Full text: The Personal Distribution of Income

Cov (w, w-y ) « Var (w) - Cov ( w,y) = Oj 
If the regression line f income on wealth is 
y “ <» + yc 
and/^ if the variance and higher moments >f the conditional 
income distributi n are independent of wealth then we should 
use instead f f(w-y) the function f ( ^w+ y t - y ) 
and this distribution will be independent of wealth. 
We can ten proceed as beforei 
y c> 
q(y) - 0 
for K, w < y -y^ . 
The result is now that the Pareto shape of the wealth 
distribution is reproduced in the income distribution, but with a 
larger Pareto coefficient ( since •< < 1 ). This is exactly what 
has to be explained ( income distributions are in fact more 
"equal'* than the wealth distributions, empirically, in the sense 
described ). The particular shape of the rate of return distribution 
has no influence onthe tail of the income distribution, as long as 
it fulfills the independence conditions mentioned. 
Concerning the res trie tin a. w >y - Vo 
it should be remarked that we are free to shift the coordinate system 
t any yo we choose so as t> make the ab ve condition valid, 
with no c nsequence except that the c nclusi n about the Pareto tail 
will be c nfin#d to incomes in excess of y a . 
It would seem that in practice, in view of the value f 
fC , must ften be more r less high s> that the Part > pattern 
will be c nflned to a rather narrow range if the income distribution 
while in the case f wealth it usually extends to the whole of the 
assessed wealth data. This, it is true partly results fr n the 
fact that the wealth data are more truncated than the income data, 
in view of the underlying tax laws.

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