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The Life-Cycle Theory of
Consumption (With Diagram)
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Let us make an in-depth study of the Life-Cycle Theory of
Consumption:- 1. Explanation to the Theory of
Consumption 2. The Reconciliation 3. Critics of the Life
Cycle Hypothesis.
Explanation to the Theory of Consumption:
The life-cycle theory of the consumption function was developed by
Franco Modigliani, Alberto Ando and Brumberg.
According to Modigliani, The point of departure of the life cycle
model is the hypothesis that consumption and saving decisions of
households at each point of time reflect more or less a conscious
attempt at achieving the preferred distribution of consumption over
the life cycle, subject to the constraint imposed by the resources
accruing to the household over its life time.
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An individual’s or household’s level of consumption depends not
just on current income but also, and more importantly, on longterm expected earnings.
Individuals are assumed to plan a pattern of consumer expenditure
based on expected earnings over their lifetime.
To see the implications of this theory for the form of the
consumption function, we first look at a simplified example.
Consider an individual of a given age who is in the labour force, has
a life expectancy of T years, and plans to remain in the labour force
for N years. Our representative consumer might, for example, be 30
with a life expectancy of 50 (additional) years, plan to retire after 40
years, and, therefore, have expected years in retirement equal to (T
– N), or 10. We make the following assumptions about the
individual’s plans.
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The individual is assumed to desire a constant consumption flow
throughout life. Further, we assume that this person intends to
consume the total amount of lifetime earnings plus current assets
and plans no bequests. Finally, we assume that the interest paid on
assets is zero; current saving results in dollar-for-dollar future
consumption. These assumptions are purely to keep the example
simple and are relaxed later.
These assumptions imply that consumption in a given period will be
a constant proportion, 1/T, of expected lifetime resources. The
individual plans to consume lifetime earnings in T equal
installments. The consumption function implied by this simple
version of the life cycle hypothesis is:
Ct is consumption in time period t. The term is brackets in expected
lifetime resources, which consist of
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Yt1 = the individual’s labour income in the current time period (t)
Y-1e = the average annual labour income expected over the future (N
– 1) years during which the individual plans to work
At = the value of presently held assets
It can be seen from Equation (1) that according to the life cycle
hypothesis, consumption depends not only on current income but
also on expected future income and current asset holdings (i.e.,
current wealth). In fact, the life cycle hypothesis suggests that
consumption would be quite unresponsive to changes in current
income (Y,1) that did not also change average expected future
income. From equation (1), for example, we can compute
An increase in income that was expected to persist throughout the
work years would mean that y-le also rose and that the effect on
consumption would be much greater:
A one-time or transient change in income of, say, Rs. 100 will have
the same effect as a change in wealth (note that ΔCt/ΔYt1 =
ΔCt/ΔAt = 1/T) of the same amount. Lifetime resources will go up by
Rs. 100, and this will be spread out in a planned consumption flow
of 100/T = 100/50 = 2 per period in our example of an individual
who expects to live for 50 additional years.
A permanent increase in income of Rs. 100 will lead to an increase
of consumption of Rs. 80 in each of the remaining periods,
including the 10 planned periods of retirement. The increase of Rs.
80 in each of these 10 retirement years, a total of Rs. 800, is
financed by a saving of Rs. 20 (100 – 80) in each of the, 40
remaining working years.
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The life cycle hypothesis accounts for the dependence of
consumption and saving behaviour on the individual’s position in
the life cycle. Young workers entering the labour force have
relatively low incomes and low (possibly negative) saving rates. As
income rises in middle-age years, so does the saving rate.
Retirement brings a fall in income and might be expected to begin a
period of dissaving (negative saving rates).
This lime profile of consumption and saving is depicted in Figure
6.16. Here the desired pattern of consumption is taken to rise mildly
with time instead of maintaining the constant desired consumption
pattern assumed in our individual example. The pattern of income
rises more sharply, though, and the typical individual smoothest out
consumption flow by a short period of early dissaving, a period of
positive saving, then a longer period of dissaving in retirement.
The general form of the aggregate consumption function implied by
the life cycle hypothesis is:
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where the variables Ct,Y1t,Y-le, and At, arc as defined for Equation (1)
but should now be interpreted as economy-wide averages. If the
simplifying assumptions made previously of no bequests, zero
interest on saving, and a uniform consumption pattern over time
are relaxed, the parameters b1, b2and b3 will no longer be simple
functions of N and T as were the coefficients in Equation (1).
Still, in the aggregate consumption function (2), as in the case of
Equation (1), consumption depends not just on current labour
income (Yt1) but also on average future expected labour income (Y-le)
and wealth (At). It will also be true in the aggregate, as in the
simplified individual example, that the response to a transient or
one-time increase in labour income (an increase in Ytl) will be quite
small, much less than the response to a permanent income change
(an increase in Y1t and Y-le).
Consumption is shown as rising gradually over the life cycle.
Income rises sharply over the early working years, peaks, and then
declines, especially with retirement. This pattern of consumption
and income results in periods of dissaving in the early working
years and the late stage of the life cycle, with positive saving over
the high-income middle period of the life cycle.
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To use Equation (2) to study actual consumer behaviour, we must
make some assumption about the way in which individuals form
expectations concerning lifetime labour income. In a study for the
United States, Ando and Modigliani make the assumption that
expected average future labour income is just a multiple of current
labour income:
According to this specification, individuals revise their expectation
of future expected labour income Y-1e by some proportion β of a
change in current labour income. Substitution of Equation (3) for Y1e in the aggregate consumption function (2) yields
A representative statistical estimate of the equation based
on the work of Ando and Modigliani is the following:
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An increase in current labour income of Rs. 100 with the assumed
effect on future labour income will increase consumption by Rs. 72.
An increase in Wealth of Rs. 100 will increase consumption by Rs.
6. As noted previously, an increase in income that was known to be
temporary and therefore would not affect future expected labour
income would have the same effect as an increase in wealth. Thus,
according to this estimate, the MPC out of such a transient income
flow is of the order of 0.06, the MPC out of wealth.
The Reconciliation:
The life cycle hypothesis can explain the puzzles that emerged from
the early empirical work on consumption functions. According to
the life cycle hypothesis, the relationship between consumption and
current income would be non-proportional, as seems to be the case
in short-run time series estimates.
The intercept of the function measures the effect of wealth [0.06/1,
in Equation (5)]. But the intercept is not constant over time; such
short-run consumption functions shift upward over time as wealth
grows. These upward shifts in the short-run consumption function
(SCF) are illustrated in Figure 6.17. The shifting short-run
consumption functions trace out a long-run consumption function
(LCF).
If the ratios of wealth and labour income to disposable personal
income are relatively constant over time, the life cycle consumption
function [Equation (5)] is also consistent with the evidence from
long-run time series data that the long-run consumption-income
relationship (LCF in Figure 6.17) is proportional, with the
APC(C/Yd) relatively stable in the neighborhood of 0.9. To see this
relationship, first note that the ratio of labour income to disposable
personal income has been approximately 0.88; that is, Yt1 = 0.88 YD.
The ratio of wealth to disposable income is approximately 4.75; A, =
4.75 YD. Substitution of these expressions for At and Yt1 in the
estimated aggregate consumption function (5) yields which is
approximately the average value of the APC over the post-World
War II period.
The life cycle hypothesis also explains the evidence from crosssectional family budget studies showing that higher-income families
consume a smaller proportion of income (have a lower APC) than
do lower-income families. A larger proportion of high-income
families might be expected to be those in their peak earning years,
that is, in the “humped” portion of Figure 6.16.
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It is in this range, according to the life cycle hypothesis, that income
should exceed consumption by the greatest amount and the APC
should be lowest. Conversely, a sample of low-income families
would have a high proportion of new entrants to the labour market
and retirees, groups that tend to disserve. These groups with high A
PCs would push up the APC for the sample of low-income families.
Finally, the life cycle hypothesis explains why quarter-to-quarter
movements in consumption do not closely mirror quarter-toquarter movements in income, the other anomalous finding of early
research on the consumption function. The change in income from
any given quarter to the next will be the result, in large part, of onetime factors that will not affect individuals’ perceptions of lifetime
average income. We have seen that transient income changes have
little impact on consumer behaviour according to the life cycle
hypothesis.
Critics of the Life Cycle Hypothesis:
Although the life cycle hypothesis explains several features of the
consumption- income relationship, the approach is not without its
critics. Gardner Ackley for example, points out that the life cycle
theory assumes that each household in making consumption
decisions has at all times a definite, conscious vision of the family’s
future size and composition, including the life expectancy of each
member; of the entire lifetime profile of the income from work of
each member after the then applicable taxes ; of the present and
future extent and terms of any credit available to it; of the future
emergencies, opportunities, and social pressures which will impinge
upon its consumption spending.
Further, each household must hold such a vision with enough
certainty that it would be worthwhile to use this vision as a basis for
rational planning of consumption decisions. Ackley finds these
assumptions to be unrealistic. In essence, Ackley will not accept the
point of departure for the life cycle hypothesis ; that is, Modigliani’s
statement that consumption and saving decisions of
households “reflect a more or less conscious attempt at
achieving the preferred distribution of consumption over
the life cycle.”
Another criticism of the life cycle approach is that it fails to
recognize the presence of liquidity constraints. Even if a household
possessed a concrete vision of future income, there is little
opportunity in real-world capital markets for borrowing for a long
period on the basis of expected future income.
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As a result, consumption may be much more responsive to changes
in current income, whether temporary or not, than would be
predicted on the basis of the life cycle hypothesis. The response of
consumption to current income, however, may not be the simple
mechanical one predicted by the “absolute income” hypothesis.
The consumption pattern of younger households facing liquidity
constraints may be very responsive to changes in current income.
The consumption of older households with more accumulated
wealth may not be responsive to temporary variations in current
income. Small temporary changes in income may be financed out of
a buffer of liquid assets, but larger changes may cause liquidity
constraints to become binding and begin to affect consumption
behaviour. Consideration of liquidity constraints on households
therefore leads one to believe that current income may be a more
important influence on consumption than would be predicted on
the basis of the life cycle hypothesis, but the consumption-tocurrent-income relationship may be more complex than that
implied by Keynes’s absolute income hypothesis. Statistical work
does in fact suggest the importance of liquidity constraints in
explaining the considerable response of consumption to current
income.
Other research emphasizes the importance of bequests in
determining saving, rather than the life cycle motive, which
emphasizes saving to finance consumption in retirement. A study by
Laurence Kotlikoff and Lawrence Summers concluded that the
desire to make bequests was the most important motive for saving.
Franco Modigliani has disputed the evidence. To him, the data
suggest that only 15 to 20 percent of saving is for bequests. The bulk
is life cycle saving.
Conclusion:
From the review of the theories of consumption function, we
conclude that there have been laudable attempts at integrating the
micro behaviour of households with macro level consumption
function. But empirical research tells us that these theories are not
the last word.
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TABLE OF CONTENTS
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Explanation to the Theory of Consumption:
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The Reconciliation:
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Critics of the Life Cycle Hypothesis:
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