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

Utility Analysis and the Consumption Function 35
If the quantity L i were a constant, this equation would be identical in form with
the equation Klein proposed to test; 63 although, in the actual statistical test he has
found it convenient to approximate the first two terms by an expression of the
form l + mlog y i , and the variable
y
i
-y-1i
yi
-y-1i
by .
y y
i
-1i
If we now look at Klein’s results, we can take courage from the fact that all
his coefficients have at least the sign required by our model; namely, a positive
sign for income, income change, and age (t in our notation, a in Klein’s) and
negative for assets
Ê a
in our notation,
Ë y
L
Y
ˆ
in Klein’s
¯.
This result is of some significance, especially in the case of the age variable.
According to our model, the positive sign of this coefficient reflects the fact that
within the earning span, for a given level of income and assets, the older the
household the smaller will tend to be its resources per remaining year of life, and
therefore the smaller the consumption (i.e., the higher the saving).
It would be interesting to compare the size of Klein’s coefficients with the
values implied by our model. At this point, however, we must remember that the
analogy between Klein’s equation and our equation (A.5) is more formal than
real; for Klein treats his coefficients as if they were constant, whereas, according
to our model, they are all functions of age since they all involve the quantity L i .
Consideration of the sensitivity of the coefficients of our equation to variations
in t suggests that the error involved in treating them as constants might be quite
serious. We must further remember that the specific value of the coefficients in
(A.5) is based on Assumptions III and IV. As we have repeatedly indicated, these
Assumptions are introduced for expository convenience but are not an essential
part of our model. With the elimination of Assumption III and the relaxation of
IV, along the lines suggested note 23, the form of our equations and the sign of
the coefficients are unchanged, but the value of these coefficients is not necessarily
that given in equation (A.5), nor is it possible to deduce these values
entirely on a prior grounds, except within broad limits.
We might, nonetheless, attempt a comparison, for whatever it is worth, by
replacing the variable t i , in the expression L i by a constant, say, by its average
value in Klein’s sample. Unfortunately, this average is not published, but we
should not go far wrong by putting it at between 15 and 25 and computing a range
for each coefficient using these two values.” We must also take a guess at the
value of b 1 and b 2 . These quantities, it will be noted, are not observable. On the