microfoundations. modern theories of consumptioncoin.wne.uw.edu.pl/siwinska/macro2_lecture12.pdf ·...

Microfoundations, part 1

Modern theories of consumption

Macroeconomics II Joanna Siwińska-Gorzelak

WNE UW

Lecture overview

This lecture focuses on the most prominent work on consumption.

John Maynard Keynes: consumption and current income

Irving Fisher: Intertemporal Choice

Franco Modigliani: the Life-Cycle Hypothesis

Milton Friedman: the Permanent Income Hypothesis

We will also take a glimpse at:

Robert Hall: the Random-Walk Hypothesis

David Laibson: the pull of instant gratification

Consumption

The contemporary theory of consumption was developed independently in the 1950s by Milton Friedman as the permanent theory of consumption, and by Franco Modigliani as the life cycle theory of consumption.

Consumption for a foresighted consumer depends on: – Financial wealth: The value of checking and saving accounts

– Housing wealth: The value of the house owned minus the mortgage due

– Human wealth: After-tax labor income over working life

– Nonhuman wealth: The sum of financial wealth and housing wealth

The Keynesian Consumption Function

Here’s a consumption function with the properties Keynes conjectured: C

Y

1

c

C C cY

C

c = MPC

= slope of the consumption function

Keynes’s Conjectures

1. 0 < MPC < 1

2. Average propensity to consume (APC )

falls as income rises.

(APC = C/Y )

3. Current disposable income is the main

determinant of consumption.

The Keynesian Consumption Function

C

Y

C C cY

slope = APC

As income rises, the APC falls (consumers save a bigger fraction of their income).

C Cc

Y Y APC

Early Empirical Successes: Results from Early Studies

Households with higher incomes:

consume more

MPC > 0 save more

MPC < 1 save a larger fraction of their income

APC as Y

Very strong correlation between income and consumption income seemed to be the main

determinant of consumption

Problems for the Keynesian Consumption Function

Based on the Keynesian consumption function, economists predicted that C would grow more slowly than Y over time.

This prediction did not come true:

As incomes grew, the APC did not fall, and C grew just as fast.

Simon Kuznets showed that C/Y was very stable in long time series data.

The Consumption Puzzle

C

Y

Consumption function from long time series data (constant APC )

Consumption function from cross-sectional household data

(falling APC )

Irving Fisher and Intertemporal Choice

The basis for much subsequent work on consumption.

Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction (utility).

Consumer’s choices are subject to an intertemporal budget constraint, a measure of the total resources available for present and future consumption

The basic two-period model

Period 1: the present

Period 2: the future

Notation

Y1 is income in period 1

Y2 is income in period 2

C1 is consumption in period 1

C2 is consumption in period 2

S = Y1 - C1 is saving in period 1

(S < 0 if the consumer borrows in period 1)

Deriving the intertemporal budget constraint

Period 2 budget constraint:

2 2 (1 )C Y r S

2 1 1(1 )( )Y r Y C -

Rearrange to put C terms on one side and Y terms on the other:

1 2 2 1(1 ) (1 )r C C Y r Y

Finally, divide through by (1+r ):

The intertemporal budget constraint

2 21 11 1

C YC Y

r r

present value of lifetime consumption

present value of lifetime income

The budget constraint shows all combinations of C1 and C2 that just exhaust the consumer’s resources.


C1

C2

1 2 (1 )Y Y r

1 2(1 )r Y Y

Y1

Y2 Borrowing

Saving Consump = income in both periods

2 21 11 1

C YC Y

r r

The slope of the budget line equals -(1+r )


C1

C2

Y1

Y2

2 21 11 1

C YC Y

r r

1

(1+r )

An indifference curve shows all combinations of C1 and C2 that make the consumer equally happy.

Consumer preferences

C1

C2

IC1

IC2

Higher indifference curves represent higher levels of happiness.

Marginal rate of

substitution (MRS ):

the amount of C2

consumer would be

willing to substitute for

one unit of C1.

Consumer preferences

C1

C2

IC1

The slope of an indifference curve at any point equals the MRS at that point. 1

MRS

The optimal (C1,C2) is

where the budget line

just touches the

highest indifference

curve.

Optimization

C1

C2

O

At the

optimal point,

MRS = 1+r

Formal approach to optimization – the method of Lagrange multipliers

])1()1(

[),(

)1()1(..),(

21

21121

21

2121

r

CC

r

YYccuL

r

CC

r

YYtsccuU

--

The solution is that:

)1(21

rc

U

c

U

An increase in Y1 or Y2

shifts the budget line

outward.

How C responds to changes in Y

C1

C2 Results:

Provided they are

both normal goods,

C1 and C2 both

increase,

…regardless of whether the income increase occurs in period 1 or period 2.

Keynes vs. Fisher

Keynes: current consumption depends only on current income

Fisher: current consumption depends on the present value of lifetime income; the timing of income is irrelevant because the consumer can borrow or lend between periods.

A

An increase in r

pivots the budget

line around the

point (Y1,Y2 ).

How C responds to changes in r

C1

C2

Y1

Y2

A

B

As depicted here,

C1 falls and C2 rises.

However, it could

turn out differently…

How C responds to changes in r

income effect If consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods.

substitution effect The rise in r increases the opportunity cost of current consumption, which tends to reduce C1 and increase C2.

Both effects C2.

Whether C1 rises or falls depends on the relative size of the income & substitution effects.

Constraints on borrowing

In Fisher’s theory, the timing of income is irrelevant because the consumer can borrow and lend across periods.

Example: If consumer learns that her future income will increase, she can spread the extra consumption over both periods by borrowing in the current period.

However, if consumer faces borrowing constraints (aka “liquidity constraints”), then she may not be able to increase current consumption

and her consumption may behave as in the Keynesian theory even though she is rational & forward-looking

The budget line with no borrowing constraints


C1

C2

Y1

Y2

The borrowing constraint takes the form:

C1 Y1


C1

C2

Y1

Y2

The budget line with a borrowing constraint

The borrowing constraint is not binding if the consumer’s optimal C1 is less than Y1.

Consumer optimization when the borrowing constraint is not binding

C1

C2

Y1

The optimal choice is at point D.

But since the consumer cannot borrow, the best he can do is point E.

Consumer optimization when the borrowing constraint is binding

C1

C2

Y1

D

E

due to Franco Modigliani (1950s)

Fisher’s model says that consumption depends on lifetime income, and people try to achieve smooth consumption.

The LCH says that income varies systematically over the phases of the consumer’s “life cycle,”

and saving allows the consumer to achieve smooth consumption.

The Life-Cycle Hypothesis

The Life-Cycle Hypothesis

The basic model:

Wt = wealth in time t

Yt = annual disposable income until retirement (income net of taxes)

R = number of years until retirement

T = lifetime in years

Assumptions:

– zero real interest rate (for simplicity)

– consumption-smoothing is optimal

The Life-Cycle Hypothesis Lifetime resources To achieve smooth consumption, consumer divides her

resources equally over time: If we assume constant income, we can write:

C = aW + bY

a = (1/T ) is the marginal propensity to

consume out of wealth b = (R/T ) is the marginal propensity to consume out

of income

R

tttt

YYW1

1

][1

11

R

ttttt

YYWT

C

Implications of the Life-Cycle Hypothesis

The Life-Cycle Hypothesis can solve the consumption puzzle:

The APC implied by the life-cycle consumption function is C/Y = a(W/Y ) + b

Across households, wealth does not vary as much as income, so high income households should have a lower APC than low income households.

Over time, aggregate wealth and income grow together, causing APC to remain stable.


The LCH implies that saving varies systematically over a person’s lifetime.

Saving

Dissaving

Retirement begins

End of life

Consumption

Income

$

Wealth

Implications

The saving rate changes over the life-time of the consumer

Consumption is not very responsive to changes in current income

Consumption may change even if current income does not

Important role for expectations

The Permanent Income Hypothesis

due to Milton Friedman (1957)

The PIH views current income Y as the sum of two components:

permanent income Y P (average income, which people expect to persist into the future)

transitory income Y T (temporary deviations from average income)

Consumers use saving & borrowing to smooth consumption in response to transitory changes in income.

The PIH consumption function:

C = aY P

where a is the fraction of permanent income that people consume per year.



Current income differs from permanent income

Yt = Yt P + Yt

T

Yt = current income in time t

Y P = permanent income

expected (in time t) average yearly income from human capital (earnings) and wealth

Y T = transitory income

transitory deviations of current income from permanent income


Consumers have to somehow estimate the amount of permanent income

Friedman assumed an adaptive formula

Consumers correct their previous estimates of permanent income by the j amount of deviation of current income from previous period estimated permanent income

10),(11

---

jYYjYY perm

tt

perm

t

perm

t

The PIH can solve the consumption puzzle:

The PIH implies

APC = C/Y = aY P/Y

To the extent that high income households have higher transitory income than low income households, the APC will be lower in high income households.

Over the long run, income variation is due mainly if not solely to variation in permanent income, which implies a stable APC.


PIH vs. LCH

In both, people try to achieve smooth consumption in the face of changing current income.

In the LCH, current income changes systematically as people move through their life cycle.

In the PIH, current income is subject to random, transitory fluctuations.

Both hypotheses can explain the consumption puzzle.

In applied work, reseraches often use PILCH (an approach that combines both theories)

The Random-Walk Hypothesis

due to Robert Hall (1978)

based on Fisher’s model & PIH, in which forward-looking consumers base consumption on expected future income

Hall adds the assumption of rational expectations, that people use all available information to forecast future variables like income.

The Random-Walk Hypothesis

If PIH is correct and consumers have rational expectations, then consumption should follow a random walk: changes in consumption should be unpredictable.

• A change in income or wealth that was anticipated has already been factored into expected permanent income, so it will not change consumption.

• Only unanticipated changes in income or wealth that alter expected permanent income will change consumption.

If consumers obey the PIH

and have rational expectations, then policy

changes will affect consumption

only if they are unanticipated.

Implication of the R-W Hypothesis

The Psychology of Instant Gratification

Theories from Fisher to Hall assumes that consumers are rational and act to maximize lifetime utility.

Famous studies by David Laibson and others consider the psychology of consumers.

The Psychology of Instant Gratification

Consumers consider themselves to be imperfect decision-makers. E.g., in one survey, 76% said they were not saving

enough for retirement.

Laibson: The “pull of instant gratification” explains why people don’t save as much as a perfectly rational lifetime utility maximizer would save.

Two Questions and Time Inconsistency

1. Would you prefer (A) a candy today, or (B) two candies tomorrow?

2. Would you prefer (A) a candy in 100 days, or (B) two candies in 101 days?

In studies, most people answered A to question 1, and B to question 2.

A person confronted with question 2 may choose B. 100 days later, when he is confronted with question 1, the pull of instant gratification may induce him to change his mind.

Summing up

Keynes suggested that consumption depends primarily on current income.

More recent work suggests instead that consumption depends on

current income

expected future income

wealth

interest rates

Economists disagree over the relative importance of these factors and of borrowing constraints and psychological factors.

Summing up

2. Fisher’s theory of intertemporal choice

Consumer chooses current & future consumption to maximize lifetime satisfaction subject to an intertemporal budget constraint.

Current consumption depends on lifetime income, not current income, provided consumer can borrow & save.

3. Modigliani’s Life-Cycle Hypothesis

Income varies systematically over a lifetime.

Consumers use saving & borrowing to smooth consumption.

Consumption depends on income & wealth.

Summing up

4. Friedman’s Permanent-Income Hypothesis

Consumption depends mainly on permanent income.

Consumers use saving & borrowing to smooth consumption in the face of transitory fluctuations in income.

5. Hall’s Random-Walk Hypothesis

Combines PIH with rational expectations.

Main result: changes in consumption are unpredictable, occur only in response to unanticipated changes in expected permanent income.

Chapter summary

6. Laibson and the pull of instant gratification

Uses psychology to understand consumer behavior.

The desire for instant gratification causes people to save less than they rationally know they should.

Saving motives in Poland

Florczak & Jabłonowski, 2016 https://www.nbp.pl/publikacje/materialy_i_studia/252_en.pdf

Research on consumption Johnson & Parker & Souleles (2006); „Household

expenditure and the income tax rebates of 2001”; Am. Econ. Rev. 96:

They study the US large income tax rebate program provided by the Economic Growth and Tax Relief Reconciliation Act of 2001.

The program sent tax rebates, typically $300 or $600 in value, to approximately two-thirds of U.S. households.

According to the PI hypothesis, a single rebate would have little effect on spending. Furthermore , in the absence of liquidity constraints, spending should increase as soon as consumers begin to expect the tax cut, and not increase only after they actually have received the rebate check.

The rebate checks were mailed out over a 10-week period from late July to the end of September 2001. The particular week in which a check was random.

Research on consumption

This randomization allows the authors to identify the causal effect of the rebate by comparing the spending of households that received the rebate earlier with the spending of households that received it later.

The authors find that the average household spent 20%–40% of its 2001 tax rebate on nondurable goods during the three-month period in which the rebate was received.

The authors also find that the expenditure responses are largest for households with relatively low liquid wealth and low income, which is consistent with liquidity constraints

Research on consumption

A paper that stands in contrast to these is Browning & Callado (2001) „The response of expenditures to anticipated income changes: Panel Data Estimates” AER, vol.91(3)

They use Spanish micro data to examine the consumer response to the payment of institutionalized June and December extra wage payments to full-time workers & compare it to consumption of workers witouht the extra wage payments.

Browning & Collado detect no evidence of excess sensitivity – there is no significant difference in consumption profiles of both groups

They argue that the reason why earlier researchers found a large response of consumption to predicted income changes is because of bounded rationality:

Consumers tend to smooth consumption and follow the theory when expected income changes are large but are less likely to do so when the changes are small

Ricardian equivalence approach

The focus is on the effects of budget deficits on consumption and private savings

Assumptions: fully rational consumers

Infinite time horizon

Taxes are lump-sum

Conclusion: the timing of taxes does not matter for consumption

Private consumption is not on by way that that government spending is financed (by taxes or by public borrowing)

Hence, tax cuts (keeping government spending unchanged) do not make any difference

Two period model

)1(

)()(

)1(

2211

21

r

TYTY

r

CC

--

)1()1(

)(

21

21

211121

21221

r

TT

r

GG

TTTGrGG

TTrBGG

-

1. Private budget constraint

2. Government’s budget constraint

Plug 2 into 1 to get the private sector’s budget constraint

)1()1()1(

21

21

21

r

GG

r

YY

r

CC

--

Intuition

Let’s assume that government spending are unchanged, but the government cuts taxes

Will private consumption change?

Current disposable income increases, but future disposable income decreases, as the government will have to increase taxes in the future to pay back the public debt

Rational consumers, expecting an increase in taxation will not increase consumption, but will increase savings (they will save the current increase in income)

Current decrease in taxation does not have any effect on total, disposable income, so it does not affect consumption

Ricardian equivalence approach

Conclusions: when the government cuts taxes and runs a budget deficit, the government saving falls

In the same time, private sector savings increases, implying that:

Total amount of savings does not change

Consumption is not affected;

Aggregate demand is not affected

microfoundations. modern theories of consumptioncoin.wne.uw.edu.pl/siwinska/macro2_lecture12.pdf ·...

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