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

12 The Life-Cycle Hypothesis
e
dy
dy
would generally tend to lie between 0 and 1, 18 the marginal propensity to consume
would fall for different individuals between a minimum of 1/50 and a maximum
of 4/5, depending both on age and on the value of
e
dy
.
dy
Unfortunately, the empirical validity of these statements cannot be tested from
observations of actual individual behavior. The reason is that consumption and
income can only have a single value for a given individual at a given age. To be
sure, we might be able to observe the behavior of an individual whose income
had changed in time; but, even if we could control the value of y e , we could not
keep constant his age nor probably his initial assets (i.e., assets at the beginning
of each consumption period). The only way we could possibly check these conclusions
is by observing the behavior of (average) consumption of different
households at different income levels, i.e., by observing the “cross-section”
average and marginal rate of consumption with respect to income. 19
Suppose we make these observations and, for the sake of simplicity, suppose
further that all the households we examine have approximately the same age and
in every case y = y e . Should we then expect the marginal rate of consumption
to be
N - t+1 ,
L t
as equation (II.3) would seem to imply? The answer is no; the individual marginal
propensity to consume cannot be simply identified with the cross-section
marginal rate of consumption. Turning back to equation (II.1), we can easily see
that (if all individuals behave according to this equation) the cross-section marginal
rate of consumption should be
dc ¢ N+ 1- t 1 da ¢
= + ,
dy ¢ L L dy ¢
t
t
(II.4)
where the differential operator d¢ is used to denote cross-section differentials.
Although
da
dy