microfoundations consumption and investment. learning objectives understand the difference between...

Microfoundations

Consumption and Investment

Learning Objectives

• Understand the difference between the long-run consumption function and the short-run consumption function.

• Understand the logic of the permanent income hypothesis and the life cycle hypothesis.

• Know the implications of the PIH and LCH on consumption and the business cycle

• Appreciate the strengths and weaknesses of the PIH and LCH as explanations of consumer behavior.

Consumption and the Business Cycle

• Consumer spending cycles are not as extreme as those of GDP, particularly during recessions.– Consumer spending usually declines by less

than GDP.• In 1990-91, consumption declined by more than

GDP.

Consumption Spending: Selected Facts

• Durable goods spending increased 2 to 4 times faster than spending on non-durables and services in expansions.

• Durable goods spending declined in every postwar downturn except 1949 and 1953-54.

• Nondurable spending declined in only four of the last nine recessions.

• Services increased in every recession except for 1980.

Consumption Spending

• Consumption is defined as all spending done by the household sector on durables, non-durables, and services with the exception of purchases of new housing.

Consumption Spending

• Consumption spending is determined by two main factors:– The macroeconomic environment of

employment and inflation. – Individual consumer purchasing power as

reflected in household income, loans, existing savings and other wealth.

Early Consumption Theories• The absolute income hypothesis says that

consumption is directly related to income.• As income rises, consumption rises but by a

smaller amount. This means we can write:– C = a0 + bYd

• a0 is subsistence consumption. When Yd = 0, some positive consumption still occurs.

• The coefficient b is the marginal propensity to consume (MPC). It tells us by how much consumption changes when disposable income changes.

Consumption Function: Review

C

Yd0

a0

/\Y/\C

According to the absolute incomehypothesis, consumption spending isdirectly related to disposable income.

The intercept of the consumption function,a0, represents subsistence consumption.

The slope of the consumption function,/\C//\Y, is called the marginal propensityto consume. The MPC shows by how muchconsumption changes as income changes.

Consumption

• Later, economists collected data to measure the relationship between consumption and GDP and to check its validity.

• They discovered that different sets of data generated very different estimates of the marginal propensity to consume.

CLR = 0.9Yd

CSR = 0.75Yd

Consumption ConflictCLR = 0.9Yd

CSR = 0.75Yd

0

a0

C

Y

Consumption Functions

• Long-run consumption function– When income is zero, subsistence consumption is

zero.– Consumption rises by $0.90 for every dollar increase

in disposable income.

• Short-run consumption function– When income is zero, subsistence consumption is

positive.– Consumption rises by $0.75 for every dollar increase

in disposable income.

Reconciliation

• During the 1940s and 1950s, economists determined that there are two separate consumption functions.– The short run function describes how income

and consumption are related over short periods of time.

– The long run function describes how income and consumption are related over longer periods of time.

Forward Looking Theories of Consumer Behavior

• Forward-looking expectations are estimates of the future values of economic variables.

• They are based on the current and past values of several variables and an economic model that accounts for their behavior.– Consumers are assumed to prefer stable patterns of

consumption.– Consequently, they assess whether a change in

income is permanent or temporary before they spend it.

Two Theories

• Two major theories were developed to explain the relationship between the two consumption functions.– The Permanent Income Hypothesis

• Milton Friedman

– The Life Cycle Hypothesis• Franco Modigliani

The Permanent Income Hypothesis

• People simultaneously choose how much to consume now and how much to consume in the future.

• To make those decisions, they consider how much income they earn now and expect to earn in the future as well as how much savings they have accumulated.

Permanent Income Hypothesis

• Friedman suggested that people consume a constant fraction (k) of their expected/permanent income.– C = kYP = 0.9($10,000) = $9,000 where k is the

individual’s MPC.• k depends on individual tastes and on the variability of

income.

– YP = YP-1 + j(Y – YP

-1) where j is some fraction of the amount by which Y differs from YP

-1.– C = kYP

-1 + kj(Y – YP-1) = 0.9YP

-1 + 0.18(Y – YP-1)

Permanent Income Hypothesis

C = kYP-1 + kj(Y – YP

-1) = C = 0.9YP-1 + 0.18(Y-YP

-1)

• This equation shows that the PIH is based on a distinction between two concepts of the MPC.– The long-run MPC is simply the coefficient (k) of

permanent income or 0.9.

– The short-run MPC is the coefficient of a change in actual income, kj, which is equal to the product of the MPC and the fraction of the amount by which actual income differs from permanent income.

Transitory Income

• Transitory income is the difference between actual and permanent income and is not expected to recur.– Transitory income (Yt) is actual income minus

permanent income.• Yt = Y – YP = Y – YP

-1 – j(Y – YP-1) = (1 – j)(Y – YP

-1)

• Friedman assumes that the MPC out of Yt is zero.– Therefore, C = 0Yt + kYP = kYP.

Reconciling the Consumption Data

• According to the cross section data, high-income people had higher saving ratios than low income people, but the long-run saving ratio was nearly constant.

Consumption Reconciliation

Y

CCLR

0

CSR

The saving ratio, S/Y isconstant along CLR, butit differs from S/Y on CSR

at every point except theintersection of the twoconsumption functions.


CLR

CSR

0

CSR

C

YYP-1 YP

0 Y0

A

B

F

C0


• The ratio C/Y is constant at every point along CLR..

• At point A, where current income equals the last period’s permanent income, the long-run consumption-income ratio just equals the short-run consumption-income ratio and the functions intersect.


• But, if the person’s income rises to Y0, the current estimate of permanent income (YP) rises above the last period’s (YP

-1) by a fraction (j) of the excess of actual income over last period’s estimate (YP

-1).

– YP = YP-1 + j(Y – YP

-1)

• Consumption rises by k times the increase in permanent income to C0.

– C0 = kYP-1 + kj(Y – YP

-1)


• At YP0, consumption lies vertically above

point A by the fraction kj times the horizontal distance between YP

-1 and Y0.

• Consumption increases only a small amount, and at point B most of the short-run increase in income is saved.


CLR

CSR

0

CSR

If the change in income is maintained, the short-run consumption function shifts up along thelong-run function.

C

Y

A

F


• People try to keep their consumption about the same over their lifetime.– During years in which income is temporarily

high, they save most of the temporary portion in case income temporarily dips in the future.

– During years in which income is temporarily low, they borrow to maintain their level of spending.


• In the short run, most changes in income and consumption are transitory or temporary.– Therefore, studies that use short run (quarterly)

data pick up the transitory changes in income and consumption.

• The MPC is low because people are saving most of the temporarily high income.


• In the long run, most changes in transitory income and consumption average to zero.– Therefore, studies that use long run (10 year

averages) data pick up permanent income and consumption.

• The MPC is high because people have incorporated the higher income into their expectations and have increased consumption.

The Life Cycle Hypothesis

• People simultaneously choose how much to consume now and how much to consume in the future.

• To make those decisions, they consider how much income they earn now and expect to earn in the future as well as how much savings they have accumulated.

The Life Cycle Hypothesis

• Modigliani argued that people base their consumption decisions on the present value of their lifetime income.

• He suggested that consumption, income and saving vary over a person’s lifetime.

Life Cycle Hypothesis

• During working years people’s income exceeds consumption and people save and accumulate assets.

• At retirement, people begin to dissave, drawing down their accumulated assets.

• At death all assets have been depleted.

Working Years Retirement

Working Years RetirementD

ecumulationA

ccum

ulat

ion

Yd

CThis picture depicts disposable income,consumption and saving during a typicalperson’s lifetime

This picture shows the accumulation ofsaving during working years and decumulation during retirement.

W

0

0

Saving

Consumption Dissaving


• No initial assets– Total lifetime consumption of C0 per year for L

years just equals totally income Y0 per year for R years.

• C0L = Y0R or C0 = (R/L)Y0


• The simple version of the LCH explains the positive association of saving and income.– A rising GDP per capita, increases both the

saving and income of those of working age relative to those who are retired.


• The simple version of the LCH also explains the long-run constancy of S/Y – S/Y is constant if the population in each

historical era is divided into the same proportions of working and retired people, and if each age group has the same saving behavior.


• The role of assets– If a person has an initial endowment of assets,

A, and plans to spend those assets over his or her lifetime rather than leave an inheritance, consumption can be higher and saving lower in any period since the asset endowment provides more spending power.

– The consumption function becomes:• C1L = A + Y0R or C1 = A1/L + R/LY0


• Modigliani was the first to point out the importance of assets for consumption decisions.– Empirical work indicates that the marginal

propensity to consume out of accumulated assets is roughly 0.03 to 0.06 cents out of every $1 increase in wealth.


• There are two reasons why consumption spending is less volatile than GDP.– The PIH and LCH suggest that consumption

spending does not fully reflect changes in disposable income.

• When income rises (falls), consumption spending rises (falls) by less.


– Disposable income is less volatile than GDP because of the automatic stabilization properties of fiscal policy.

• Progressive taxation and transfers dampen the fall in disposable income during recessions.

PIH, LCH and Policy

• The PIH and LCH have two policy lessons:– Permanent policies will have more impact on

the economy than temporary policies.– Monetary policy, through its effect on the

value of people’s wealth, can affect consumption.

Summary

• The short run and long run consumption functions differ.– The short run consumption function has a

positive intercept and a lower MPC than the long run function.

– The long run consumption function has no positive intercept.

Summary

• According to the PIH and LCH, the short run consumption function has a lower MPC and a positive intercept because short term movements in income are dominated by transitory changes.

Summary

• The PIH and LCH assume that people try to smooth their consumption over their lifetime by saving transitory increases in income and dissaving to maintain consumption during transitory decreases in income.

Does the LCH Fit the Facts?

• The LCH suggests the following:– Elderly people dissave.– People smooth their consumption over time.

Dissaving among the Elderly

• The retired elderly do dissave on average, but they do not dissave as much as the life cycle model predicts. Why?– A person’s lifespan is uncertain and the elderly

may be hesitant to dissave too quickly and run out of money.

– The elderly want to leave an inheritance to their heirs.

• Some research supports this idea; other research indicates that most inheritances result from sudden death.

Consumption Smoothing

• People do not tend to smooth their consumption as much as predicted.– According to the LCH, the MPC from

transitory income is about 5 to 10 percent as large as the MPC from permanent income.

– The data show that the MPC from transitory income is about 30 percent as large as the MPC from permanent income.

Consumption Smoothing

• The early work on these hypotheses suggested that people base their estimates of future income on past income using simple rules of thumb such as the average income over the past several years.

• Robert Hall suggested that people form expectations about future income using rational expectations.

Rational Expectations and Consumption

• Rational expectations means that people use all available information, avoid systematic mistakes, and know the economic model that is generating their lifetime income.

• Anticipated changes in income, then, would not change consumption. Only unexpected changes in income would affect consumption decisions as people update their expectations of their permanent income.


• Hall’s theory means that because people are rational, only random changes in income are not anticipated.

• Therefore, changes in consumption are also unexpected and random.

• Hall’s theory does not fit the data.– Changes in aggregate consumption are not random.– When income rises even if it is expected, consumption

also rises.


• Hall concluded that either people did not form expectations about future income rationally or they are unable to borrow against future income to finance their present consumption.

• Of the two possibilities, economists favor the liquidity constraint hypothesis.– Even if people could perfectly anticipate their lifetime

earnings, it is unlikely that they could borrow enough from future income to completely smooth consumption over their lifetimes.

Investment

Learning Objectives

• Understand the relationship between changes in GDP and changes in investment as hypothesized by the accelerator model.

• Appreciate the strengths and weaknesses of the accelerator model.

• Learn how an interaction between the multiplier and the accelerator can generate a business cycle.

• Know the limitations of the multiplier/accelerator model.

Investment and the Business Cycle

• Investment increases more rapidly in expansions and decreases more rapidly in recession than other GDP components.– This volatility is the main cause of cyclical

fluctuations in overall economic activity.

Investment: Selected Facts

• Plant and equipment spending increased more rapidly than GDP in seven of the nine expansions. – Plant and equipment outlays typically

increased 60 to 75 percent faster than GDP.• In 1980-81 expansion, investment increased 135%

faster. In the 1982-1990 expansion, it was 40% faster.

Investment: Selected Facts

• Plant and equipment spending declined more rapidly than GDP in eight of the nine recessions.– Plant and equipment investment most

commonly fell by two to three times the rate of decline in GDP.


• The sharp cyclical pattern arises because investment in plant and equipment is deferrable.– Firms can make do with existing equipment

although doing so may result in profits below potential.

• The facilities are less efficient than technology would permit and are unable to meet sudden surges in demand.


• Residential fixed investment increased faster than real GDP in five of the last nine recessions, and decreased more than real GDP in five of the last nine expansions.

The Accelerator Theory of Investment

• The acceleration principle asserts that net investment is a function of the rate of change in final output, not the absolute level of output.– Let Y = Output– Let K = Capital Stock– Let A = K/Y= Capital-output ratio

The Accelerator Model

• Assumptions:– Other things remaining the same at full

capacity with no change in technical conditions, increases in output require additional capital equipment.

• If the capital-output ratio is $3/$1, then every $1 increase in output requires an additional $3 in capital equipment.

• A = K/Y = /\K//\Y


• Assumptions:– A change in capital is the same thing as a

change in investment.• A = I//\Y Substitute I for /\K

• I = A x /\Y Solve for I


• Model:– I = A x /\Y is the formal algebraic expression of

the acceleration principle.– It says that there is some coefficient A which,

when multiplied by the change in output, will yield the required net investment expenditure.


• Logic:– Given a fixed technical relationship between

capital and output, the amount of investment will vary directly with the size of the absolute change in output.

• The acceleration principle means that investment is a function of the rate of change in final output.

Acceleration Principle

• The acceleration principle helps to explain why the output of capital goods fluctuates much more violently than the output of goods in general.

• The acceleration principle can also be used to explain why inventories fluctuate more violently than the output of goods in general.

Acceleration Principle: ExamplePeriod Capital Output Replacement Demand for Total Demand Stock Demand New Capital for Capital

1 300.0 100.0 30.0 0.0 30.02 34

Output = 100 units per period and the capital-output ratio is 3.Capital has an average economic life of 10 periods, so normalreplacement demand for capital equipment is 30 units per period or10% of the capital stock.


1 300.0 100.0 30.0 0.0 30.02 330.0 110.0 30.0 30.0 60.03 4

Period 2:Demand for final output increases by 10%, causing output to rise to 110.Given a capital-output ratio of 3/1, demand for new capital increases by 30. Total demand for capital increases by 60 (new plus replacement).


1 300.0 100.0 30.0 0.0 30.02 330.0 110.0 30.0 30.0 60.03 346.5 115.5 30.0 16.5 46.54

Period 3:Demand for final output increases by 5%, causing output to rise to 115.5.Given a capital-output ratio of 3/1, demand for new capital increases by 16.5. Total demand for capital increases by 46.5 (new plus replacement).


1 300.0 100.0 30.0 0.0 30.02 330.0 110.0 30.0 30.0 60.03 346.5 115.5 30.0 16.5 46.54 346.5 115.5 34.6 0.0 34.6

Period 4:Demand for final output does not increase.Given a capital-output ratio of 3/1, demand for new capital is zeroTotal demand for capital increases by 34.6 (replacement = 10% of capital stock).

Acceleration Principle: Example

• New investment expenditures increased only so long as final demand was increasing at an increasing rate.

• Once final demand stabilized at a new higher level, new investment expenditures ceased.

• Total investment rose to a peak and then fell back to replacement level.

Evaluation of the Accelerator Principle

• The acceleration principle has been used as part of the explanation of the business cycle.– It helps to explain the accelerated increase in

demand for capital and inventories in the upswing of a cycle.

Evaluation of the Accelerator Principle

– It also helps to explain the accelerated decrease in demand for capital and inventories in the downturn.

• The downturn may occur because the rate of increase in the demand for consumer goods has slowed.

The Multiplier-Accelerator Interaction Hypothesis

• The multiplier process explains why income and expenditures rise or fall in a cumulative process given an autonomous change in spending.

• The accelerator principle states that some portion of investment is determined by the change in output or income.

• The combination of the multiplier and the accelerator can generate cycles.

Multiplier/Accelerator Example

• Let the consumption function be:– C = 60 + 0.8Y

• Let the accelerator function be:– /\I = A(Y1 – Y0) where A = 1

• Let the initial levels in period 0 of Y, C and I be 800, 700 and 100 respectively.

• Let I rise in period 1 by 10.

Period Y C I /\I=A/\Y Total I

0 800.0 700.0 100 0 100.0 1 810.0 700.0 110 0 110.0 2 828.0 708.0 110 10.0 120.0 3 850.4 722.4 110 18.0 128.0 4 872.7 740.3 110 22.4 132.4 5 890.5 758.2 110 22.3 132.3 6 900.2 772.4 110 17.8 127.8 7 899.8 780.1 110 9.7 119.7 8 889.5 779.8 110 -0.36 109.6 9 871.2 771.6 110 -10.3 99.710 848.8 757.0 110 -18.2 91.711 826.5 739.0 110 -22.5 87.512 809.0 721.2 110 -22.2 87.713 799.7 707.2 110 -17.5 92.414 800.4 699.7 110 - 9.3 100.715 811.1 700.4 110 0.75 110.8

Multiplier-Accelerator Model

• Given these assumptions about the values of the MPC and A, the model generates two turning points.– In period 6, the model peaks– In period 13, the model bottoms

Multiplier-Accelerator Model

• Note that investment declines in period 5 and that the increase in output from period 4 to period 5 was less than the increase from period 3 to 4.

• Similarly, investment increases in period 13 after the decrease in output from period 11 to period 12 was less than the decrease from period 10 to 11.

Limitations of the Model

• Net investment does not respond instantaneously to changes in output growth, but rather displays noticeable lags that are not uniform in length.

• Net investment does not respond to accelerations and decelerations in real GDP growth with uniform speed.

• The overall level of net investment relative to real GDP does not have a consistent long-term relationship to real GDP growth.


• The acceleration principle is effective only when an industry or economy is operating at full capacity.– Additional capital is needed only if the existing

capacity is fully utilized.• When an expansion begins, there is usually unused capacity in

an industry so that the first effect of an increase in demand for consumer goods is a fuller utilization of existing capacity, followed by the addition of more shifts, and then the purchase of new capital.


– As the economy approaches full employment of workers and other resources, prices, especially those of basic raw materials, are bid up.

• Therefore, the full acceleration principle cannot hold completely.

Flexible Accelerator

• According to the flexible accelerator hypothesis, investment spending is linked to a gap between the desired capital stock and the actual capital stock.– The gap is not expected to be wholly closed in

one period.

Flexible Accelerator

• Model:– I = a(K* – Kt-1)

• a = proportion of the gap between K* and Kt-1

• K* = desired capital stock

• Kt-1 = capital stock in the previous period

• Logic:– When there is a change in demand that requires

more capital goods, the adjustment will be spread over a number of periods.

Flexible Accelerator: Determinants of Gross Investment

• The larger the gap between desired capital and last period’s actual capital, the more current investment responds to the change in last period’s output.

• The higher the response of expected output to last period’s error in estimating actual output, the more expected output and investment respond to any unexpected change in last period’s actual output.

Flexible Accelerator: Determinants of Gross Investment

• The proportion of the capital stock that is replaced each year. – Long-lived capital investment can be delayed. If it is

delayed until sales are strong, total investment will respond ever more than the simple accelerator suggests.

• Investment responds more to changes in expected output in capital intensive industries. – Thus, faster growth expectations in more capital

intensive industries will spur more investment.

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