
Percentile Graphs:
Here we can see that incomes increased for all
percentiles between 1980 and 1990.
But who enjoyed the greatest increase?
To find this out we can plot the ratio between 1990
incomes and 1980 incomes.


Change in Income: 1980  1990
Here we look at change in incomes as a function of
percentile. The top percentiles did, in fact, get the
greatest increase.
Note1: the zigzag in the middle of the graph is probably
data "noise" arising from changes in the way incomes were
reported.
Note2: A better comparison would normalize this data to
the inflation rate.

Inverse frequency Plots
More can be learned from the data if its shown as an
inverse frequency plot on a logarithmic grid. This makes it
easier to see the incomes distribution of the rich (although
it makes it harder to the the distribution for the poor.
Explanations:
 Logarithmic Plot  each division between black lines
represents an increase of 10 times. The lines represent
numbers of that magnitude: ie: between 10 and 100 the
green lines represent 20, 30, 40, 50, 60, 70, 80,90
 Inverse Frequency Plot  each mark on the Xaxis
means that only one person out of that number earn more
than that income. For example in 1980 (red line) only 1 out of every 10
earned more than 30,000. In 1990 (blue dash) only 1 out of 2 earned
more than 20,000, and only 1 out of 20 earned more than
60,000.


Notice there is a greater separation between the two
lines at the higher incomes. This, again, shows that the
greater gains were at the higher incomes.
Note: this data is not normalized to inflation, or
anything else.

Normalizing :
means assume some numbers represent the same value and
adjust all the others accordingly. This is what is done when
inflation numbers are reported. Below, we normalize the 1980
and 1990 incomes at the 1 out of 2 frequency.

Note: 1 out of 2 is the same as the 50th percentile


With normalization, no change is noticeable until the earner is doing
doing better than about 1 out of 10 (90th percentile.)
That means IRS data implies that the the only real increases in standard
of living occurred for top 10% of earners.

Distribution of Incomes:
A distribution plot tells us how many are at each level.
We would expect that there are more middle class than rich,
and we would desire that there are less poor than middle
class. This description implies that ideally we should see
the characteristics of a "bandpass filter."



Here the plots of incomes for 1980, 1984, 1988, and 1990
all look like low pass filters.
Thinkers challenge: what forces could have caused the
corner income to be about 22,000 in 1980 and about 42,000 in
1990?

Derivative of Density:
a derivative means how much did it change from one level
to the next. By looking at the derivatives of density for
each year it is easy to see the corner incomes and some
other interesting characteristics.

Data noise  fluctuation resulting from the way
that the data is recorded, not from the data itself.


Notes:
some of the zigzags before the corner incomes could be
data "noise."
Thinkers challenge: why does the dropoff decrease for
incomes above 60,000 for 1980, and above 130,00 for 1990?
Could it be these are the incomes where it is hard to spend
more than your return on your investments?
