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

44 The Life-Cycle Hypothesis
assumption (II.10) by the more realistic one suggested at the end of note 37, the conclusion stated in
the text would still stand, although the relation between (c¯/ȳ) i and i would be more complex than
indicated by the right-hand side of the above equation.
49. For example, see James Duesenberry, Income, Saving and the Theory of Consumer Behavior.
50. Making use of equations (II.10¢), (II.12) and of the expression for ā(y) of note 39, it can be
verified that
2
∂ cy ( ) < 0 ,
∂y∂t
i.e., the slope of the cross-section consumption-income relation falls with age, provided
1 M v
E > M + - b( 1-
)
1 ( M + 1) ( 1-
b )
.
A very similar condition on E must be satisfied in order for the constant term to rise with age. Since
1/(M + 1) should be in the order of 0.1, and b and n are typically smaller than unity, the right-hand
side of the above inequality cannot significantly exceed zero and is, in fact, likely to be negative.
51. Op. cit., p. 90 and p. 99.
52. There is ample evidence of a very pronounced correlation between assets and income, at least as
far as liquid assets are concerned. See, for example, Lawrence Klein, “Assets, Debts, and Economic
Behavior,” Studies in Income and Wealth, Vol. XIV, Table 1, p. 209; and Fisher, loc. cit., table 6,
p. 86.
53. Gustave Cassel, The Theory of Social Economy, 1932 ed., p. 244; Horst Mender-hausen and
Raymond W. Goldsmith, “Measuring Estate Tax Wealth,” Studies in Income and Wealth, Vol. XIV,
table 4, p. 140; and Fisher, loc. cit. The most systematic information we have found on this subject
is that presented by Janet Fisher, although, unfortunately, her most interesting tabulations relate to
liquid assets only. For this reason we will not attempt an extensive comparison of her findings with
our theory. We may point out, however, that in terms of liquid assets, her data agree remarkably well
with our theory in several respects. For example, a comparison of the mean income ratio (table 1, p.
81) with the mean ratio of liquid asset holdings (table 4, p. 84) by age groups, reveals that the ratio
of assets per spending unit to income per spending unit rises steadily with age. For the age group
45–64, which is her oldest group wherein active households presumably predominate, this ratio is
nearly three times as large as for her youngest group, 18–24. For the age group 65-and-over, wherein,
presumably, retired people predominate, the ratio nearly doubles again. This very high ratio is
precisely what should be expected from our model where assets are drawn down slowly but income
falls much faster with retirement. In terms of assets, rather than of the income/asset ratio, the peak
should be reached just before retirement. Confirmation of this inference is found in the tabulations
of table 5 (p. 85).
Also, suggestive of this relation is the complaint by Lawrence Klein, “Assets, Debts, and Economic
Behavior,” that: “There is some indication that the influence of age on savings may be obscured by
a significant positive correlation between (L/Y) are a” (where Y = income, L = liquid assets, and a =
age of the spending-unit head in years).”
54. All this has, of course, some significant implications about the “Pigou effect” which are developed
in Modigliani and Brumberg, op. cit.
55. Cf. Klein, ibid., pp. 220 ff.
56. More generally, the essential implication of our theory that should be tested is that the (average)
relation between consumption and net worth, given income and income expectations, is linear and
with a slope which tends to grow with the age of the household. The specific value of the slope given
by (II.15) depends on Assumptions III and IV which are convenient for exposition but are not essential
to the theory.
57. In the very early years these motives might possibly lead to a somewhat faster rate of accumulation
than might occur otherwise. On the other hand, in his early years, an individual may feel less