# Full text: The Personal Distribution of Income

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Thus in ur case the inc me is y » K w ^ where we supp se
that the distribution >f income and wealth reflects in some way
a growth pr cess which has taken place in the past
In the ordinary fonulation we should have
and after elimination of time
y - In c* •» ( w • In c . )
<* . _ A
which corresponds to our regression with »v *
X
(7)
how in economics random elements or shocks play a large
role and growth is influenced by them. We should therefore write,
W => c . e
Y = c ^
£ (t)
(t)
where £ (t) and Yj (t) are rand m variables. As a result we obtain
a (
In ( Y - >j(t) ) - In c ; , * ~ i ln( w - £ (t) ) - In cj
(8)
The random variables or "err rs" ( not mere ei*r rs
of observati n ( f curse ) are in both variables The common
tactics of re ressi n is to ascribe all the "e Tors" to one
variable only, which yields tw regression lines acc rding to
srf whether you choose the one or the other variable as the
rep sitory f the errors. The equation (8) will not correspond
to either >f the £ two regression lines. -*-t may be guessed that it
will lie somewhere between them. '
Let us now start from a different angle and consider
the two kinds of relations that exist between income and wealth.
One is the influence of wealth on income via the rate of return.
It mainly affects unearned income. The other is the influence of
past incomes on wealth via the propensity t® save. Since
present and past incomes are fairly strongly correlated it
will appear as if current income acts qin wealth via the
li ' \
propensity to save. I; \
At first sight it seems that the linear regression
of income on wealth represents simply the influence of wealth
via the rate of ret rn. There is h wever an alternative interpretation.
;
```

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