Full text: The Personal Distribution of Income

Outlook on further developments. 
In this paper the idea has been elaborated that the amount 
of wealth determines the chances of having certain amounts 
of income.But it may be thought that also the inverse 
relation - influence of income on wealth - plays a role. 
Certainly the increment of wealth per year depends on 
income,given the rate of saving out of various incomes. If 
we take into account that the present income is usually 
strongly correlated with the past incomes of the same 
person,or even of his ancestors, then it appears that the 
chances of a certain wealth may be determined,indirectly, 
by the present income.And we may connect this relation 
with the regression line of wealth on income (which in the 
Swedish data appears so very distorted on account of the 
truncation of the distribution). There are,then, two 
theories ,and two regression lines. It would be very 
convenient if we could regard each of the regression lines 
as a true picture of the corresponding theory. This 
correspondence is,however,marred by the greater or lesser 
dispersion of values round each of the regression lines. 
It can easily be seen that the dispersion round one of the 
regression lines will influence the shape of the other 
regression line. If the rate of return of a given wealth 
is widely dispersed then the persons with a high rate of 
return will be classified in the high income classes,those 
with the same wealth but with a low rate of return among 
the small incomes. This will more or less strongly 
counteract the tendency of wealth to increase with income, 
it will flatten out the regression line. 
It seems to me that the joint distribution of two 
variables like income and wealth should be approached from 
the standpoint of a more elaborate theory. One could 
imagine a stochastic process,in the simplest case a Markov 
chain, in two stages: One matrix would show for each 
amount of wealth at the beginning of the year the 
probabilities of various incomes in that year. Another 
matrix would show for each of these incomes the 
probability of wealth at the end of the year - which 
results from the addition of the saving out of the various 
incomes to the initial wealth.In this way both 
parameters,the rate of return on wealth and the rate of 
saving out of income, would play their role in the 
process. A multiplication of these matrices would describe 
a continuing process of accumulation,starting from 
certain initial conditions of wealth distribution. We may 
then, under certain conditions,if we allow also for new 
entries, derive a steady state of the joint distribution

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