Income Inequality

Straightjacket

Your way's making me mental
How you filter a skewed interpret
I swear you won't be happy 'til
I'm bound in a straight jacket

If incomes are skewed, who should be placed in a straightjacket?

A normal distribution of income with a mean income of $0, also has to considers negative incomes. Since the median income is equal to the mean income in a normal distribution, 50% will have incomes greater than $0 and 50% will have an income less than $0.

If the mean income is $97,026 as reported in the 2020 US Census, and the median is still equal to the mean, it would still be a normal distribution. In this case ~34% should have an income less than $0.  The top one percenters should have an income of approximately 2.33 times the mean or ~$226,070 per year, not the $538,926 that was reported in the 2020 Census.

If the upper incomes are increased, but nothing is done to change the other incomes, the mean and the median will no longer be equal.  In fact according to the US Census, the median household income is $67,521.  The distribution of income is reported as skewed towards higher incomes.  I know that normal and skewed are emotionally loaded terms, but these ARE the terms that are used in statistics.

Incomes less than zero are typically treated as if they were $0.  If these negative incomes are reported as $0, then the mean and the median can no longer be equal.  The Luxembourg Income Study, https://www.lisdatacenter.org/ , tracks income by country. The mean income is less than 120% of the median income in most countries.  It is declining over the period of analysis in all but two countries.  In the United Kingdom, the mean income increased from 110% of the median income in 1980 to 122% in 1994 before stabilizing in a cycle.  According to the LIS, in the US the mean income has increased from 111% of the median income in 1980 to 124% of median income in 2018 and appears to be still increasing.       https://dbeagan.blogspot.com/2021/07/inequality.html. 

Increasing the mean national income does NOT increase the median national income unless those incomes are also equitably distributed.  It is possible to increase the mean income without changing median income, which appears to be why the gap between mean and median income is increasing.

During the height of the COVID pandemic, the phrase “flattening the curve”  became common.  Mathematically this means that the variance of the distribution was increased, This reduces the height at the median, e. g. the maximum cases that will need ICU beds at that point in time.  The number of cases over time will not change, but “flattening the curve”, increasing the variance, is a way to reduce that maximum demand on hospital ICU beds.  It seems like a similar phrase should be used for “skewing the curve” to describe income distribution.  The number of people with zero income does not change, the national income does not change, but more of that income is skewed to higher incomes than would be expected if incomes were normally distributed.