Full text: The Personal Distribution of Income

1.6 
Thus in our case the income is 7 = fC w 4- 7q where we suppose 
that the distribution of income and wealth reflects in 3ome wa7 
a growth process which has taken place in the past. 
In the ordinar7 formulation we should have 
_ * t 
v7 = c, e 
At 
Y = <2±e 
and after elimination of time 
/3 
7 - In o., » — ( w - In c. ) 
,-o 
O 
(?) 
which corresponds to our regression with ki ~ 
•A 
How in economics random elements or shocks pla7 a large 
role and growth is influenced b7 them. i7e should therefore write, 
instead . of the above: . 
ext , , 
W = c i e + £ ( t) 
at 
r - o a e + nj (t) 
where £ (t) and 
In ( T - ^(t) ) 
>0 (t) are random variables. As a result we obtain 
A r 
- In c ^ = 
or "? 
--jlnC W - £(t).) . b o>, 
(a) 
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 onl7, which 7ields two regression lines according to 
. whether 70U choose the one or the other variable as the 
repositor7 of the errors. The equation (3) will not correspond 
to either of the two regression lines, ^t nay 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 mainl7 affects unearned income. The other is the influence of 
past incomes on wealth via the propensit7 to 3ave. Since 
present and past incomes are fairl7 strongl7 correlated it 
will appear as if current income acts on wealth via the 
propep.sit7 to save. 
At first sight it seems that the linear regression 
of income on wealth represents simpl7 the influence of wealth 
via the rate of return. There is however an alternative interpretation.
	        

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