# Income Inequality: How unequal is the income distribution?

Income is not equally distributed, not in the U.S. nor in any other country.  How unequal is the distribution?  How has the distribution changed over time?   (Note:  In this post, we only focus on income inequality facts.  Here, we do not seek to explain WHY incomes are unequal or why the degree of inequality changes.  Ideas on WHY income inequality occurs and changes will be presented in a separate post.)

In 1947, the U.S. Department of Commerce (2020) developed an income inequality measure using money income, a broad measure that includes income from private and public sources including public assistance.  The approach ranks household money incomes from lowest to highest.  This ordering this then divided into five “quintiles,” where each quintile includes an equal numbers of households.  We can then characterize inequality by presenting the share of total money income received by the different quintiles.  If there were no inequality, each quintile would receive 20% of total money income.  A common way of measuring the degree of income inequality is comparing the top 20% of income earners to the bottom 20%.

From 1947 to 1966, there was a move toward greater equality.  The share of total income received by the top (richest) 20% decreased from 43.0% to 40.5%, while the share of the bottom (poorest) 20% increased from 5.0% to 5.6%.

Since 1966, the income distribution has become less equal.  In 2016, the top 20% of U.S. income earners received 50.1% of U.S. money income, while the bottom 20% received 3.1%.

Piketty, Saez, and Zucman (2018) assemble an income distribution measure for the U.S..  They claim that the Census income measure just reported captures less than 60% of all incomes received, and claim their income measures captures 100%.  They assemble a pretax income measure and a post tax income measure, which allows the impacts of taxes and government transfers to be examined.

Average incomes have grown in the U.S. over time, but incomes at all levels have not grown proportionately.  From 1980 to 2014, U.S. pretax income per adult grew by 60%.  Over that period, the average pretax income of the bottom 50% of adults remained about the same in real terms, while it roughly tripled in real terms for the top 1% of adults.  As a consequence, the share of pretax income earned by the bottom 50% decreased from 20% to 12%, while the share of the top 1% increased from 12% to 20%.  Piketty, Saez, and Zucman (2018) report that government taxes and transfer payment programs do not change this distribution much because the transfer payment programs, being dedicated primarily to the elderly and to health care, primarily support those already in the middle class.

Alvaredo, Chancel, Piketty, Saez, and Zucman (2017) used income data from the World Wealth and Income Database (WID.world) to examine income inequality worldwide.  They focused to some extent on trends in China and India.  In China, economic growth has also generated additional inequality, but the growth has raised the incomes of the richest and the poorest.  From 1978 to 2015, real national income per adult increased 811 percent in China.  The bottom 50 percent experienced 401 percent growth, while the top 10% experienced 1,898% growth.  As rapid growth has occurred in traditionally poor countries, China and India being the most important examples, inequality between countries has been falling as inequality within countries has been rising.

The Gini coefficient is a single number aimed at measuring the degree of inequality in a distribution. To calculate the coefficient, the first step is to obtain a Lorenz Curve, which plots the proportion of the total income earned as it depends upon the proportion of the population earning it.    If there is perfect equality, the Lorenz Curve is a straight line intersecting the axis at a 45 degree angle.  With greater inequality, the Lorenz Curve bows further down and to the right.  The Gini coefficient is the ratio of the area that lies between the line of equality and the Lorenz curve to the total area under the line of equality, as shown in the diagram below.   That is, in the diagram, the Gini Coefficient is the area A/(A + B).

The Organization for Economic Cooperation and Development (OEDC, 2020) reports Gini Coefficients for a wide variety of countries.  The use an after government taxes and transfers measure of income.  Specifically, they define household income to include earnings, self-employment and capital income and public cash transfers, and they deduct income taxes and social security contributions paid by households.  We show the Gini Coefficients they calculate (for 2018 or another most recent year) for a variety of countries in the figure below.    The Gini Coefficient for the U.S. is .39.  The only countries shown with more inequality are Turkey, Mexico (.46), Chile (.46), Costa Rica (.48), and South Africa (.62).    As shown in the figure, some Eastern European countries (Slovak Republic (.24), Slovinia (.24), Czech Republic (.25)) and some Northern European countries (Iceland (.26), Denmark (.26), Norway (.26)) have less inequality.

The Gini Coefficient is difficult to interpret.  What does the U.S. value of .39 mean?  We know it means the U.S. is less equal than Denmark with a .26 Gini Coefficient.  But, how much less equal is the U.S. than Denmark?

Another measure the OEDC (2020) makes available is an S80/S20 measure, which is equal to the average income of the richest 20% of households divided by the average income of the poorest 20% of households.    The following figure shows inequality according to the S80/S20 measure.  According to this measure, we again observe that the U.S. has one of the least equal income distributions.  The income of the richest 20% is 8.4 times that of the poorest 20%.  Chile (10.3), Mexico (10.3), Costa Rica (13.2), and South Africa (37.6) are less equal.  In contrast, the countries with the most equal income distributions are the Czech Republic (3.6)., Iceland (3.6)., and Slovenia (3.6).

It is more intuitive to see how much more equal the income distribution is in other countries than the U.S. using the S80/S20 measure.    For example, instead of having and average income 8.4 times that of the poorest 20% as in the U.S., the richest 20% in Sweden have an average income that is 4.2 times that of the poorest 20%.    Norway, Belgium, Finland, the Slovak Republic, and Denmark join Slovenia, Iceland, and the Czech Republic with S80/S20 ratios that are less than half that of the U.S.

References

Alvaredo, F., Chancel, L. Piketty, T., Saez, E., and Zucman, G. 2017.  Global Inequality Dynamics: New Findings from WID.world, American Economic Review: Papers & Proceedings 107(5), 404–409.

OECD (2020), Income inequality (indicator). doi: 10.1787/459aa7f1-en (Accessed on 28 January 2020)

Piketty, T., Saez, E., Zucman, G., 2018. Distributional National Accounts: Methods and Estimates for the United States, The Quarterly Journal of Economics 133 (2), 553-609.

U.S. Department of Commerce, 2020.  https://census.gov/data/tables/time-series/demo/income-poverty/historical-income-households.html   Accessed January 19, 2020.