The Distribution of Wealth

 

If I Were A Rich Man

Lord who made the lion and the lamb,
You decreed I should be what I am
Would it spoil some vast eternal plan?
If I were a wealthy man.

What does it mean to be wealthy?

Donald Trump, Jr. famously was taken to task when he said that when the average increased everyone benefits because that is how math works.  Unless they taught a different version of math at the Wharton School than I learned UPenn’s nearby Towne School of Engineering, the problem is that average is often taken to be the mean and what DJT, Jr. probably meant is that when the median increases everyone benefits.  It is possible for the mean to increase and only those at the top to benefit, and the median to be unchanged or even become worse.  Under a normal statistical distribution the mean, median and the, seldom used statistic, mode, are all the equal.  ( Mathematicians  also call this a Gaussian distribution, but  the bell-shaped curve is popularly called the normal distribution.)

The normal distribution is what may be used by the general public to determine when a distribution is “fair and equitable”.  In that case when people say the average, they may intend to use the median, not the mean.  The mean is easier to compute.  It requires only the totals of the two values, e.g. wealth and population.  The median, the point where 50% is above and below a quantity, e.g. wealth, requires knowledge of the value for every member of the population.  If in a normal distribution, the mean and median are equal,. The ratio of the mean to the median is an indication of how skewed is the distribution.

The United States is the wealthiest country in the world based on the 2021 Global Wealth Databook published by Credit Suisse. https://www.credit-suisse.com/media/assets/corporate/docs/about-us/research/publications/global-wealth-databook-2021.pdf.  Its wealth is 168% of second place China even though it has only 22% of the adult population of China.  The United States is in second place for mean wealth per adult to Switzerland. The US’s mean wealthper adult is 76% of the mean wealthper adult in Switzerland.  However the United States is in 26^th place among countries ranked by median wealth. The ratio of mean to median wealth, weighted by adult population, among the countries listed in the Global Databook is 3.54.  The ratio of mean to median wealth in the United States is 6.48 which places it third behind Brunei (7.63) and Bahamas (7.56) and just ahead of Bahrain (6.03) and the United Arab Emirates (5.34).  The country with the lowest ratio of mean to median wealth is Iceland (1.46)

According to an article in Business Insider, https://www.businessinsider.com/personal-finance/average-american-net-worth, all subgroups of the population in the United States are higher than 3.54, the weighted global ratio of mean to median wealth per adult population.  The group coming closest to the weighted world average is households living in rural areas (3.59) compared to  those living in urban areas (6.40).  This probably is because the very wealthy, those that are cause of this disparity, have chosen to live in urban areas, not because of some attribute of those rural areas.  The ratio for Blacks is 6.02 which is higher than the ratio of White, Non Hispanics, but that ratio (5.06) is still higher than the global ratio. The ratio of mean to median worth is greatest for those owning a home (4.32) versus those not owning a home (15.17).  This suggests that computing means and medians, excluding the principal residence from net worth, might be instructive.