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

Recent Declines in the Savings Rate 117
S = YL+ rW - C = ( 1-a) Y+ ( d -ar)
W
or:
s = ( 1-a)-( d -ar)
w
(4.2)
where: s = S/Y and w = W/Y.
But with steady growth s = gw, implying:
( 1- a)-( d -arw ) = gw
or:
w = ( 1-a) ( g+ d -ar)
s = g( 1-a) ( g+ d -ar)
(4.3)
(4.3a)
(4.3b)
It is apparent from (4.3a) that the wealth-income ratio will tend to decline with
g while the saving ratio will be an increasing function of g for any finite value
of g, at least as long as the parameters a and d are not very sensitive to g, which
is consistent with simulation reported in Modigliani and Brumberg [15].
A comparison of equations (4.2) and (4.3b) shows that there are two alternative
ways to express the saving ratio, s; first, in terms of wealth-income ratio (as
in (4.2)), and second in terms of the growth rate, g, as in (4.3b). The formulation
of equation (4.2) has some advantages in that it may be expected to hold reasonably
well even in the short run. The drawback is the very limited availability
of data on wealth, whereas g is available as long as there exist national income
accounts. For this reason in our test we have used a linear approximation to equation
(4.3b).
1.3.2 Other Factors Affecting the Saving Rate
Besides depending on growth, s will also be affected by any factor which affects
the wealth-income ratio. Equation (3) suggests that one such factor is the interest
rate, and that a rise in r will then raise w and s. However the second inference
is not warranted because the parameters a and especially d are generally
themselves a function of r. Results presented in Modigliani and Brumberg [15]
suggest that d rises with r and may rise even faster, in which case s and w will
decline with r.
Other factors at work include, in addition to length of retirement, the timing
and size of other major expenditures for which provisions must be made, such as
for the purchase of a house, children’s education, or other major durables. The
need for accumulation will be increased in the presence of credit rationing.
Another reason for the accumulation of assets is the precautionary motive
(Keynes [10], p. 107) which in turn interacts with the availability of public and