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Economics 122. InvestmentFall 2009

PET Scan of PIB molecule

NOAA’s weather supercomputer

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The Macroeconomics of Investment

Capital• Produced, durable, used for further production• Examples:

– tangibles (structures, equipment)– intangibles (software, patents)

Basic role of investment in macro• Short run: most volatile part of aggregate demand

– Recall decline of I in Great Depression• Long run: key determinant of growth of potential output

and major way that governments affect economic growth.

Investment decline in the Depression

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Real GDP (1929 = 1)Real I (1929 = 1)

Note on data: Very convenient place is “FRED”: http://research.stlouisfed.org/fred2

Investment-GDP ratio

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Shaded areas are NBER recessions

Investment/GDP (nominal $)

Today’s housing crunch

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Housing Starts / Population

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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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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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Isoquants with fixed capital-output ratio

L

K

fixed K/L ratio in accelerator

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Graph shows relation between investment and change in output (accelerator model)

I

δK

δK+vΔY

ΔY

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2. 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 theoryStart 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

K

fixed K/L ratio in accelerator

Cobb-Douglas in neoclassical

- fixed K/L corresponds to accelerator model - variable proportions (such as Cobb-Douglas)

corresponds to neoclassical model

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Investment Criteria

There are a number of return concepts.– present value (V0 today)

– internal rate of return (i per year)

– rental price of capital ($ per apartment per month)– cost of capital (usually, “user cost of capita”)

• Central concept in macro theories of investment• Def. Cost of renting capital for one period• Appropriate for perfect capital market.• Estimate as imputed in most circumstances because firms

own capital (also for housing in NIPA)

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Formula for cost of capital

u ≈ (1+τ) pK [r + δ]

whereu = user cost of capitalpK = price of capital goodr = real interest rateδ = depreciation rateτ = 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. 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) + u20,000 = 18,000/(1.05) + u

Solve for break-even (competitive-market) rental:u = 20,000 – 18,000/1.05

= 20,000 – 17,143 = 2857≈ pK (r+ δ) = 20,000(.15) = 3,000

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This is a slightly more realistic version that has both debt and equity capital.

Cost of capital with no taxes and P = 1

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Real cost of capital (% per year)

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Real cost of capital (% per year)

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Basic approach in the neoclassical model

We start with a production function; and then derive the demand for capital.

Demand for capital:

Assume a Cobb-Douglas production functionY = A Kβ L1-β

Then derive the value of MPK:

p MPK = p ∂Y/∂K=p βA Kβ-1 L1-β = pβY/K

Finally, the firm sets its desired capital stock (K*) by equating the cost of capital to the MPK:

u =p∂Y/∂K=pβY/K

Now normalize prices = 1 for simplicity and ignore taxes:

u = (r+δ) = βY/K

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This yields a demand for capital (K*):

K* = βY/(r+δ)

Note the various components of the demand for capital– output (like accelerator)– interest rate (r)– depreciation rate (δ)– With taxes: K* = βY/[(r+δ) (1+τ)]

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- Note that the impact of interest rates on investment is powerful but depends importantly on the lifetime of the capital:

- Where biggest impacts? Housing- Where smallest? Computers and inventories

User cost of capital Change in userDepreci- (per $ capital) cost with increase

Lifetimeation rateat real interest rate: in r fromInvestment item (years) δ 2% 4% 2% to 4%

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%

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From demand for capital to demand for investment

• How do we get investment demand (or equilibrium investment)?

• Generally, go from demand for capital to demand for investment

• Several approaches:- Costs of adjustment of investment

- Capacity in the capital goods industry (Boeing aircraft)- Construction lags (power plants)

- Internal funds constraint

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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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The collapse in shipping prices on dry cargo

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A glut of cargo ships

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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 scrappedHow 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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Rental of ships

Number of ships

Demand for shipping

S2009

Current ship rental

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Rental of ships

Number of ships

Demand for shipping

Sfuture

“cost of capital” for new ships

S2009

Current ship rental

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Q

I/K

1

δ

I/K = f (Q)

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Housing bubble:1.Note that Q rose about 50 percent from mid-1990s.2. Note huge decline in residential construction (I)

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Q of housingResidential construction (2005 $)

Q (left scale)

I housing (right scale)

Investment ratio and Q for housing

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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 stock prices

• fiscal policy through things like depreciation policy and investment tax credits.