16
Thus in our case the income is y = fC w -^-ye where we suppose
that the distribution of income and wealth reflects in some way
a growth process which has taken place in the past.
W = Cj e
In the ordinary formulation we should have
act
ßt
Y = C2.e
and after elimination of time
ß
y “ In c 2= —
Z OC
( w - In C| )
3
(7)
which corresponds to our regression with r— ^
Now in economics random elements or shocks play a large
role and growth is influenced by them. We should therefore write,
instead , of the above:
W = c,
Y =
aft
e +
ßt
0 % e
£(t)
+ y (t)
(8)
where £ (t) and VJ(t) are random variables. As a result we obtain
ln ( Y - yj(t) ) -lnoj- jfci( W - £(t) ) - In c^.
The random variables or "errors" ( not mere errors
of observation^of course ) are in both variables. The common
tactics of regression is to ascribe all the "errors" to one
variable only, which yields two regression lines according to
> whether you choose the one or the other variable as the
repository of the errors. The equation (8) will not correspond
to either of 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 to save. Since
present and past incomes are fairly strongly correlated it
will appear as if current income acts on wealth via the
propensity to save.
At first sight it seems that the linear regression
of income on wealth represents simply the influehce of wealth
via the rate of return. There is however an alternative interpretation.