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

10 The Life-Cycle Hypothesis
Assumption IV All the g t t are equal; i.e., our hypothetical prototype plans to
consume his income at an even rate throughout the balance of his life.
Let g t denote the common values of the g t t for an individual of age t. From (I.6)
we then have
L
t
 g t = ( L+ 1-t) g t = 1;
t = t
(I.7)
or,
g
t t
1
= g t =
L+ -t ∫ 1 ,
1 L t
where L t ∫ L + 1 - t denotes the remaining life span at age t.
Part II: Implications of the Theory and the Empirical Evidence
II.1 The Individual Consumption Function and the Cross-section
Consumption-Income Relation
Substituting for g t t in equations (I.4¢) the value given by (I.7), we establish immediately
the individual consumption function, i.e., the relation between current
consumption and the factors determining it:
c c y y a t
L y (
e
N - t)
e
= ( , , , )= 1 + y +
1
L L a ;
t
t
t
(II.1)
where the undated variables are understood to relate to the current period. 15
According to equation (II.1), current consumption is a linear and homogeneous
function of current income, expected average income, and initial assets, with
coefficients depending on the age of the household.
In principle, equations (II.1) and (II.2) could be directly tested; but they cannot
easily be checked against existing published data because, to our knowledge, data
providing joint information on age, assets (which here means net worth and not
just liquid assets), and average expected income, do not exist. 16 We must, therefore,
see whether we can derive from our model some further implications of a
type suitable for at least indirect testing in terms of the available data. Since most
of these data give us information about the relation between consumption in a
given short interval and income over the same interval (or some small neighbor-
L-
t
s y c
L y N - t
L y e
= - = - - 1 L a .
t
t
t
(II.2)