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