11
Income and Wealth: Empirical Patterns
The following remains refer to the cross-classifications
of wealth and income published in Holland and Sweden. These data
show certain characteristics which are found a}.so in other
cross-section data concerned with size 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 w&rds 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 a* linear regression of a very regular,- pattern is obtained.
( This "regression of the first kind" as we—may cali^ 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 Metheds of Statistics,Princeton 194
if the regression of the means turns out to be linear as is the case
here, then it shoitld be the same as the result of a linear ieast
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 pictures 1 '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 curvisdinearity 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 wealth
in all income classes but it wiuld reduce it the more the lower the