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

Utility Analysis and the Consumption Function 25
II.4 Some Evidence on the Constancy of the Saving Ratio for a
Stationary Cross Section
In order to understand the foundations of Reid’s highly ingenious techniques and
the meaning of her results, we must turn back to our figures 1.1 and 1.2, and to
the reasoning underlying their construction. Suppose that, somehow, we had been
able to locate a sample of households, within their earning span, each of which
fulfilled completely our stationary specifications. For every member of this
sample, because of the complete absence of short-term income fluctuations, we
would have the chain of equalities y = y e = y e -1 = y -1 so that the correlation between
current and previous income, r yy-1 , would be unity. Furthermore, if our theory is
correct, the elasticity of consumption with respect to current income, h cy , would
also be unity. Moreover, this conclusion would continue to hold if the above chain
of equalities were replaced by “proportionality,”
e e
y y-1
y-1
ie .., y= = = .
k k k
1
2
3
In this case, all the households are out of stationary equilibrium but, so to
speak, by the same proportion; this would affect the slope of the c¯(y) curve of
figure 1, but not its intercept, so that the consumption-income elasticity would
remain unity. 44
Now, since information on the permanent component of income and the degree
of adjustment to it is not available, it is impossible to locate a sample fulfilling
exactly our specifications. On the other hand, it may not be impossible to find
one for which short-term fluctuations are of relatively minor importance and
current income is relatively close to the level to which the household is adjusted.
These conditions might be satisfied, for instance, by a sample of government
employees or of college professors. For such a sample we would expect to find
a correlation between current and previous income, r yy-1 , close to unity and, if our
model is correct, an elasticity of consumption with respect to income, h cy , close
to unity. At the other extreme, for a group of households for which random shortterm
fluctuations play a dominant role, say, a sample of farmers over a wide geographical
region, we would have a low value of r yy-1 and, as we know from the
analysis of figure 1.2, a low elasticity of consumption with respect to income.
This implication of our model clearly forms the basis for a crucial experiment;
this experiment has not been carried out as such, although we look forward to its
being performed in the near future by anyone having the resources and interest.
Meanwhile, Reid’s method is very similar to the comparison we have just proposed.
The discussion that has led us to the formulation of our crucial experiment
suggests that the correlation between current and previous income can be taken