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Unformatted text preview: Consumption and Saving
A Micro Foundation
Micro
Intertemporal Choice and the 2Period Model,
2The LifeCycle Model,
LifePermanent Income Hypothesis,
Rational Expectations Topic 6 (Text: 4.1, Appendix 4.A; Pres Topic #4) 1 9000 10000 11000 The Effects of the Recent Tax Rebates
Tax rebate
Aftertax income Consumer expenditures 2006 2007 2008 savrt
012345 month 2006 Saving rate 2007 2008
month
5 Household saving rates in many OECD
OECD
countries have fallen sharply in recent years
(U.S. is at 0.5%)
(U.S.
Economist, April 7 2005. 7 Ja
n 62 07 04 01 98 95 92 89 86 83 80 77 74 71 68 65 25.0% Ja
n 53 56 59 30.0% Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Ja
n Percent 19
76
I 20
08
I 20
06
I 20
04
I 20
02
I 20
00
I 19
98
I 19
96
I 19
94
I 19
92
I 19
90
I 19
88
I 19
86
I 19
84
I 19
82
I 19
80
I 19
78
I 19 20 20 20 20 20 19 19 19 19 19 19 19 19 19 19 19 76 08 06 04 02 00 98 96 94 92 90 88 86 84 82 80 78 I I I I I I I I I I I I I I I I I 10.0% Ja
n Ja
n 50 47 2.5% Ja
n Ja
n Savings Behavior 22.5% U.S. Savings 20.0% 17.5% 15.0% 12.5% Pers Sav/GDP
Private Sav/GDP 7.5% 5.0% 2.5% 0.0% Consumption Trends 72.5% U.S. Consumption 70.0% 67.5%
Cons/GDP 65.0% 62.5% 60.0% Components of Consumption 45.0% 40.0% Components of Consumption 35.0% Cons Dur Cons Non Dur 20.0% Cons Serv Gov Cons 15.0% 10.0% 5.0% 0.0% Intertemporal Choice
• Keynes hypothesized that consumption and
therefore saving depend on the current level of
income alone
Recall that Saving = Income – Consumption – Taxes
Recall • But sensible consumers know they are really
trading off present for future consumption
What is not consumed today is saved to be consumed
What
tomorrow, and vice versa • Irving Fisher formalized this tradeoff, and
introduced the interest rate as an important
determinant of consumption and saving
consumption
saving
11 The TwoPeriod Model
Two• Assume that consumer lives only for two
periods
Period 1: youth
Period
Period 2: old age
Period • Y1, Y2: income in periods 1 & 2
• C1, C2: consumption in periods 1 & 2
• r:
real interest rate at which consumer
real
can borrow or lend in period 1
12 The TwoPeriod Model (cnt.)
cnt.)
Two• Budget constraints in the two periods:
Uses = Resources
Resources C1 + S = Y1
C2 = (1 + r) S + Y2
If S > 0, the consumer is saving
If
C >=< Y If S < 0, the consumer is borrowing
If 13 The 2Period Model Example #1
2• Let Y1 = 150, Y2 = 220, C1 = 120
220,
• What would be maximum C2 if r = 10%? 14 The TwoPeriod Model (cnt.)
cnt.)
Two• Substitute for S from the second equation into the
first to get a single intertemporal budget constraint:
S = Y1  C1
C2 = (1 + r) S + Y2 ⇒ S = C1 + C2
Y
−2
1+ r 1+ r Y
C2
= Y1 + 2
1+ r
1+ r PV (Cons) = PV (Income)
21 The TwoPeriod Model (cnt.)
cnt.)
Two• If there is initial financial wealth, AA0 ≥ 0,
AA
the PV of income is augmented C1 + C2
Y
= Y1 + 2 + AA 0
1+ r
1+ r PV (Cons) = PV (Income) + Initial Wealth 22 Example #1 Repeated (cnt.)
cnt.)
• You can see that her total resources
PV of income
PV are allocated to the PV of consumption 150 + 220
C
= 350 = C1 + 2
1.10
1.10 24 The TwoPeriod Model (cnt.)
cnt.)
TwoC2
Y
= Y1 + 2
1+ r
1+ r
1/(1+r) unit of goods today = 1 unit of good
tomorrow
Today’s price of consuming a unit of good
Today’
tomorrow is 1/(1+r)
Can represent the above budget constraint
budget
graphically
C1 + •
•
• It makes things clearer (hopefully)
It
25 The TwoPeriod Model (cnt.)
cnt.)
TwoHow do consumers choose how to
choose
consume?
• Consumer’s preferences over 1st and 2nd
Consumer’
period consumption can be represented with
indifference curves
indifference
• An indifference curve gives combination of
consumption bundles that makes consumer
equally happy
Higher curves (NE) represent higher utility than
Higher
lower curves
26 The TwoPeriod Model (cnt.)
cnt.)
TwoHow do consumers choose how to
choose
consume?
• The budget constraint line gives all the
possible consumption combinations
On the line no resources are wasted!
On
Below the line resources are wasted
Below
Above the line points are unattainable
Above
unattainable • The optimum is the highest utility that can
be attained with the given budget constraint
The optimum is where the indifference curve is
The
tangent to the budget constraint
27 The TwoPeriod Model (cnt.)
cnt.)
TwoMain point:
• Consumption depends on the present value of
present
income
It doesn’t matter if the higher income is in the first or second
It doesn’
period • Critical: the ability to borrow and lend
• The consumer tends to smooth consumption
smooth
She spreads consumption relatively evenly over both periods,
She
regardless of the income profile
Think of retirement and short unemployment spells
Think
28 The 2Period Model Examples
2• What happens when:
1. Y1 ⇑ ?
2. Y2 ⇑ ?
Consumption smoothing
Consumption 29 The Relative Price of Future Consumption
Relative
• 1 Why is the relative price of C2 1 + r ?
If you save 1 unit of output in period 1, you are forgoing
If
this consumption in period 1
But you get 1+r units of output (consumption) in period 2
But
The tradeoff is 1 to 1+r
The trade1+ • To get 1 unit of output in period 2, you need to
save 1 units of output in period 1
1+ r 30 The TwoPeriod Model Again
TwoAn ↑ in “r” has two effects on saving (S):
• Relative price of period 2 consumption ↓
$1 saved in 1st period gives more consumption in
$1
2nd period
So reduce today’s consumption by saving more to
So
today’
increase tomorrow’s consumption
tomorrow’
Substitution effect tends to ↑ S
Substitution • But there is an income effect!
income
32 The TwoPeriod Model Again
TwoSome things to keep straight
• Around what point does the budget line
rotate?
• What about the Income Effect?
Income
When the interest rate rises • If you are a borrower,
you
You are worse off
You
Substitution effect consume less now
Substitution
consume
Income effect consume less now and later
Income
consume Income effect reinforces the substitution effect for C1
Income
33 The TwoPeriod Model Again
TwoWhen the interest rate rises • If you are a lender,
You are better off
You
Substitution effect consume less now
Substitution
consume
Income effect consume more now and later
Income
consume The income effect fights the substitution effect for C1
The • The further away you are from autarky, the
bigger the income effect will be
• We assume the substitution effect dominates
34 The TwoPeriod Model Again
TwoAn ↑ in “r” has two effects on saving (S):
• Relative price of period 2 consumption ↓
$1 saved in 1st period gives more consumption in
$1
2nd period
So reduce today’s consumption by saving more to
So
today’
increase tomorrow’s consumption
tomorrow’
Substitution effect tends to ↑ S
Substitution • But there is an income effect!
income
40 The TwoPeriod Model Again
TwoSome things to keep straight
• Around what point does the budget line
rotate?
• What about the Income Effect?
Income
When the interest rate rises • If you are a borrower,
you
You are worse off
You
Substitution effect consume less now
Substitution
consume
Income effect consume less now and later
Income
consume Income effect reinforces the substitution effect for C1
Income
41 The TwoPeriod Model Again
TwoWhen the interest rate rises • If you are a lender,
You are better off
You
Substitution effect consume less now
Substitution
consume
Income effect consume more now and later
Income
consume The income effect fights the substitution effect for C1
The • The further away you are from autarky, the
bigger the income effect will be
• We assume the substitution effect dominates
42 Review Income & Substitution Effects Saver r⇑ r⇓ Substitution Effect C1 ⇓ C1 ⇑ Income Effect C1 ⇑ C1 ⇓ Borrower r⇑ r⇓ Substitution Effect C1 ⇓ C1 ⇑ Income Effect C1 ⇓ C1 ⇑
43 Consumption Behavior in Recessions
Real Consumption Growth Rate in Recessions
(per quarter)
4% Rec81
Rec07
Ground 0 3% Mean
P1Sd
M1Std 2% 1% 0%
2
1% 2% 0 2 4 6 8 10 12 14 16 Complementary Models
• The twoperiod model provides all the
twonecessary intuition on how intertemporal
consumption decisions are made
• There are 2 complementary models we’ll
complementary
we’
discuss next
The Life Cycle model (Modigliani)
The
Insights into the life cycle of earnings
Insights The Permanent Income hypothesis (Friedman)
The
Primacy of wealth in the consumption decision
Primacy • There are no new principles here
46 The LifeCycle Model
Life• The twoperiod model suggests that an
twoindividual
Saves when income is high (e.g., while working),
Saves
and
Dissaves when income is low (e.g., while retired)
Dissaves • Franco Modigliani extended the twoperiod
twomodel to many periods to understand
lifetime patterns of income, consumption,
and saving
47 The LifeCycle Model (cnt.)
cnt.)
Life• The typical real income path is inverse
Ushaped, with peak earnings occurring
between the ages of fifty and sixty
• Consumers dislike changes in their
consumption levels
they spread their lifetime resources to maintain a
they
fairly even standard of living over time
smooth consumption
smooth • They borrow while young, save in middle
age, and dissave while old
48 Figure 4.A.5 LifeCycle Consumption,
LifeIncome, and Saving 49 The LifeCycle Model (cnt.)
cnt.)
Life• Therefore, national savings rates depend on
the country’s age distribution
country’
• Countries with unusually young or
unusually old populations have low saving
rates
Saving rate = Amount saved / Income
Saving rate Amount 50 The LifeCycle Model (cnt.)
cnt.)
Life• The decline in the US personal saving rate
from 9% in the 50s and 60s to 3% in the 90s, and to 1% or
from 9%
3%
1%
less (even negative) currently
negative is attributed to:
Ageing population
Ageing
Increase in taxation of the younger workers to pay for
Increase
Social Security and Medicare
Increases consumption of the old more than it decreases
Increases
consumption of the young
Increase in oldage security causes people to save less for
Increase oldretirement Increase in the share of income used for medical
Increase
expenditures (are medical expenditures consumption?)
Nonmedical consumption shares have stayed roughly
Nonconstant
51 How Is Amount Saved Defined?
• S = Y – C – G at the national level
Personal Saving rate =
Disposable personal income
– consumption
– interest and transfer payments 52 Saving Example
Example:
• A person earns $100,000 in a year and
consumes exactly $100,000
• This person started the year with a portfolio
worth $500,000 which increased to
$2,500,000 because of capital gains
How much did she save?
How
By how much did her wealth increase?
By 53 Permanent Income Hypothesis
• Milton Friedman used the idea that consumption
depends on the present value of income to study
the effect of temporary and permanent changes in
temporary
permanent
income on consumption and saving
He called the PV of income Permanent Income
He
PV
Permanent • A permanent 1unit ↑ in income raises permanent
1permanent
income more than a temporary 1unit ↑
1A temporary ↑ in income is an increase in Y1, with Y2 held
temporary
fixed
A permanent ↑ in income is an ↑ in both Y1 and Y2
permanent
both 54 PermanentIncome Hypothesis (cnt.)
cnt.)
Permanent• Therefore, a permanent 1unit increase in income
1increases current and future consumption more
and
than a temporary 1unit increase
1Amount saved from a permanent increase in income will be
Amount saved
less than amount saved from a temporary increase in income • Temporary income increases would be mostly
saved, permanent increases mostly consumed
This explains why aggregate consumption is smoother than
This
income 55 PermanentIncome Hypothesis (concl.)
concl.)
Permanent• The algebraic statement of this idea is: C = λ * P.Income, 0 < λ < 1
λ is endogenous, it increases as the person ages
endogenous
It converts your “Permanent Income” or your “wealth” to an
It
Income”
wealth”
annuity (it could be made to grow over time)
annuity
You consume the annuity yield of your wealth each period
You
i.e., the annual payment that you can get from the annuity
i.e., If your annuity increases you increase your consumption
If
increases
only by the increase in the “yield” of your annuity
yield”
It is calculated exactly like the payment to a mortgage that
It
exactly
is required to pay it off by a certain date
56 Rational Expectations and
Consumption
• Consumption
theory
highlights
the
important role of expectations about future
expectations
income (and policies) in determining
current consumption
current
• The rational expectations hypothesis
maintains that people use all available
information to make optimal forecasts about
the future 57 Rational Expectations and
Consumption (cnt.)
cnt.)
• The permanent income and rational
expectations hypotheses combined lead to
the conclusion that:
only unexpected changes in income and
unexpected
policies will change current consumption
current
All anticipated changes to income are already
All
programmed into the consumption plan
What if you want to borrow when young but can’t?
What
can’ 58 What Is the Evidence?
DispI
= 0.89
C • MPC out of disposable income is ~ 85%  95%
Maybe higher
Maybe • Souleles (1999) finds that people consume 9 % of
their tax rebates in strictly nondurable form but
non54% in consumer durables form
• Johnson, Parker, Souleles (2005) report somewhat
higher numbers for the 2001 tax rebates
All report higher MPCs for liquidityconstrained
All
MPC
liquidityhouseholds
59 Example #3
• Suppose the permanentincome consumption for
permanentan individual with 20 years of remaining life is
1
given by
C=
P.Income
10.00 Interest rate is 7.75469%
Interest How much will she consume this year if her P. Income
How
or PV(Y) = $500,000?
If she receives an unanticipated $1,000 additional
If
income this year, by how much will her current
consumption increase?
Use a spreadsheet to verify for yourselves that she can
Use
indeed consume this amount every year for 20 years!
Hint: Her current wealth at any point in time earns interest
62 Example #4
• Y = 9,000, G = 2,000
r
2%
3%
4%
5%
6% Cd
6,100
6,000
5,900
5,800
5,700 Id
1,500
1,400
1,300
1,200
1,100 1. Why does Cd & Id fall as r rises?
rises?
2. What are the equilibrium values for r, S and I ? 66 Appendix 1
• Given a PV(Y), what is the current Permanent
Income consumption? Let
r
be the real interest rate
g
the rate at which desired consumption grows
N
the number of periods of life remaining
• Then we have
⎧ 1 ⎡ ⎛ 1 + g ⎞N ⎤⎫
⎪
⎪
PV0 (Y ) = C0 ⎨
⎟ ⎥⎬ ∀ r > g
⎢1 − ⎜
⎪ r − g ⎢ ⎝ 1 + r ⎠ ⎥⎪
⎣
⎦⎭
⎩ • Consumption will start at C0 and grow at g
68 Glossary of Terms
Y 1, Y 2
C1, C2
r
S
P.Income Income in the two periods, 1 and 2
Consumption in the two periods
Interest rate on saving
Consumer saving
Permanent Income 69 THE END 86 ...
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 Spring '07
 Safarzadeh

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