persons, workers, and work effort. Naturally, the demographic imbalance between the quintiles has a considerable effect on the apparent income imbalance between them.
Stage 3 uses the comprehensive post-tax income data developed in Stage 2 and then makes a demographic adjustment so that each income quintile in fact contains one-fifth of the population.12 This adjustment ensures that the economic status of each individual in the population is treated as having equal value or importance. By contrast, individuals are not treated equally in the current Census methods; in general, individuals in married couple families are underrepresented by the Census data and treated as less significant than single persons or people in single-parent families.

Chart 3 (Stage 4):


Stage 4: Explaining the Remaining Variance--Hypothetical Equalization of Work Performed.

Even after the quintiles are adjusted to contain equal numbers of persons in Stage 3, an enormous difference remains in the amount of work performed within each corrected quintile. The annual number of hours of employed labor in the top quintile is still nearly twice that in the bottom quintile. This imbalance in work certainly can be expected to contribute to an imbalance in income.

"Income Inequality: How Census Data Misrepresent Income Distribution" by Robert Rector & Rea Hederman Jr. can be found in its entirety at

World Wide Income Distrubution

The chart below was taken from showing data on world wide income distribution.

Percentage of world population
Percentage of world income
Yearly individual income
Daily individual income
external image red.gif
Bottom 10 percent
Bottom 20 percent
Bottom 50 percent
Bottom 75 percent
Bottom 85 percent
external image red.gif
Top 10 percent
Top 5 percent
Top 1 percent