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

42 The Life-Cycle Hypothesis
which can be expressed entirely in terms of y by making use of equation (II.10¢). The above expression
must fall as income rises, as stated in the text, since its derivative with respect to y is proportional
to -[E(1 - b) + b(1 - v)], which is necessarily negative (provided E > 0, which is assumed).
In fact, we can establish that
e >
E{ [ a- a( y , t)
] y}= <
0
<
as y= y
È l -1
1-
˘
,
>
ÎÍ l[ E( 1- b+ b( 1-v)
)]
˚˙
which shows explicitly the level of income at which the average gap between a and a(y e ,t) is zero.
40. We have seen that a high elasticity of expectations tends to pull ȳ e (y) closer to the 45-degree
line; at the same time, however, it will tend to flatten the p¯ (y) curve relative to the ȳ e (y) curve, for,
if assets are approximately adjusted to y e -1, then the larger the gap between y e and y -1 , the larger will
tend to be the unbalance in assets. Since, however, the second effect does not quite offset the first
(see the discussion of section II.2, especially page 20), a high value of E will on the whole, increase
the slope and reduce the intercept of p¯ (y) and thus of c¯(y).
41. They may, in fact, have an average consumption level below the over-all average for two reasons:
(a) because it seems likely that the level of consumption planned for after retirement will, on the
whole, tend to be smaller than the average level during the earning span; (b) because of the secular
rise in income per capita which characterizes most of the economies for which we have budget data.
See, on this point, Modigliani and Brumberg, op. cit.
42. Our statements about retired households find strong support in the data on the size distribution
of income by age, reported by Janet A. Fisher, in “Income, Spending, and Saving Patterns of Consumer
Units in Different Age Groups,” Studies in Income and Wealth, Vol. XV, especially tables 1
and 2, pp. 81 and 82. Actually, these tables are likely to overestimate the income (used in our sense)
of elderly people, since income, there, is defined to include such items as pensions and retirement
pay (p. 81, note 6). These inclusions also reduce the usefulness of the information on saving and dissaving
by age groups presented in table 11 (p. 93). Even with the upward-biased definition of income,
the proportion of positive savers is smaller in the age group 65 and over than in any other group
except the group 18 to 24. For this latter group, of course, the figures are seriously affected by the
inclusion of durable goods purchases in consumption. Presumably, had our definitions of income and
saving been adopted, the relative scarcity of savers and predominance of dissavers in the elderly group
would be much more pronounced.
43. These results were first reported in a brief communication presented at the Conference on Saving,
Inflation and Economic Progress, University of Minnesota, in May, 1952. The authors have also had
the opportunity to consult a preliminary draft on “The Relation of the Within-Group Permanent Component
of Income to the Income Elasticity of Expenditures,” and have had the benefit of extensive
discussion and consultations with Miss Reid. The hypothesis tested in the above-mentioned paper had
already been partly anticipated in Reid’s earlier contribution, “Effect of Income Concept upon Expenditure
Curves of Farm Families,” Studies in Income and Wealth, Vol. XV, especially pp. 133–139.
44. If the equalities are replaced by proportionality, the correlation r yy-1 remains unity. Furthermore,
replacing in (II.1) y e by k i y, and a by
( t-1)
M e
( t -1)
Mvk2
vy-1
=
y,
L
L
(since by assumption, up to the beginning of the current year the assets of every household are proportional
to the stationary equilibrium value, n being the proportionality factor and having the same
meaning as in note 41), we obtain
L+ L( N-t) k1+ M( t-1)
vk2
c =
y,
LL
t
so that, for any given age t, the consumption-income relation is still a straight line through the origin
and therefore h cy is still unity. Since, however, the slope varies with age, if we fail to stratify by age,