11
Income and Tealth: -muirical Patterns
The following remaiprs refer to the cross-classification::
of wealth and income published in -olland and Sweden. These data
show certain characteristics which are found a].3o in other
cross-section data concerned with sise distributions, especially
data from official publications like censuses etc.
The first feature is that the great bulk of the observations
is concentrated in the corner of the first ( the north-east ) quadrant.
In other wards these distributions are very skew, A great many of the
units are small in either dimension.
The second feature is that the wealth distribution is
heavily truncated ( in Sweden for example at 150.000 crowns)
while the income distribution is given down to rather low levels.
If the mean income in the various wealth classes is
calculated at linear regression of a very regular pattern is obtained.
( This "regression of the first kind" as we may call it differs
from the usual least squares regression in that it does not
assume a -priori a certain mathematical function for the regression?
see Harald Cramir, Mathematical Meoheds of Statistics,Princeton
if the regression of the means turns out to be linear as is the case
here, then it shoild be the same as the result of a linear least
squares regression; this may be not quite true only in so far as
we fail to use weights for the means corresponding to the various
frequencies in the different wealth classes ).
The same regression of the first kind in the other dimension -
wealth on income - gives a completely different picture: ' L he mean
wealth in the lower income classes does not indrease with income
at all;- for higher incomes it increases very strongly, so that
a strongly curved regression line results.
At least one, and probably the most important reason for
the curvi—linearity of this regression line lies in the truncation
of the wealth data. If we try to fill in the missing wealth data
in our imagination, according to plausible and common sense prior
knowledge, we find that the regression of wealth on income might
well be quite linear and rather steep; at least it would be very
much nearer to linearity than it is now. The inclusion of cases■
with wealth below the tax limit, which is probably the lower and
the more frequent the lower the income, would reduce the mean weal oh
in all income classes but it w'uld reduce it the more the lower one