Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Saturday, November 23, 2013

Interpretation of scaling laws for US income

It has been remarked that if one tells an economist that inequality has increased, the doctrinaire response is "So what?"
                                          - Oxford Handbook of Inequality

h/t Bruce Krasting

Social Security online has published a full report on income distribution in America.

Two years ago we looked at the distribution of wealth in America. Today we are looking at income.

There were a total of about 153 million wage earners in the US in 2012, which is why the graph suddenly terminates there.

As we have discussed before, in self-organizing systems, we expect the observations, when plotted on logarithmic axes, to lie on a straight line. Casual observation of the above graph shows a slight curve, which gives us some room for interpretation.

I have drawn two possible "ideal states"--the yellow line and the green line. Those who feel the yellow line best represents the "correct" wealth distribution in the US would argue that the discrepancy at the lower income (below about $100k per year) represents government redistribution of wealth from the pockets of the ultra-rich to those less deserving. Followers of the green line would argue the opposite--that the ultra-wealthy are earning roughly double what they should be based on the earnings at the lower end.

Which is it? Looking at the graph you can't tell. But suppose we look at the numbers. Adherents of the yellow line would say that roughly 130 million people are getting more than they should. The largest amount is about 40%, so if we assume that on average these 130 million folks are drawing 20% more than they should (thanks to enslavement of  the ultra-wealthy), we find that these excess drawings total in excess of $1 trillion. Thanks Pluto!

The trouble with this analysis is that the combined earnings of the ultra-wealthy--the top 100,000--earned a total of about $400 billion. They simply aren't rich enough to have provided the middle class with all that money.

Now let's consider the green line. Here we are suggesting that the ultra-wealthy are earning about twice as much as they should be, and let's hypothesize that this extra income is somehow transferred from the middle and lower classes.

As above, the total income of the ultra-rich is about $400 billion. If half of this has been skimmed from the aforementioned 130 million, they would each have to contribute about $1500.

I expect a heavier weight has fallen on those at the upper end of the middle-class spectrum; but even so, $1500 per wage earner does seem doable. Of the two interpretations, the green line looks to be at least plausible, and we are forced to conclude that those who believe the ultra-wealthy are drawing a good portion of their salaries from everyone else have a point.

But isn't $1500 per year a small price to pay to create a really wealthy super-class?

Paper on causes of income inequality full of economic axiomatic gibberish here (pdf).


  1. You might have seen this stuff or might like it:

    Log log slope information on income distributions in different economies.
    I calculated alpha=2 slope for your graph which matches 1.95 slope for USA in 1945.
    Log N=A-alpha*LogY
    (Think this is for cumulative incomes)
    p. 43~46

    Old United States Data (probably not cumulative)
    p. 188~

  2. I used the Social Security Administration's Average Wage Index, and fitted it to a LogNormal distribution (2012). mu=10.2 sigma=1.496. When I checked it against the fit it showed the actual distribution as being skewed more towards the poor. I had hoped to fit income to a gamma distribution as that would give a canonical interpretation to the data, While it did a reasonable job of explaining the lower 99% of the wealth distribution it failed to explain the tails of the high income earners (>200k). Here is my analysis: http://statisticaleconomics.org/2013/11/13/theft-at-the-grandest-scale/

    1. That's good. In your analysis you've gone more into the mechanism of the wealth transfer--something which I avoided.

      I had not seen a thermodynamic treatment of economics previously.