Download Economic 157b - Yale University

Economics 122.
Investment
Fall 2012
NOAA’s weather supercomputer
PET Scan of PIB molecule
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The Macroeconomics of Investment
Capital
• Produced, durable, used for further production
• Examples:
– tangibles (structures, equipment)
– intangibles (software, human capital)
Basic role of investment in macro
• Short run: most volatile part of aggregate demand
– See next slides
• Long run: key determinant of growth of potential output and major
way that governments affect economic growth
– In growth theory
2
Gross Investment, US, 2011
Sector
Counted as investment in National Accounts
2010
% of GDP
GROSS DOMESTIC PRODUCT
Total, investment type
Residential/Household
Durable goods
Residential structures
Gross busines domestic investment
Fixed investment
Structures
Equipment and software
Change in private inventories
Government gross investment
Federal
National defense
Nondefense
State and local
Other investment-type private spending
Health
Private education
Research and development
15,076
100.0
1,485
39.6
9.9
1,516
10.1
480
3.2
2,484
16.5
1,146
339
1,480
405
1,075
37
National accounts
include only a
small part of
“investment-like”
spending: 12% of
40%.
109
52
320
1,752
252
480
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Investment decline in the Depression
1.4
Real GDP (1929 = 1)
Real I (1929 = 1)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
29
30
31
32
33
34
35
36
37
38
39
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Note on data: Very convenient place is “FRED”: http://research.stlouisfed.org/fred2
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Investment in the Great Recession
.20
.18
.16
.14
.12
.10
60
65
70
75
80
85
90
95
This is only gross domestic private investment.
00
05
10
5
Today’s housing depression
Housing starts/population
.014
.012
.010
.008
.006
.004
.002
.000
1960
1970
1980
1990
2000
2010
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The major theories of investment
1. Accelerator theory: states that investment is a function of
change in output
2. Neoclassical theory: Desired capital stock a function of output
and cost of capital
3. Q theory: Investment a function of Tobin’s Q (Q =ratio of
market value of K to replacement cost)
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Summary of Neoclassical Theory of Investment
• Define the user or rental cost of capital as uc = (r+δ) PK as implicit
rental on capital.
• Assume that Y is given by short-run aggregate demand
• Cobb-Douglas for simplicity and pK = p = 1.
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Summary of Neoclassical Theory of Investment
• Define the user or rental cost of capital as uc = (r+δ) PK as implicit
rental on capital.
• Assume that Y is given by short-run aggregate demand
• Cobb-Douglas for simplicity and pK = p = 1.
Y  AK  L1
Profit maximization leads to MPK = user cost of capital.
uc  ( r   )  MPK  Y / K  Y / K
K  Y / ( r   )
In steady state, I  ( g   ) K , so
I  ( g   )Y / ( r   )
• So the demand for investment is inverse to the user cost of capital, and
therefore also to the interest rate.
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Now the details….
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1. Accelerator Theory
- Oldest and simplest theory is the accelerator model.
- Here, the idea is that there is a target capital-output ratio
K* = v Y
- Hence the desired change in investment is equal to the change
in output (I is gross investment):
I* = ΔK* + δK = v Δ Y + δK
-
The actual investment might differ from the desired, but this
is a simple and useful model. It shows why there is a close
relationship between investment and output change.
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Accelerator captures basic elements
1.10
.24
1.08
.22
1.06
.20
1.04
.18
1.02
.16
1.00
.14
0.98
.12
One-year change in real GDP
Investment/GDP
0.96
.10
0.94
.08
60
65
70
75
80
85
90
95
00
05
10
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What is missing from accelerator?
Financial markets!
1. Why does investment go down with tight money, high
interest rates, and high risk premiums? (Neoclassical theory)
2. Why does investment decline when the market price of
capital (e.g., housing) goes down? (Q theory)
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Housing and interest rates with tight money
1981-1983
16
Mortgage interest rate
15
14
13
12
11
.003
.004
.005
.006
.007
.008
.009
Housing starts/population
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Neoclassical Theory
The mainstream theory is the neoclassical model.
- This is closely related to the accelerator model.
- The difference is that in the neoclassical model there is a
variable capital-output ratio
- Hence, K/Y depends upon relative factor prices, and in
particular upon the user cost of capital and taxes.
Using standard production theory
Start with aggregate production function:
Y = F(K,L)
Next figure shows the difference of the accelerator and
neoclassical models for an isoquant.
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Isoquants with fixed capital-output ratio v.
variable proportions
L
fixed K/L ratio in accelerator
Cobb-Douglas in neoclassical
K
- fixed K/L corresponds to accelerator model
- variable proportions (such as Cobb-Douglas)
corresponds to neoclassical model
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Investment Criteria
– User cost of capital, uc
•
•
•
•
Central concept in macro theories of investment
Definition. Cost of renting capital for one period
Appropriate for perfect capital market where Q=1
Estimate as imputed in most circumstances because firms own
capital (also for housing in NIPA)
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Formula for cost of capital
uc ≈ (1+τ) pK [r + δ]
where
u = user cost of capital
pK = price of capital good
r = real interest rate
δ = depreciation rate
τ = effective rate of tax (or subsidy when negative) on capital
goods
Linkage to policy:
- through real interest rate
- through taxation of capital
In practice, u is complicated to measure; off to B School!
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Derivation and example:
• Buy a car, rent it for one period, and then sell at the end.
No inflation or taxes. Real interest rate = r = .05.
• Pay $20,000 sell for 20,000(1-.1) = $18,000; collect rent u.
• What cost of capital (u) would just break even?
when pK = pK (1- δ)/(1+r) + u
20,000 = 18,000/(1.05) + u
uc = 20,000 – 18,000/1.05
= 20,000 – 17,143 = 2857
≈ pK (r+ δ) = 20,000(.15) = 3,000
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Cost of capital with no taxes and P = 1
This is a
slightly
more
realistic
version that
has both
debt and
equity
capital.
Real cost of capital (% per year)
14
12
10
8
6
4
2
0
60
65
70
75
80
85
90
95
00
05
10
Equal 0.3 x real bond rate + 0.7 x earnings-price ratio
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Derivation of Basic Theory
• Define the user or rental cost of capital as uc = (r+δ) PK as implicit
rental on capital.
• Assume that Y is given by short-run aggregate demand
• Cobb-Douglas for simplicity and pK = p = 1.
Y  AK  L1
Profit maximization leads to MPK = user cost of capital.
uc  ( r   )  MPK  Y / K  Y / K
K  Y / ( r   )
In steady state, I  ( g   ) K , so
I  ( g   )Y / ( r   )
• So the demand for investment is inverse to the user cost of capital, and
therefore also to the interest rate.
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- Note that the impact of interest rates on investment is
powerful but depends importantly on the lifetime of the
capital:
User cost of capital Change in user
Depreci- (per $ capital) cost with increase
Lifetime ation rate at real interest rate:
in r from
2% to 4%
Investment item (years)
2%
4%
δ
Structures
50
0.02
4%
6%
50.0%
Major
equipment
10
0.10
12%
14%
16.7%
Computers
3
0.40
42%
44%
4.8%
Inventories
1
1.00
102%
104%
2.0%
- Where biggest impacts? Housing
- Where smallest? Computers and inventories
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From demand for capital to demand for investment
• What happens to demand for investment out of equilibrium?
• Generally, go from demand for capital to demand for
investment
• Several approaches:
- Costs of adjustment of investment (standard in modern macro)
- Capacity in the capital goods industry (Boeing aircraft)
- Construction lags (power plants)
- Internal funds constraint
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Now a major puzzle for neoclassical model:
Housing and interest rates
Housing price crash
Tight money
2006 - 2010
16
6.8
15
6.4
Mortgage interest rate
Mortgage interest rate
1981-1983
14
13
5.6
12
5.2
11
.003
4.8
.001
.004
.005
.006
.007
Housing starts/population
.008
.009
?
6.0
.002
.003
.004
.005
.006
.007
.008
Housing starts/population
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A glut of cargo ships in 2009
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Airplanes in mothballs (Tucson, Arizona)
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More formally:
Q = (market value of K)/(replacement cost of K)
Example:
- Cargo ships are selling for a Q of 0.25
- E.g., cost of production is $20 million, but ships sell for $5 million
- How is this possible?
• Inelastic supply and high demand for cargo → low rentals
• PV of ships is low.
• Therefore, little to no shipbuilding, and the stock gradually
depreciates or is scrapped
How does Q affect investment?
- Because Q < 1, shipping firms buy old ships rather than build new
ones
- This depresses investment.
- Therefore I/K = f(Q), f’(Q) > 0.
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3. Q theory of investment
Idea here is that investment is determined by relationship between the
value of firms or houses and the cost of new or replacement capital.
Keynes:
“The daily revaluations of the Stock Exchange, though they are
primarily made to facilitate transfers of old investments between
one individual and another, inevitably exert a decisive influence on
the rate of current investment. For there is no sense in building up a
new enterprise at a cost greater than that at which a similar existing
enterprise can be purchased; whilst there is an inducement to spend
on a new project what may seem an extravagant sum, if it can be
floated off on the Stock Exchange at an immediate profit.”
Tobin:
"It is common sense that the incentive to make new capital investments
is high when the securities giving title to their future earnings can
be sold for more than the investments cost, i.e., when q exceeds
one."
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Investment and Q
Q
I/K = f (Q)
1
I/K
δ
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Housing market collapse, 2006 – 2012+
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Investment ratio and Q for housing
1.7
900
I housing (right scale)
1.6
1.5
Housing bubble:
800 1.Note that Q rose
about 50 percent
from mid-1990s.
700
2. Note huge
decline in
600 residential
construction (I)
Q of housing
Residential construction (2005 $)
1.4
1.3
Q (left scale)
1.2
1.1
500
1.0
400
0.9
0.8
88
90
92
94
96
98
00
02
04
06
08
10
300
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Housing Q and housing starts, 2006:m1 – 2010:m7
Housing Q (3 month moving average)
1.4
1.3
1.2
1.1
1.0
0.9
0.8
400
800
1,200
1,600
2,000
2,400
Housing starts (3 month moving average)
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Summary of investment theory
1.. The major components of investment are residential, business plant
and equipment, software, and inventories.
2. These are among the most volatile components of output in the short
run.
3. In equilibrium, demand for capital determined where the cost of
capital equals the marginal productivity of capital.
4. The major theories are the accelerator theory, the neoclassical theory,
and the Q theory. These apply differently in different sectors.
5. Economic policy affects investment through both monetary and
fiscal policy:
• monetary policy through real interest rate and unconventional
policies (buying mortgage backed securities)
• fiscal policy through things like depreciation policy and
investment tax credits.
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