Distribution of Income II

 

Who Needs Money?

What if my pockets are empty as can be?
Who need money?Not me
Tell me about it

How are incomes distributed?

If you want to describe a distribution you need to define:

•         the mean, the first moment of the distribution;
•        the variance, the second moment of the distribution; 
•        the skewness, the third moment of the distribution; and
•        the kurtosis, the fourth moment of the distribution.

If the skew is zero, then the distribution is said to be “normal”.  In a normal distribution, the median and the mean are equal.  The difference between the mean and the median defines the magnitude of the skew of the data, and the direction of that skew.  If the mean is greater than the median, then the skew is positive and it is skewed towards higher values.  If the mean is less than the median, then the skew is negative and it is skewed towards lower values.

The ratio of the mean to the median is an indication of the magnitude of the skew of the distribution.  If the ratio is greater than 1, then not only is the distribution is skewed towards higher values, but the higher this ratio, the more the distribution is skewed to these higher values.  If the ratio is less than 1, then not only is distribution skewed towards these lower values, but the lower this ratio, the more the distribution is skewed to these lower values. If the ratio is equal to 1, the distribution is not skewed, aka is “normal”.

The Luxembourg Income Study https://www.lisdatacenter.org/, reports on Mean and Median income  for numerous countries over a period of time.  The distribution of income can not be “normal”, have a ratio of 1.0, because that would require reporting negative incomes.  For all  of the countries over the reporting period, the weighted average ratio of Mean to Median income is 1.37.  In almost all countries the trend is towards a decreasing ratio.  For developed countries, the income distribution seems to have reached an equilibrium near a ratio of 1.2.  The variation in this ratio once an equilibrium has been reached appears due to randomness of incomes and their reporting.  

The United States appears to be an outlier to the trend of a decreasing ratio, and thus is skewed towards higher incomes.  The United Kingdom also showed this trend during the period 1970 to 2009, however it has reversed this trend and shows a decreasing skew from higher incomes since that time.

It appears that the United States supports economic conditions that increase the skew towards higher incomes and that is in contrast to economic conditions for the rest of the countries that are reporting.