"Life Cycle" Hypothesis of Saving: Aggregate ... - Arabictrader.com

The “Life-Cycle” Hypothesis of Saving 71
2
DC = 0. 731DY+ 0. 047DA R = 0.
44
( 0. 180) ( 0. 037) DW = 2.
48
C
Y
A
2
= 0. 505 + 0. 112 R = 0.
51
Y
( 0. 144) ( 0. 021) DW = 1.
05
(b)
(c)
B Biases in Estimating the Consumption Function by Regression on
Saving
Suppose that true consumption c* and true income y* are related by a linear function
(all variables being measured from their means),
c * = ay
* + e
and measured income and measured consumption are related to their respective
true values by
(a)
c= c* + h
y= y* + x
(b)
(c)
where e, h, and x are random variables. For simplicity, let us assume that e is
uncorrelated with h, and x; h and x are uncorrelated with c* and y*. We also
have the definitions
s* = y* -c*
s = y- c = y* - c* + x - h
Using (a) and (d), We have
(d)
(d¢)
c* a
s* e
= + ∫ s* + ¢ .
1 - a 1 - a b e
(e)
In order to concentrate first on the effect of errors of measurements, let us
momentarily accept the unwarranted assumption that saving is equal to investment
which in turn is truly exogenous. Under this assumption s* can be taken
as independent of e¢ and therefore, if we could actually observe s* and c*, by
regressing c* on s* we could secure an unbiased estimate of b from which we
could in turn derive a consistent estimate of a. If, however, we estimate b by
regressing c on s, then remembering that s is obtained as a residual from y and
c, we obtain the estimate
Â
Â
bˆ
cs
= =
s
Â
* *
*
2
( bs
+ e¢+
h) ( s + x-h)
b s + h( x-h)
=
.
( * + x-h)
*
2 2
s
s + ( x-h)
Â
2 2
Â
Â
Â
Â
(f)