econ 314: macroeconomics ii - university of … · econ 314: macroeconomics ii consumption and...

ECON 314:

MACROECONOMICS II

CONSUMPTION AND

CONSUMER EXPENDITURE

1 Macroeconomics II Lecture Notes Prepared

by Dr. Emmanuel Codjoe

CONSUMPTION AND CONSUMER

EXPENDITURE

• Explaining the observed patterns in data

on consumption and income: short-run

and cross-sectional data show that MPC <

APC, whilst long-run data show MPC =

APC.

• Several explanations put forward to solve

the consumption puzzle.




EXPENDITURE

Franco Modigliani and the Life Cycle

Hypothesis (LCH)

• Key names: Franco Modigliani, Albert Ando

and Richard Brumberg

• The LCH was put forward in a series of

papers written in the 1950s




EXPENDITURE

• Modigliani emphasised that income varies systematically over individuals’ (people’s) life time.

• According to the LCH, the typical individual has an income stream which is relatively low at the beginning and end of his/her life (retirement), when his/her productivity is low, and high during the middle of his/her life.




EXPENDITURE

• The LCH therefore views individuals as

planning their consumption and savings

behaviour over long periods with the intention

of allocating their consumption in the best

possible way over their entire lifetimes.

• Individuals are assumed to maintain a more or

less constant, if slightly rising level of

consumption throughout their lifetime. 5

Macroeconomics II Lecture Notes Prepared by Dr. Emmanuel Codjoe


EXPENDITURE

• The constraint to this consumption stream is

that the present value of this total consumption

does not exceed the present value of total

income.

• This implies that in the early years of a person’s

life, s/he is a net borrower. In the middle years,

s/he saves and repays debt and provides for

retirement. In the retirement years, s/he

dissaves. 6



EXPENDITURE

• This pattern of consumption and saving can be

illustrated below:

T t

Income

c

Y

Net Borrower/Dissaving




EXPENDITURE

• This pattern of consumption and saving can be

illustrated below:




EXPENDITURE

• Thus, instead of relying on a single value

(based on a psychological rule of thumb)

for the MPC, the LCH (based on

optimizing behaviour) implies different

MPCs out of permanent income,

transitory income and wealth.




EXPENDITURE

• The key assumption (as noted earlier but

stated in other words) is that individuals

choose stable lifestyles, not saving

furiously in one period for a huge

spending spree in the next.




EXPENDITURE

• Remember that if the assumptions made,

both about individuals and the

population, are stable then we can add up

all the individual consumption functions to

obtain a stable aggregate function in which

the population consumes k percent of the

present value of its income stream in each

period:




EXPENDITURE

• The aggregate consumption function can be

expressed as follows:

• Where the variables are as previously

defined

)( 00 PVkc




EXPENDITURE

• The next crucial step is to operationalize the

PV0 term.

• Ando and Modigliani provided an excellent

answer. They noted that income can be

divided into income from labour (work)

and income from assets and property

(wealth)

Ly

Py13



EXPENDITURE

• Thus, the PV0 term can be expressed as:

• Where 0 is the current period, and t ranges

from 0 to the remaining years of life, T.

T T

t

P

t

t

L

t

r

y

r

yPV

0 0

0)1()1(




EXPENDITURE

• Let us now attempt a simplification of this

decision-making over a life time.

• Let us suppose the individual starts life at

the age of 20, and plans to work until 65,

and will die at 80.




EXPENDITURE

• Again we can suppose that is now

initial wealth (W), and is now Y, which

is income from earnings.

• If the number of years an individual

expects to work before retirement, can be

defined as R.

Py



Ly


EXPENDITURE

• Then the individual’s lifetime resources is

made up of initial wealth, W, and lifetime

earnings (R x Y).

• For simplicity we assume that interest rate

is zero, although if this were positive then

interest on savings will be included.




EXPENDITURE

• The individual’s decision now involves

ensuring a smooth consumption path over

the remaining life, T.

• The individual is expected to divide his/her

lifetime resources (W + RY) equally over the

remaining number of years, T.

18



EXPENDITURE

• The consumption function can be written as

TRYWC /)(

YT

RW

TC

1




EXPENDITURE

• Thus with our example, R = 45 and T = 60.

• The consumption function can be written as

• The equation above shows that consumption

depends on both wealth and income.

YWC 75.0017.0




EXPENDITURE

• For the whole economy, the aggregate

consumption function can be expressed as:

• Where is the MPC out of wealth and is

the MPC out of income.

YWC




EXPENDITURE

• Implications:

• For any given wealth, W, the LCH yields a

conventional consumption function (we

already know).

• However, the intercept of the consumption

function is not fixed, but depends on the level

of wealth.

• See figure on next slide!

22



EXPENDITURE




EXPENDITURE

• Implications:

• The LCH can also solve the puzzle. Given the

consumption function, the APC is below:

Y

W

Y

C




EXPENDITURE

• Implications:

Here is the explanation in respect of the puzzle:

Because wealth does not vary proportionately

with income from person to person or from

year to year, we should expect to find that high

income corresponds to low APC when looking

at data across individuals or over short periods

of time. 25



EXPENDITURE

• Implications:

• Nevertheless, over long periods of time, wealth

and income grow together resulting in a

constant W/Y ratio, and thus a constant APC.

• Put differently, as wealth increases the

consumption function shifts upward. This

upward shift prevents the APC from falling as

income rises.

26



EXPENDITURE

• Implications:

• Once we have a theory of consumption we

also have a theory of saving.

• The LCH also predicts that saving varies

over an individual’s lifetime.




EXPENDITURE

• Implications:

• If an individual begins working life, s/he will

accumulate wealth during the working years,

and then run down their wealth during

retirement years.

• Thus, the young who are working save,

whilst the old who are retired dissave.

28



EXPENDITURE

Milton Friedman’s Permanent-Income

Hypothesis

• The Permanent-Income Hypothesis (PIC) is based on a book written in 1957.

• The Permanent-Income theory of consumption argues that consumption is related not to current income but to a longer-term estimate of income: what Friedman termed permanent-income.




EXPENDITURE


Hypothesis

• The P-I theory complements Modigliani’s

LCH. But unlike the LCH which argues that

income follows a regular pattern over an

individual’s lifetime, the P-IH emphasises

that individuals experience random and

temporary changes in their incomes from year

to year.




EXPENDITURE


Hypothesis

• Permanent income is the steady rate of

consumption an individual could maintain for

the rest of his/her life, given the present level

of wealth and income earned now and in the

future.




EXPENDITURE


Hypothesis

• Friedman’s model of consumption begins

with the assumption of individual consumer

utility maximisation.

• This gives us the consumption function

between an individual’s consumption and

present value.

32



EXPENDITURE


Hypothesis

• This is the consumption function for a

representative individual, ‘i’, over time.

• Only note that Friedman’s treatment of PV is

different from Ando-Modigliani’s.

0);( iiii fPVfc




EXPENDITURE


Hypothesis

• The present value of the total income stream is

the current asset value of the income stream.

Multiplying this asset value by the rate of return,

r, yields Friedman’s permanent income from that

asset value:

ii

P PVry .




EXPENDITURE


Hypothesis

• But as with Ando-Modigliani, Friedman assumes

that the consumer wants to smooth his/her actual

income stream into a more or less flat

consumption pattern.

• This gives a level of permanent consumption,

that is proportional to .

i

Pci

Py




EXPENDITURE


Hypothesis

• This may be stated as follows:

• is the ratio of permanent consumption to permanent income, this depends on the interest rate, individual tastes, and the variability of expected income.

i

P

ii

P ykc ik




EXPENDITURE


Hypothesis

• Aggregating over the entire population and

generalising, we have a simple form of the

equation:

• Where YP is permanent (disposable) income.

cYPC




EXPENDITURE


Hypothesis

• Friedman also suggested we view current

income as the sum of two components:

permanent income and transitory income.

TP YYY 38



EXPENDITURE


Hypothesis

• How can we think about the measurement of

permanent income?

• We know that an individual has a current

level of income, and forms some idea of the

level of consumption s/he can maintain for

the rest of his/her life.




EXPENDITURE


Hypothesis

• But suppose income goes up! Then the individual has to decide whether the increase is permanent or merely transitory/temporary!

• Permanent income is that part of income that individuals expect to persist into the future. Transitory income is that which individuals do not expect to persist.

40



EXPENDITURE


Hypothesis

• Nevertheless, in any particular case, an

individual may know whether an increase is

permanent or transitory.

• But in general an individual is not likely to be

so sure whether a change is permanent or

transitory.

41



EXPENDITURE


Hypothesis

• Implications:

• Regarding the consumption puzzle, the P-IH argues that the Keynesian consumption function uses the wrong variable; that is, current income instead of permanent income.

• Relating current income to consumption results in what Friedman termed errors in variables problem.

42



EXPENDITURE


Hypothesis

• Implications:

• According to the P-IH, the APC depends on the

ratio of permanent income to current income.

Y

Y

Y

cYP

Y

CAPC

P




EXPENDITURE


Hypothesis

• Implications:

• When current income temporarily rises above

permanent income, the APC temporarily falls.

• When current income temporarily falls below

permanent income, the APC temporarily rises.

44



EXPENDITURE


Hypothesis

• Implications:

• Regarding studies using household data, Friedman reasoned that these data reflect a combination of permanent and transitory income.

• Households with high permanent income, have proportionately high consumption. And if all variations in income came from permanent income, then the APC will be the same for all households.




EXPENDITURE


Hypothesis

• Implications:

• However, some of the variations are the results of

transitory income, and households with high

transitory income do not have higher consumption.

• Therefore, the evidence from the data tend to

show that households with high-income, have on

average lower APC.




EXPENDITURE


Hypothesis

• Implications:

• Regarding time series data, Friedman argued that

year-to-year fluctuations in income are

dominated by transitory income.

• Therefore, years of high income should be

years of low APC.




EXPENDITURE


Hypothesis

• Implications:

• But over long periods of time, say from decade

to decade, variations in income are the result of

permanent income.

• Therefore, in long time series one should

observe a constant APC.




EXPENDITURE

Consumption Under Uncertainty: Robert Hall’s

Random-Walk Hypothesis

• The Random-Walk Hypothesis combines Irvin

Fisher’s assumptions on forward-looking

consumers with rational expectations.

• Rational expectations assumes that individuals

use all available information to make optimal

forecasts about the future.




EXPENDITURE



• From our knowledge of the P-IH, we know

that if permanent income were known

exactly, then consumption will never

change.




EXPENDITURE



• However with the RWH, there is a link

between income uncertainty and changes in

consumption.

• Changes in consumption therefore arise

from surprise changes in income.




EXPENDITURE

Consumption Under Uncertainty: Robert Hall’s Random-Walk Hypothesis

• According to the rational expectations theory, the surprise must be truly random and unpredictable.

• Thus the combination of permanent-income hypothesis and rational expectations implies that consumption follows a random walk.

• Robert Hall’s famous random walk model is specified as:




EXPENDITURE



• This states that consumption tomorrow should

equal consumption today plus a truly random

error,

tt CC 1

tt CC 153



EXPENDITURE


• Implications:

• This approach to consumption has implications for the analysis of economic policies.

• If consumers are believed to follow this approach, then only unexpected policy changes influence consumption. These policy changes become effective when they change expectations.

54



EXPENDITURE


• Implications:

• Essentially, the effectiveness of a policy is dependent on how the policy announcement affects expectations. If expectations are unaffected, the policy is ineffective.

• Thus, policy makers influence the economy not only through their actions but also through the public’s expectation of their actions.




EXPENDITURE

Liquidity Constraints and Myopia

• It is worth noting that the LCH and P-IH do not explain all of consumption behaviour.

• Why might this be so? Two explanations are liquidity constraints and myopia.

• The first argues that when permanent income is higher than current income, consumers are unable to borrow to consume at the higher level predicted by the LCH and P-IH.




EXPENDITURE


• The second suggests that consumers simply aren’t as forward-looking the theories argue.

• A liquidity constraint exists when a consumer cannot borrow to sustain current consumption in the expectation of higher future income.

• This condition is faced by most students, and those who are unable to borrow when their incomes drop temporarily.




EXPENDITURE


• Fisher’s model suggests that individuals can

borrow and save. The ability to borrow allows

current consumption to exceed current income.

• But with a liquidity constraint, current

consumption cannot exceed current income. A

borrowing constraint exists when .

11 YC




EXPENDITURE


• The figure below illustrates how the

borrowing constraint restricts the consumer’s

set of choices.

• In these circumstances, the consumer’s choice

must satisfy both the inter-temporal budget

constraint and borrowing constraint.

59



EXPENDITURE




EXPENDITURE


• The shaded area represents the combinations of

the first-period consumption and second-period

consumption that satisfy both constraints.

• In the next figure we show two possibilities. In (a)

the consumer wishes to consume less in period one

than s/he earns. Hence the liquidity constraint is not

binding.

61



EXPENDITURE


• In (b) the consumer will like to consume at point D, where s/he will consume more in period one than s/he earns, but the liquidity constraint prevents this outcome.

• The best outcome is for the individual to consume all of his/her period one income.

• The foregoing analysis suggests that there are two consumption functions, one for those facing liquidity constraints and one for those who are unconstrained by borrowing.




EXPENDITURE

• the shad




EXPENDITURE


• For such students who face the liquidity constraint, when they complete their education and get jobs, their incomes will rise and their consumption too will rise.

• But according to the LCH (and PIH), consumption should not rise much when income rises, so long as the increase in income was expected.




EXPENDITURE


• Because liquidity constraint is relieved, consumption will rise a lot when income rises. This implies that consumption will be more closely related to current income than is implied by the LCH and PIH.

• The explanation for myopia is hard to distinguish in practice from the liquidity constraints hypothesis. That is any expectation of a rise in income does not change consumption until the actual increase takes place.




EXPENDITURE

David Laibson and the Pull of Instant

Gratification

• Laibson argues that consumers judge themselves

to be imperfect decision-makers.

• Consumption decisions are influenced by

psychological factors, in contrast to the rational

utility maximisation presumption.

• This raises the possibility that consumers’

preferences are time-inconsistent.

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econ 314: macroeconomics ii - university of … · econ 314: macroeconomics ii consumption and...

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