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

38 The Life-Cycle Hypothesis
14. For a discussion of the effects of removing them, see Modigliani and Brumberg, op. cit. Also,
see various notes below.
15. For an individual of age t > N, by assumption, y = y e = 0 and only the last term on the right-hand
side of (II.1) remains.
16. The valuable work in progress at the Survey Research Center of the University of Michigan gives
hope that the variety of data required for such a test may sometime become available. Clearly, the
problem of measuring average expected future income may prove a serious challenge. On this point,
however, see text below and the Appendix.
17. Obviously, both y e and a will generally be nonnegative.
18. See below, section 3, especially note 37.
19. We speak here advisedly of average and marginal rate of consumption, rather than of “crosssection
marginal propensity to consume,” for, as will become clear, the sue of the latter term is likely
only to encourage a serious and already too frequent type of confusion. The word “propensity” denotes
a psychological disposition and should refer to the way in which a given individual reacts to different
stimuli, and not to the way in which different individuals react to different stimuli. The differential
reaction of different individuals in relation to different stimuli may give us information about the
individual propensity, but it is not, in itself, a propensity.
20. For a generalization of the notion of stationary household, see below note 23.
21. This proposition may be established by mathematical induction. Suppose that the proposition
holds for t, i.e., that
1
( t-1)
M
at
= at
= y1;
L
then, since by assumption
y = y = y , t
N-
,
we have, from (II.2),
s
t
and
t e
M
L y
t = 1
1 1
( t-1)
M M
a a s y
L L y tM
t+ = t + t =
L y a 1
1 1+ 1 = 1 = t+
1.
Thus, if equation (II.7) holds for t it holds also for t + 1. But equation (II.7) holds for t = 1, since
( L-1)
M
a1 = 0 = y1 = a1 1 .
L
(II.7)
Hence, equation (II.7) holds for all t N. By similar reasoning, it can be shown that it holds also
for N + 1 t L.
22. While this result implies that, at zero income, consumption itself would have to be zero, it should
be remembered that, under our stationary assumptions, the current level of income coincides with the
level received in the past and expected in the future. A household whose income is permanently zero
could hardly survive as a separate unit. Or, to put it differently, a household, within its earning span,
whose current income is zero or negative cannot possibly be in stationary equilibrium.
23. It can be shown that if we eliminate Assumption III, our model still implies that, for a stationary
cross section, the proportion of income saved is independent of income; however, this proportion
will tend to rise with age, up to retirement. The conclusion that the proportion of income saved is
independent of income, given age, also continues to hold if we relax our Assumption IV and assume
only that there exists a typical pattern of allocation of resources to current and future consumption