Wealth Inequality, the Gini Coefficient and the Pandemic Economy
A pedagogical calculation of a statistical tool is presented for wealth distribution in the US in 2019, followed by some comparisons and comments about our economy.
Discussions of wealth inequality often are general and somewhat vague, and rarely refer to mathematically precise definitions. Wealth inequality can be quantified using a standard statistical metric called the Gini coefficient. The calculation method is easy to understand and has been presented in a number of books and web posts. Here, an illustrative calculation is shown with the aid of Figure 1. The red curve in panel (a) is an arbitrary Lorenz Curve. A Lorenz Curve is used to visualize a comparison between the actual distribution of some commodity across a population and an ideally equal distribution. The x-axis represents the share of a population receiving the commodity, beginning with those receiving the least, continuing with those who have more and ending with the highest percentile value, 100%. The y-axis is the cumulative share of the commodity, measured from least to most and again ending with 100%. Equal distribution is represented by the diagonal blue line from the beginning point (0, 0) to the end point (100, 100) and the interpretation is simple: Each percentile receives an equal share. The first percentile, from 0 to 1, has a share of 1%. The second percentile, from 1 to 2, has an equal share of 1% and so the cumulative share is 2%. This continues and, finally, the last percentile, from 99 to 100, has a 1% share that adds up to a cumulative value of 100%.
To plot a cumulative distribution, one starts with a graph of the simple distribution of the commodity for each percentile, arranged in increasing order. Then the y-value for each percentile p in the cumulative plot represents the sum of all y values from 0 through p in the simple plot. Equivalently, the y-value at p in the cumulative plot is the sum of the value in the previous percentile, p-1, plus the increment that is assigned to p in the simple plot. The Gini coefficient, G, measures the deviation from equal distribution for the curve of interest. It is the ratio of the area between the diagonal line and the red curve, area A in the figure, and the total area under the diagonal line, area A + B. Areas A and B are bounded by the red trace and the blue dotted lines. For the example curve Fig. 1(a), G = 0.35. This is a quantitative statement of the qualitative interpretation that the red curve is closer to the diagonal line than it is to the other blue lines.
A Gini analysis can be used generally for a variety of distribution plots. An example could be the number of computers in a home or commercial office. The plots in the two bottom panels are examples of cumulative wealth distribution and show two extreme cases. In Fig. 1(b), the distribution curve represents perfectly equal distribution. The y-axis represents the fraction, in percent, of total wealth. Each percentile has the same wealth, so the accumulated wealth increases by one percent for each percentile, exactly as we discussed for the diagonal line in the top panel. Comparing the sample distribution with the diagonal line, there is no deviation at all and therefore the Gini coefficient is G = 0. At bottom right, Fig. 1(c), all wealth (100%) is held in the top percentile, 99 to 100%. The total area A + B is ½ (100% x 100%) = 5,000. The area B is 100% x 1% = 100, and therefore area A is 5,000–100 = 4,900. For this extreme wealth inequality, G = 4,900 / 5,000 = 0.98. This illustration shows that calculating the Gini coefficient depends on the accuracy of the data. Here, all wealth is assumed to be shared equally by the top one percent. If all the wealth were held by a single person, G would have value 1. In general, a calculated G value is more accurate when wealth data are provided using a large number of brackets, such as units of one percent or, better, a fraction of a percent. In practice, the brackets are typically one percent. Similarly, the G value becomes relatively inaccurate if data are available only for population quartiles or for brackets of ten percent. To summarize, statisticians typically state that the G value varies from 0 to 1, representing wealth distribution of perfect equality or inequality, respectively.
Let’s perform a sample Gini calculation for data that represent recent wealth distribution in the United States. Data for “Wealth by Percentile” are plotted as the simple distribution in panel (a) of Fig. 2. The units of wealth are millions of dollars. The data are provided at the website DQYDJ [1]. Using the description on the site, the data were taken from the Federal Reserve’s 2019 Survey of Consumer Finances (SCF), released in Sept. 2020. The wealth values are reported in 2019 dollars. Each data point represents the threshold value of the given percentile, i.e. the wealth required to enter that percentile. In Fig. 2(a), I plot the average of the threshold values to enter a leave each percentile. Each value for p represents the household wealth of a single household in that percentile. There are about 165 million households in the US. To find the approximate total wealth for a percentile, multiply the given value by the number of households in each percentile, 1.65 million.
The last data point in the table is the threshold to enter the percentile 99 to 100%. Since there is no threshold datum for 100%, I complete the graph by estimating the average wealth in the top percentile. An addendum to the SCF [2] reported that the wealth for the top 1%, as of the second quarter of 2020, was $34.7 trillion (T). I divided this by 1.65 million to find the average value of wealth of the top percentile to be about $21 million. There are limits to the validity of mixing separate reports [3], even when they are from the same source. However, I proceed in the spirit of providing an example of a Gini calculation that will be reasonably correct. The same article [2] stated that the total household wealth of the US, as of Quarter 2, 2020, was $113 T. The sum of total wealth in Fig. 2(a) agrees with this value. As an aside, although it’s difficult to see because of the scale of this plot, entries up to the eleventh percentile have negative values. This reflects that the those with the least wealth are in debt: Their debts are larger than their assets.
Panel (b) plots the cumulative wealth in the US as a function of population percentile. As described above, the value in percentile p is the sum of values in percentiles 0 through p in the plot of the top panel. It’s interesting to note that the wealth of one household in the top one percent of panel (a), about $21 million, matches the cumulative wealth of one household in percentile 93 of panel (b). This means that the wealth of all members of the top 1 percent in the US equals the combined wealth of all those in the bottom 93 percent. The Gini coefficient is found to be G = 0.83.
The focus of the discussion here is wealth distribution. More generally, discussions in publications and other media focus on income inequality. Figure 3 plots a simple distribution of the household income for each percentile in increasing order. The data are from DQYDJ using a survey published in 2020 [4]. Each income value represents the threshold income required for one household to enter that percentile. To estimate the income in the top bracket, 99 to 100%, Bloomberg reported that the top 1% earned 21% of all US income. Using the data provided in Ref [4], this gives an average income of $2.38 M for each household in this bracket. In the figure, the single symbol at top right is a recent estimate (2021) of income for the top percentile. An article in Business Insider, citing a Forbes study [5], states that 644 US billionaires added $1.3T to their wealth from March 2020 to February 2021. The plot in Fig. 3 does not have brackets smaller than one percent. A crude estimate of the recent increase of income for the top one percent is found by dividing $1.3T by 1.65 million households, giving an added income of $0.79M per household, as represented by the symbol. The article notes that the average American worker saw a 10.3% decline in earnings during the same period. Forbes also notes that the number of billionaires in the world increased to 1,275, and the US share increased to 724.
Wealth inequality for about 180 of the world’s 193 nations was studied by Credit Suisse. They compiled data and calculated the Gini coefficient. Their study is available as a pdf download [6] and their list of Gini coefficients can be found at the Wiki site “List of Countries by Wealth Inequality” [7]. The Credit Suisse calculation uses data that differ somewhat from the SCF data I used. Their calculation for 2019 gives G = 0.85 for the US. The calculation I presented above is in good agreement, but the Credit Suisse calculation is probably more accurate. The table at the Wiki site displays other relevant data, including the “fraction of world GDP” and “GDP per capita” for each country. The latter data set can be thought of as a crude way of comparing average incomes.
It’s interesting to consider some of the values in this table. The countries with the highest Gini coefficients are Netherlands, Russia, Sweden and the US, in that order. What’s unique about the US is the staggering amount of wealth at the top. The US contributes 24% of world GDP, by far the single largest portion and far larger than the shares from the other three countries, each less than 2%. At the very top, the ten wealthiest Americans account for about $1.12 T. This surpasses the entire privately held wealth of numerous nations, such as Ireland. It’s also remarkable that 9 of the 10 are from a single economic sector, high technology, and they made their vast fortunes in a span of a few decades [8]. It’s interesting to note that if the NASA Apollo program were to be initiated today, the entire program could be funded personally by Jeff Bezos, who would still have $40B left [9].
At the other end of the spectrum and among countries that contribute more than 0.5% of the world GDP, Belgium has a low Gini coefficient of 0.60 while maintaining a high GDP per capita of $47,300. Other notable entries near the bottom are South Korea, G = 0.61, and Japan, G = 0.63. Note that Japan has a high GDP, contributing 5.8% of the world total. More broadly, it’s interesting that the Gini value for the world at large is 0.89, slightly smaller than the Netherlands and about the same as Russia. Most nations have G values between 0.60 and 0.85, and most have little wealth. The high world Gini value is because most of the world’s wealth is held by a small number of people in a small number of nations.
One can make a variety of comments about wealth inequality in the US. I already noted that the wealth of the top 1% equals the total wealth of the bottom 93 percent. Jeff Bezos has a reported wealth of $192 B. This value is roughly equivalent with that of the bottom 36 percent (59 million households). As another comparison, the wealth of all the 1.6 million households in the 49th percentile sums to $188 billion, approximately the same as Bezos. This percentile bracket is very close to the median percentile of 50%, and one can state that the wealth of a single person, Jeff Bezos, is about 1.6 million times larger than the wealth of a person who has approximately achieved the median household value. The personal wealth of Bill Gates, about $127 B, is larger than the entire market capitalization of the company he outsmarted 40 years ago. IBM was once the giant of the tech world. Big Blue was so big it was considered a monopoly and it fought antitrust litigation of the US government for many years. Decades later, Bill Gates’ personal wealth exceeds IBM’s market cap, about $112 B at the end of 2020.
The political discussion of Wealth Inequality is highly polarized. One side of the argument presents capitalism as a pure philosophy based on free markets and supply and demand. In this view, poor people are poor because that’s what they deserve. Their own character weaknesses keep them poor: “If they would just work harder, they would have more money.” Rich people are rich because they deserve to be rich. There should be no limits imposed on a free market, and therefore no limits imposed on the wealth of the richest people. A different viewpoint is that there are two economies, one for the 1% and the other for the 99%, and each has separate rules. This can be illustrated by discussing the coronavirus economy of the last 14 months.
The pandemic dictated economic areas where demand rose and/or supply fell. Many people adopted conditions nearing self-quarantine and the demand for delivery services rose. People spent more time working from home, less time in the office, and the demand for toilet paper packaged for home use rose. People were afraid to travel and the demand for air travel and hotel rooms fell. But really, the most crucial areas of the economy were (1) health care and (2) biochemical research, development and manufacturing of vaccines and medications. With 34 million cases of covid and 600 thousand deaths, the US health care system was frequently at the breaking point because of the demand for medical care. Similarly, the single commodity in the highest demand has been a cure for the virus, an effective vaccine.
Registered nurses are on the front lines of the pandemic care response. Many have been infected by the virus and many have died. According to the Bureau of Labor statistics, the median salary for a registered nurse in 2020 was $65,600 (the 49th percentile in Fig. 3). According to nursingprocess.org, nursing salaries have risen about 2% per year for the past 6 years, and are projected to rise about 2% in 2021. If emergency health care has such high demand, and supply is approximately constant, why aren’t their salaries rising at a rate higher than inflation? As another example, the workers who are devoted to the research that led to the three successful covid vaccines are biochemists and the workforce is dominated by those with a doctorate degree. Similarly, these are the workers who are instrumental in developing and then monitoring manufacturing processes. The major pharmaceutical companies employ thousands, if not tens of thousands, of Ph. D. Biochemists. According to “Best Jobs US News,” the median salary in the US for this position was $94,500 in 2020 (63rd percentile). Like health care, these salaries have risen at a rate approximately equal to inflation for the last 5 years. But the vaccines are the single product that has the highest demand during the pandemic. Why don’t their salaries rise faster than inflation? In these cases, there is a social judgment that individuals or companies should not profiteer (make unfair profit) from a national emergency. This judgment applies to the economy of the 99%.
The economy of the 99% has wobbled during the last 12 months of the pandemic. There were staggering job losses in the Spring of 2020 and, a year later, the unemployment rate is 6.1%. This is approximately 80% higher than it was in 2019. The US Gross Domestic Product (GDP) shrank 3.5% in 2020, with service industries suffering the most. By contrast, the economy of the 1% has boomed. As mentioned above [5], Forbes reports that US billionaires increased their wealth by 44% from March 2020 to February 2021. More broadly, major corporations have enjoyed large increases in their market capitalization, as measured in mid-March, 2021 compared with mid-March, 2020: Amazon (+60%), Microsoft (+44%), Facebook (+61%), Tesla (+370%), Walmart (+37%), and Moderna (+430%). Moderna reported that its vaccine, which was developed with the help of $480M of government funds, is expected to bring revenues of $18.5B in 2021. Will Moderna’s scientists receive any of this income? Will the corporate managers receive this income? The pandemic has caused illness and death in the US on a scale not seen in a hundred years, but it’s been good for some businesses and for our wealthiest citizens. The principles of free markets seem to apply here. One would argue that there has been surging demand for shopping and working online. And, apparently, there is swelling need to spend more time on social media.
A contrary view is that the rules that guide the economy are controlled by the largest corporations and the wealthiest people. In the economy of the one percent, individual wealth grows without limit and the largest companies become monopolies. Historically, Standard Oil (John Rockefeller) controlled 88% of refined oil in the US in 1890, and the company was divided into smaller companies by anti-trust laws in 1911. US Steel (JP Morgan and Andrew Carnegie) controlled 67% of American steel production in the early 1900s. Steel production in America diminished in the following decades and no anti-trust action was taken. In the 1960s, IBM controlled 70% of the computer market. The US government filed an anti-trust suit in 1969. The action continued for a decade before it was dropped in 1982.
As of March 2020, Amazon had 39% of the e-commerce market in the US, about 8 times larger than the share of closest competitor Walmart (5%). Recent reports state that Amazon’s share was 47% by the end of 2020, and predict that the share will grow to 50% in 2021. Microsoft’s share of operating systems used in personal computers is between 85 and 90%. Facebook controls 61% of all traffic (visits) on social media sites. Alphabet (Google) controls 60% of global advertising revenue. These large companies are oligopolies, if not monopolies, and their owners receive enormous benefits.
Debates about wealth inequality have been the same for the last 50 years, if not longer. The non-wealthy argue that the slice of pie owned by the rich should be made smaller. The wealthy respond by stating that changing the slice of the pie is not relevant. Instead, we should make the pie bigger and then everyone would have more. However, while the pie has been growing along with the GDP, the Gini coefficient and the slice of the top 1% also have been increasing. Wealth inequality began to increase in the early 1980s and the gap has been diverging ever since. The data in Ref. [7] show that the Gini coefficient has increased from 0.80 in 2008 to 0.85 in 2019. The key feature of wealth inequality is that it provides conditions that encourage further increases of inequality. The present condition, with such enormous wealth inequality, isn’t succeeding for our society. Businesses owned by the top 1% are too big to fail and receive government support when needed. If a business in the economy of the 99% fails, there are scant resources for help. According to Forbes [10], as of September 2020 there were more than 160,000 small business closures in the US, and 100,000 of these were permanent.
US life expectancy is falling, dominated by statistics from the bottom 90%. It was 77.8 years in 2020, a year lower than the life expectancy in 2014 and the lowest since 2006. UNICEF ranked 41 advanced nations for childhood poverty [11], defined as living in households with income below 60% of the national median. Countries with the highest poverty rates are given the lowest ratings. The US ranked 38th out of 41, having 30 percent of children in poverty. For lowest poverty, the top five ratings were given to Iceland (G = 0.69), the Czech Republic (G = 0.73), Denmark (G = 0.84), Finland (G = 0.74), and South Korea (G = 0.61). Besides the US, the bottom five included Mexico, Israel, Romania and Turkey.
Wealth inequality is a natural occurrence in human societies. The extreme wealth inequality in the US is not natural and is not accidental. Using the logic of Occum’s razor, the simplest explanation is that the wealthiest people are working to increase wealth inequality. They use their economic and political power to increase their share of the pie.
References:
[1] https://dqydj.com/average-median-top-net-worth-percentiles/
[2] Wealth and Income Concentration in the Survey of Consumer Finances: 1989–2019, FEDS Notes, September 28,2020. https://www.federalreserve.gov/econres/notes/feds-notes/wealth-and-income-concentration-in-the-scf-20200928.htm
[4] https://dqydj.com/household-income-percentile-calculator/, source information for methodology and data are available at this website.
[6] “Global wealth databook 2019” (PDF). Credit Suisse.
[7] https://en.wikipedia.org/wiki/List_of_countries_by_wealth_equality
[8] Rhys McCarney, “Inventions That Built the Information Technology Revolution,” (Lulu Publishing, 2018); available as an eBook from Amazon and Apple Books.
[9] Significant funding for the Apollo program started in 19960 and the program ended in 1974, having spent a total of $29.3B, measured in 1975 dollars. Allowing for inflation to the present the total cost was $145B. Even Elon Musk could pay for the program, though that might leave him with only a few hundred million. See also [8].
[10] https://fortune.com/2020/09/28/covid-buisnesses-shut-down-closed/
[11] https://www.unicef-irc.org/publications/pdf/Report-Card-16-Worlds-of-Influence-child-wellbeing.pdf
