The economics of consumption
1
From: President Ella Eli
To: Yale Students
Re: Generous Gift
My dear students,
I am delighted to report that a generous alumna has made a
gift of $1000 per Yale student, available immediately. You can come
by the office and pick up your check any time.
Professor Nordhaus has requested that you detail how you
would spend the funds. Would you please write this down in your
notebooks in class today. You will find it instructive as you discuss
Consumption in class this week.
With best wishes,
President Ella Eli
P.S. Professor Nordhaus has told me about “elevator quizzes,” which
are a great idea. This is not an elevator quiz, but you should hold on
to your answers for later reference. EE
2
Importance of consumption in macro
1. Consumption is two-thirds of GDP –
understanding its determinants is major part of
the ball game.
2. Consumption is the entire point of the economy:
3. Consumption plays two roles in microeconomics:
a. AD: It is a major part of AD in the short run:
recall IS curve in which
Y = C(Yd) + I + G + NX
b. AS: What is not consumed is saved and
influences national investment and economic
growth
3
Table 2.1. Personal Income and Its Disposition
[Billions of dollars]
Bureau of Economic Analysis
Last Revised on: August 29, 2012
Item
Personal income
Compensation of employees, received
Proprietors' income
Rental income of persons
Personal income receipts on assets
Personal current transfer receipts
Less: Contributions for government social insurance, domestic
Less: Personal current taxes
Equals: Disposable personal income
Less: Personal outlays
Equals: Personal saving
Personal saving as a percentage of disposable personal income
2011
Percent of income
12,947
8,295
64%
1,157
9%
410
3%
1,685
13%
2,319
18%
919
1,398
11,549
11,060
489
4.2
4
Table 2.4.5. Personal Consumption Expenditures
by Type of Product
[Billions of dollars]
Bureau of Economic Analysis
Last Revised on: August 02, 2012
Personal consumption expenditures
Goods
Durable goods
Motor vehicles and parts
Furnishings and durable household equipment
Recreational goods and vehicles
Other durable goods
Nondurable goods
Food and beverages purchased, off-premises
Clothing and footwear
Gasoline and other energy goods
Other nondurable goods
Services
Housing and utilities
Health care
Transportation services
Recreation services
Food services and accommodations
Financial services and insurance
Other services
Higher education
2011
10,729
3,625
1,146
374
252
340
181
2,478
810
349
428
891
7,104
1,930
1,752
302
395
671
807
956
168
33.8%
10.7%
3.5%
2.3%
3.2%
1.7%
23.1%
7.6%
3.3%
4.0%
8.3%
66.2%
18.0%
16.3%
2.8%
3.7%
6.3%
7.5%
8.9%
1.6%
5
Growth in C and GDP (quarterly)
Chicken or egg:
- ΔC causes recession?
- Recession causes ΔC?
.02
.01
.00
-.01
-.02
Consumption
GDP
-.03
00
01
02
03
04
05
06
07
08
09
10
11
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Alternative Theories of Consumption
The basic Keynesian insight is that consumption depends
fundamentally on personal income (“consumption function”)
This enters into the Keynesian models as C = α + βYd
On a closer look, a major puzzle: the short-run and cross-sectional
consumption functions looked very different from the long-term
consumption function.
7
Consumption and Disposable Income
12,000
Real consumption
10,000
8,000
6,000
4,000
2,000
0
0
2,000
4,000
6,000
8,000 10,000 12,000
Real disposable income
8
Short-run v. Long-run Consumption Function
9
Alternative Theories of Consumption
There are four major approaches in macroeconomics:
*1. Fisher's approach: sometimes called the neoclassical model
2. Keynes original approach of the consumption function
*3. Life-cycle or permanent income approaches (Modigliani,
Friedman)
4.Rational expectations (Euler equation) approaches (in Jones)
*We will do in class, but more Fisher in section.
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Intertemporal Consumption Choice: Fisher’s model
Basic idea:
People have expectations of lifetime income; they determine their
consumption stream optimally; this leads consumers to “smooth”
consumption over their lifetime.
Assumptions of two period model:
Periods 1 and 2
Income Y1 and Y2
Maximize utility:
U(C 2 )
max U(C1 ) +
{C1 ,C 2 }
(1+ δ)
Budget constraint:
C1 +
C2
Y2
= Y1 +
(1+ r)
(1+ r)
We will do graphical case now and calculus later.
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Budget constraint:
C1+C2/(1+r)=Y1
[no income in retirement]
C2
Indifference curve
between current and
future consumption
C 2*
E*
S1 *
C 1*
Y1
C1
C2
Key result: consumption
independent of timing of
income!!!
Called “consumption
smoothing”
C 2*
E*
S1 *
C 1*
Y1
C1
Summary to here
Income over life cycle is the major determinant of
consumption and saving.
In idealized case, have consumption smoothing over
lifetime.
Now move from two-period (Fisher model) to multi-period
(life cycle model).
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Basic Assumptions of Life Cycle Model
Basic idea:
People have expectations of lifetime income; they determine their
consumption stream optimally; this leads consumers to “smooth”
consumption over their lifetime.
Assumptions:
“Life cycle” for planning from age 1 to D.
Earn Y per year for ages 1 to R.
Retire from R to D.
Maximize utility function:
max V(C 1 , C 2 , ..., C D ) 
D
 (1   ) z U(C z ),
for ages z  1 to D.
z1
Budget constraint:
D
 (1  r )
z 1
-z
Cz 
D
 (1  r )-z Yz
z 1
Discount rate on utility (δ) = real interest rate (r) = 0 (for simplicity)
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Techniques for Finding Solution
1. Two periods:
max U(C1 )  U(C2 )  U(C1 )  U(Y1  Y2 - C1 )
{Cz }
Maximizing this leads to U’(C1)=U’(C2). This implies that C1 = C2 ,
which is consumption smoothing. The Cs are independent of
the Ys.
2. Lagrangean maximization (advanced math econ):
D
 D
-z
max L C1 ,...,CD  =  (1+ δ) U(C z ) + λ   (1+ r ) C z -  (1+ r )-z Yz

{C z }
z=1
z=1
 z=1
D
-z




Maximizing implies that U’(C1)=U’(C2)=-λ. This implies that Ct  C
which again is consumption smoothing independent of Y.
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U
U '(C )
U(C )
Since U’(C1)=U’(C2)=…
= -λ, C is constant over
time.
Note: this assumes
diminishing marginal
utility or U”(C)<0.
Make sure you know
what this means.
C
C1
Review of last time
Life-cycle model:
People plan their consumption over the future
Assumptions:
“Life cycle” for planning from age 1 to D.
Earn constant Y per year for ages 1 to R.
Retire from R to D.
Maximize discounted utility:
max V(C 1 , C 2 , ..., C D )  U(C 1 ) /(1   )  U(C 2 ) /(1   ) 2  
subject to the budget constraint:
C 1 /(1  r )  C 2 /(1  r )2    Y1 /(1  r )  Y2 /(1  r ) 2  
For simplicity, assume r = δ = 0.
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Initial Solution
C, Y, S
Diagram of Life
Cycle Model
Showing
Consumption
Smoothing
Income, Y
Consumption, C
Saving, S
|
0
R
age
|
D
19
Anticipated change in timing of income
C, Y, S
Income “splash” (Y’) with no W increase
Income, Y
Anticipated income
change of ΔY.
Consumption, C’=C
Because it is
anticipated, no
change in lifetime
income, so no
change in
(smoothed)
consumption. MPC
= 0; MPS = 1.
Saving, S’
|
R
0
age
|
D
20
What about anticipated taxes?
C, Y, S
Income “splash” from tax cut
Income, Y
No C change!
Saving, S’
|
R
0
age
|
D
21
Unanticipated change in permanent income
C, Y, S
Y’ =unanticipated increase; W increases.
Unanticipated windfall
of ΔY in period z.
Leads to smoothing
the windfall over
remaining lifetime.
(a) one time splash:
MPC = ΔY/(D-z).
For life expectancy
of 40 years, would
be MPC = .025.
(b) Permanent income
increase: MPC =
ΔY(R-z)/(D-z) = .6
to .8
Y
C’
C
|
R
0
age
|
D
22
Example of the Life Cycle Model at Work:
• How would the consumption and saving of people with volatile or
stable income streams look?
• See figure for Internet Entrepreneur and Yale Professor.
23
Major result of LCM: consumption smoothing
eLove.com
Professor
C of both!
age
R
D
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Example of consumption smoothing: the 2008 tax rebate
Changes in C, DY, and S
800
600
C
DY
S
Estimated MPC= 0.25 (+0.04)
400
200
0
-200
-400
06M01
06M07
07M01
07M07
08M01
08M07
25
Vector auto-regressions (VAR)
Nobel prize in Economics for 2011 won by Chris Sims (Princeton) in
part for development of VAR technique.
Vector autoregression (VAR) is a statistical model used to capture the
linear interdependencies among multiple time series (vector Yt ):
Yt = A0 + A1Yt-1 + A2Yt-2 + A2Yt-2 + et
Sims emphasized it as “theory-free estimation.”
Example of short run MPC using VAR:
MPC = 0.16 ( + 0.04)
Smaller than other estimates because of autoregressive properties.
Summary: Econometric estimates of short-run MPC > life-cycle
theory.
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How about a nice car?
• What is your favorite car?
• What do you have?
• Why not smooth consumption to get your favorite car?
Liquidity constraints
• Case of Yale students where income growing rapidly.
• Here consumption is limited by borrowing constraint.
• In class: A picture of the model with liquidity constraints.
• Is this reason for MPC higher than life cycle prediction?
(Partially, but cannot explain response of non-constrained
consumers)
27
Behavioral economics
Basic idea: That people are not optimizers:
- Draw upon behavioral psychology: anchoring, loss aversion,
hyperbolic discounting, and similar phenomena
Real-world examples for all of us:
- Procrastination (as in procrastinate saving for the future).
- Addictive substances (shop until you drop)
Why is it “behavioral”? Because lead to inconsistent
decisions that are regretted later
- cheating, hangovers, unwanted pregnancies, jail
Examples from macroeconomics:
- MPC too high; low savings for retirement; subprime mortgages;
sticky housing prices; too high discount rate in energy use
28
Press button
for Econ 122
29
Elevator quiz
1. Look back to your answer from Monday on how you
would allocate your $1000 unexpected generous gift.
2. Explain how this decision fits into the economics of
consumption that we discussed in class and in the
textbook.
3. We will discuss our answers when you are done.
4. Then hand it in at the end of class.
30
Taxes, interest rates, and saving
“Raise the tax on the returns for saving, and people will
save less. We can argue the magnitude, but to argue that
saving does not respond at all is simply to argue that
incentives and disincentives are irrelevant to behavior.”
“Of Course Higher Taxes Slow Growth,” J.D. Foster and
Curtis Dubay
31
Impact of higher interest rates on saving
Important question for economics
A common theme:
- The country need to reduce taxes to increase savings
- Examples: lower marginal tax rates, lower capital gains
taxes, move to consumption taxes,
- Mechanism: ra = rb (1-τ)
What is the economic theory of this?
What is econometric evidence on this?
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C2
CASE I:
Higher interest rate
leads to lower
saving because
income effect
outweighs
substitution effect.
E**
C 2*
[Pension example]
E*
C 1* C 1* *
Y1
C1
C2
CASE II:
Opposite case:
higher r increases
savings as
substitution effect
dominates
E**
C 2*
E*
C 1* *
C 1*
C1
If we estimate the impact of changes in interest rates on
consumption, we get paradoxical case (δs/δr < 0):
Dependent Variable: LOG(GCQ)
Method: Least Squares
Sample (adjusted): 1960Q1 2011Q2
Variable
Constant
Ln (Yd)
LOG(Real wealth)
Real 10 year T rate
R-squared
Adjusted R-squared
S.E. of regression
Coefficient
Std. Error
t-Statistic
-0.456
0.812
0.193
0.000102
0.016
0.011
0.010
0.000
-27.0
71.1
18.9
0.22
0.999
0.999
0.012
Mean dependent var
S.D. dependent var
Akaike info criterion
Prob.
0.0000
0.0000
0.0000
0.8204
8.40
0.49
-5.93
The impact is essentially zero (and not robust to changes in
specifications, samples, etc.)
35
Econometric savings schedule: S(r)
10
8
Real interest rate
6
4
2
0
-2
-4
-6
0
2
4
6
8
10
12
14
Savings rate
36
37
What is the Effect of Stock Market
Booms and Busts on Consumption?
Price-earnings ratios, US
40
Roaring 20s
50
30
10
Roading 90s
20
0
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
38
And the housing price collapse…
300
Las Vegas, Miami
250
200
150
100
Detroit
50
88
90
Case-Shiller
92
94
96
98
00
02
04
06
08
10
39
Long-term housing trends
Real price of housing (Case-Shiller index)
250
Home Prices: estimate
as of January 2009
200
150
100
50
0
1880
1900
Source: Shiller
1920
1940
1960
Year
1980
2000
2020
40
The Wealth Effect on Consumption
Wealth effects:
– Examples: Suppose the alumna gives you $1000. Or the housing
market collapsed as after 2006? What would be the effect on C?
Life cycle model predicts that initial wealth (or surprise inheritances)
would be spread over life cycle.
• Intuition: an inheritance is just like an income splash.
So the augmented life cycle model is
p
Ct = β0 + β1 Y t + β2 Wt
p
where Y t is permanent or expected labor income and Wt is
wealth.
41
Consider a person in the middle of the life cycle
C, Y, S
Initial wealth (from saving)
Y
C
|
Age = z
0
R
age
|
D
42
Now a wealth shock
C, Y, S
Wealth shock
(falling house
prices)
Y
C
C’
|
Age = z
0
R
age
|
D
43
The stock market, the housing market, and consumption
• Economists think that the bursting of housing bubble was a
major source of current recession (US, Spain, ….)
• Reasons? Decline in consumption (today) and investment
(later)
• Rationale: the “wealth effect” on consumption
• Analysis in the life-cycle model:
p
– In augmented life-cycle model Ct = β0 + β1 Y t + β2 Wt
standard estimates are that β2 = .03 - .06 (example in a minute)
– Effect in the “Roaring 90s” and the housing crash today.
• This is often called “deleveraging” but a better description is a
“wealth effect” (leverage is a balance sheet phenomenon).
44
Regression
Dependent Variable: Real consumption expenditures
Method: Least Squares with AR correction
Sample: 1960.1 2011.2
Variable
Coefficient
Std. Error
P
Real Disposable income
0.73
0.025
.0000
Real wealth
0.035
0.0041
.0000
R-squared
0.9997
45
Wealth and Consumption through Two Bubbles
500
12,000
Financial
crisis
Tech
bubble
400
8,000
300
4,000
200
0
100
-4,000
0
-8,000
-100
-12,000
Change in consumption (left scale)
Change in new worth (right scale)
-200
-16,000
-300
-20,000
98
99
00
01
02
03
04
05
06
07
08
09
10
11
46
Loss of wealth and savings rate increase
6.8
7
Savings rate (-->)
6.4
6
6.0
5
5.6
4
5.2
3
4.8
2
4.4
1
2005
2006
2007
2008
2009
2010
Personal savings rate
Wealth/income
Wealth/income (<--)
2011
47
Key ideas on consumption and saving
1.
2.
3.
4.
Consumption derived from consumer maximization
Pure model leads to consumption smoothing
All kinds of important predictions
But pure model has “anomolies” and shows too large a
short-run MPC relative to theory
5. Reasons are probably liquidity constraints and
behavioral frictions.
6. Note the impact of interest rates and taxes on savings.
7. Remember the wealth effect
48