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

16 The Life-Cycle Hypothesis
The first form of equation (II.2¢) states the proposition that saving is equal to:
(1) a constant fraction of the permanent component of income (independent of
both age and income) which fraction is precisely the stationary equilibrium saving
ratio; plus (2) a fraction of the nonpermanent component of income [this fraction
is independent of income but depends on age and is larger, in fact much larger,
than the fraction under (1)]; minus (3) a fraction, depending only on age, of excess
assets. A similar interpretation can be given to the second form of (II.2¢).
Equation (II.2¢) is useful for examining the behavior of an individual, who,
after having been in stationary equilibrium up to age t - 1, experiences an unexpected
increase in income at age t so that y t > y e t-1 = y t-1 . Here we must distinguish
two possibilities. Suppose, first, the increase is viewed as being strictly
temporary so that y e t = y e t-1 = y t-1 . In this case a t = a(y e t,t). 26 There is no imbalance
in assets and, therefore, the third term is zero. But the second term will be positive
since a share of current income, amounting to y t - y t-1 , represents a nonpermanent
component. Because our individual will be saving an abnormally large
share of this portion of his income, his saving ratio will rise above the normal
figure
M
L .
This ratio will in fact be higher, the higher the share of current income which is
nonpermanent, or, which is equivalent in this case, the higher the percentage
increase in income. 27 Let us next suppose that the current increase in income
causes him to raise his expectations; and consider the limiting case where y e t = y t ,
i.e., the elasticity of expectations is unity.
In this case the transitory component is, of course, zero; but now the third term
becomes positive, reflecting an insufficiency of assets relative to the new and
higher income expectation. Accordingly, the saving ratio rises again above the
normal level
M
L
by an extent which is greater the greater the percentage increase in income. Moreover,
as we might expect, the fact that expectations have followed income causes
the increase in the saving ratio to be somewhat smaller than in the previous case. 28
Our model implies, then, that a household whose current income unexpectedly
rises above the previous “accustomed” level (where the term “accustomed” refers
to the average expected income to which the household was adjusted), will save
a proportion of its income larger than it was saving before the change and also
larger than is presently saved by the permanent inhabitants of the income bracket