Full text: The Personal Distribution of Income

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

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