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
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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
1,146
339
1,480
405
1,075
37
109
52
320
15,076 100.0
1,485
39.6
9.9
1,516 10.1
480 3.2
National accounts include only a small part of
“investment-like” spending: 12% of
40%.
Other investment-type private spending
Health 1,752
Private education
Research and development
252
480
2,484 16.5
3

Investment decline in the Depression
1.4
1.2
1.0
0.8
0.6
Real GDP (1929 = 1)
Real I (1929 = 1)
0.4
0.2
0.0
29 30 31 32 33 34 35 36 37 38 39 40
Note on data: Very convenient place is “FRED”: http://research.stlouisfed.org/fred2 4

Investment in the Great Recession
.20
.18
.16
.14
.12
.10
60 65 70 75 80 85 90 95 00 05 10
This is only gross domestic private investment.
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) P K as implicit rental on capital.
• Assume that Y is given by short-run aggregate demand
• Cobb-Douglas for simplicity and p K = p = 1.
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Summary of Neoclassical Theory of Investment
• Define the user or rental cost of capital as uc = (r+δ) P K as implicit rental on capital.
• Assume that Y is given by short-run aggregate demand
• Cobb-Douglas for simplicity and p K = p = 1.
Y

AK L
1
 
Profit maximization leads to MPK = user cost of capital.
uc ( r

)

MPK
 
Y /
  
/
K
 
Y / ( r
 
)
In steady state, I

( g
 
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
1.08
1.06
1.04
1.02
1.00
0.98
0.96
0.94
60 65 70 75
One-year change in real GDP
Investment/GDP
80 85 90 95 00 05 10
.24
.22
.20
.18
.16
.14
.12
.10
.08
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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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1981-1983
16
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) p K [r + δ] where u = user cost of capital p K = 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 p K = p K (1- δ)/(1+r) + u
20,000 = 18,000/(1.05) + u uc = 20,000 – 18,000/1.05
= 20,000 – 17,143 = 2857
≈ p K (r+ δ) = 20,000(.15) = 3,000
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Cost of capital with no taxes and P = 1
Real cost of capital (% per year)
14
12
10
8
6
4
2
0
60 65 70 75 80 85 90
Equal 0.3 x real bond rate + 0.7 x earnings-price ratio
95 00 05 10
This is a slightly more realistic version that has both debt and equity capital.
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Derivation of Basic Theory
• Define the user or rental cost of capital as uc = (r+δ) P K as implicit rental on capital.
• Assume that Y is given by short-run aggregate demand
• Cobb-Douglas for simplicity and p K = p = 1.
Y

AK L
1
 
Profit maximization leads to MPK = user cost of capital.
uc ( r

)

MPK
 
Y /
  
/
K
 
Y / ( r
 
)
In steady state, I

( g
 
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:
Investment item (years)
δ
User cost of capital Change in user
Depreci- (per $ capital) cost with increase
Lifetime ation rate at real interest rate: in r from
2% 4% 2% to 4%
50
0.02
4% 6%
50.0% Structures
Major
equipment 10 12% 14%
Computers
3
0.10
0.40
42% 44%
16.7%
4.8%
Inventories
1
1.00
102% 104%
- Where biggest impacts? Housing
- Where smallest? Computers and inventories
2.0%
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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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Housing price crash
16
Tight money
1981-1983
6.8
2006 - 2010
15
14
13
12
11
.003
.004
.005
.006
.007
.008
.009
Housing starts/population
6.4
6.0
5.6
5.2
?
4.8
.001
.002
.003
.004
.005
.006
.007
.008
Housing starts/population
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A glut of cargo ships in 2009
25

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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1
Q
I/K = f (Q)
δ
I/K
29

Housing market collapse, 2006 – 2012+
30

1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
Investment ratio and Q for housing
I housing (right scale)
Q of housing
Residential construction (2005 $)
Q (left scale)
900
800
700
600
Housing bubble:
1.Note that Q rose about 50 percent from mid-1990s.
2. Note huge decline in residential construction (I)
500
400
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
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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