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Micro foundations, part 1
Modern theories of consumption
Joanna Siwińska-GorzelakFaculty of Economic Sciences, Warsaw University
slide 2
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:
The Ricardian Approach
slide 3
The Keynesian Consumption Function
𝐶𝑡 = 𝑐0 + 𝑐𝑦 𝑌𝑡 − 𝑇𝑡 − consumption function with the properties Keynes conjectured:
C
Y
1
cY
C
𝑐𝑌 = MPC
= slope of the consumption function
slide 4
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.
slide 5
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
slide 6
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.
slide 7
The Consumption Puzzle
C
Y
Consumption function from long time series data (constant APC )
Consumption function from cross-sectional household data
(falling APC )
slide 8
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
slide 9
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)
slide 10
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 ):
slide 11
The intertemporal budget constraint
2 21 1
1 1
C YC Y
r r
present value of lifetime consumption
present value of lifetime income
slide 12
The budget constraint shows all combinations of C1 and C2
that just exhaust the consumer’s resources.
The intertemporal budget constraint
C1
C2
1 2 (1 )Y Y r
1 2(1 )r Y Y
Y1
Y2Borrowing in period 1
Saving in period 1
Consump = income in both periods
2 21 1
1 1
C YC Y
r r
slide 13
The slope of the budget line equals -(1+r )
The intertemporal budget constraint
C1
C2
Y1
Y2
2 21 1
1 1
C YC Y
r r
1
(1+r )
slide 14
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.
slide 15
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 MRSat that point.1
MRS
slide 16
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
slide 17
An increase in Y1 or Y2
shifts the budget line
outward.
How C responds to changes inY
C1
C2Results:
Provided they are
both normal goods,
C1 and C2 both
increase,
…regardless of whether the income increase occurs in period 1 or period 2.
slide 18
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.
slide 19
A
An increase in r
pivots the budget
line around the
point (Y1,Y2 ).
How C responds to changes inr
C1
C2
Y1
Y2
A
B
As depicted here,
C1 falls and C2 rises.
However, it could
turn out differently…
slide 20
A
An increase in r
pivots the budget
line around the
point (Y1,Y2 ).
How C responds to changes inr
C1
C2
Y1
Y2
A
B
As depicted here,
C1 falls and C2 rises.
However, it could
turn out differently…
slide 21
How C responds to changes inr
income effectIf consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods.
substitution effectThe 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.
What happens when the consumer is a borrower?
slide 22
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
slide 23
The budget line with no borrowing constraints
Constraints on borrowing
C1
C2
Y1
Y2
slide 24
The borrowing constraint takes the form:
C1 Y1
Constraints on borrowing
C1
C2
Y1
Y2
The budget line with a borrowing constraint
slide 25
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
slide 26
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
slide 27
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
slide 28
The Life-Cycle Hypothesis
The basic model:
Wt = wealth in time t
Yt = annual disposable income until retirement (income net of taxes)
N = number of years until retirement
T = lifetime in years
Assumptions:
– zero real interest rate (for simplicity)
– consumption-smoothing is optimal
slide 29
The Life-Cycle Hypothesis Lifetime resources, calculated at time t
To achieve smooth consumption in each period t, 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
N
t
ttt YYW 1
][1
1
1
N
t
tttt YYWT
C
slide 30
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.
slide 31
Implications of the Life-Cycle Hypothesis
The LCH implies that saving varies systematically over a person’s lifetime.
Saving
Dissaving
Retirement begins
End of life
Consumption
Income
$
Wealth
Implications of the Life-Cycle Hypothesis
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 of expectations
slide 34
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)
slide 35
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.
The Permanent Income Hypothesis
The Permanent Income Hypothesis
Current income differs from permanent income
Yt = YtP + Yt
T
Yt = current income in time t
YP = permanent incomeexpected (in time t) average yearly income from human capital (earnings) and wealth
YT = transitory incometransitory deviations of current income from permanent income
The Permanent Income Hypothesis
Consumers have to somehow estimate the amount of permanent income
Friedman assumed an adaptive formula
Consumers correct their previous estimates of permanentincome by the j amount of deviation of current income from previous period estimated permanent income
10),(11
---
jYYjYY perm
tt
perm
t
perm
t
slide 38
The PIH can solve the consumption puzzle:
The PIH implies
APC = C/Yt = aY P/Y t
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.
The Permanent Income Hypothesis
slide 39
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, researchers often use PILCH (an approach that combines both theories)
slide 40
The Psychology of Instant Gratification
Modern consumption theories assume that consumers are rational and act to maximize lifetime utility.
Famous studies by David Laibson and others consider the psychology of consumers.
slide 41
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 maximizerwould save.
slide 42
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.
slide 43
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.
slide 44
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.
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 ReliefReconciliation 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 asconsumers 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. Theparticular 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 (excess sensitivity).
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
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
