8
It would seem that in practice, in view of the value of hCj
,y must often be more or less high,so that the Pareto
pattern will be confined to a rather narrow range of the
income distribution while in the case of wealth it usually
extends to almost the whole of the assessed wealth data.
This, it is true, partly results from the fact that the
wealth data are more truncated than the income data,in
view of the underlying tax laws.
Income and Wealth:Empirical Patterns
The following illustrations are based on the cross
classification of income and wealth available in Holland
and in Sweden. These data share certain characteristics
found also in other cross section data on size
distributions given in official publications.The first
feature is that the great bulk of the observations is
concentrated in the corner of the first (the north-east
quadrantIn other words the 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. To put it in another way,only a small
proportion of all income earners are assessed for wealth.
If the mean income in the various wealth classes is
calculated,a linear regression of a very regular pattern
is obtained (fig.l). This "regression of the first kind"
as it is called (Cramer 1946 p.270 )differs from the usual
least squares regression in that it does not assume a
priori a certain mathematical function for the
regression.If the regression of the means turns out to be
linear as is the case here then we should expect it to be
the same as the result of a least squares regression on
the basis of the full data (a difference may
arise,however, in so far as we do not take into account
the weights for the means corresponding to the frequencies
in the various wealth classes).
If the same regression of the first kind is calculated in
the other dimension,that is , if we take the mean wealth
for each of the various income classes,a completely
different picture emerges:The mean wealth in the lowest
income classes does not increase with income at all; for
higher incomes it increases strongly so that a distinctly
curved regression line results.
The reason - or at least the most important of the reasons
-for the peculiar shape of this regression line lies in
the truncation of the wealth data. In the lower income
classes we find only people who have something like the