Investment

Anthony Murphy

Nuffield Collegeanthony.murphy@nuffield.ox.ac.uk

Why Does Investment Matter?

• On the demand side, investment is very volatile.• Investment spending is a primary link thru’ which

interest rates, and therefore monetary policy, affect the economy.

• Tax policies affecting investment are an important element of fiscal policy.

• On the supply side, long run growth is related to the size of the capital stock, which is just cumulated investment.

Classifications of Investment Etc.• Gross fixed capital formation plus changes in

inventories.• Gross investment – depreciation = net investment

• Business investment plus residential investment plus inventories

• What about R&D, software and other intangibles?• Private v. public investment e.g. infrastructure. • Should schooling count as investment?

1t t tK I K

Neo-Classical Investment Modelà la Jorgenson (e.g. 1979)

• Risk neutral firm (Fisher separation & Modigliani-Miller theorems) maximises present value of profits.

• Price taker if competitive firm.• Set out equations and derive demand for flow of

investment from demand for desired capital stock.

• FOC’s: MPL = w (real wage) & MPK = c = pI.(r + δ - ΔpI/pI) (real rental / cost of capital).

The Real Rental / Cost of Capital

Real rental / cost of capital c = pI.(r + δ - ΔpI/pI) is the appropriate price of a capital good.

• pI = real price of capital good;

• r = real interest rate;• δ = depreciation rate;

• ΔpI/pI = rate of appreciation of capital goods relative to output prices; assume approx zero.

Some Comparative Statics

Can look at effects of changes in:

• Technology gains;

• Real interest rates;

• Tax incentives.

Cobb-Douglas example:

• Y = ALαK1-αexp(γt) and MPK= (1-α)Y/K.

• K*= (1-α)Y/c.

Marginal productivity of capital

Output

c=slope

MPK

cK

K

K

Marginal cost of capitalC

Y=F K( )

K

K

Fig. 6.13

Output

Capital stock

Capital stock

Optimalcapital stock

Technological progress makes more output possible with the same capital stock. Desired capital stock increases.

Marginal productivity of capital

OutputcK

c=slope

K

K

MPK´

New

C

Old

MPK

K

K

Fig. 6.14

Output

Capital stock

Capital stock

Problems with Baseline Model

• Instantaneous speed of adjustment of capital stock unrealistic.

• No role for future expectations (apart from appreciation term ΔpI/pI).

• Note: The so called “accelerator model”, It = ΔKt + δKt-1= νΔYt holds when ct is approx. constant (i.e. when rt and pIt are approx. constant) in the long run or when credit constraints bind.

• Called accelerator model ‘cos estimated ν between 2 and 3.

Adding Dynamics• Add ad hoc dynamics e.g. simple partial

adjustment model:

• Add quadratic adjustment costs and rational expectations (à la Sargent).

• Now expectations of all future prices etc. matter.

• No free lunch! Need to model expectations. • Hard to model realistically.

*1 1( )t t t t tK I K K K

Tobin’s q, the Stock Market and Investment

• Share prices can be thought of as market’s best estimate of value of present and future profits, so they capture future expectations.

• Aside: Stock markets are forward looking. What about “irrational exuberance” of dot-com bubbles etc.?

• Tobin (1969) suggested that the rate of investment is related to q = market value of installed capital / replacement cost of installed capital, with q = 1 in equilibrium.

The q-theory of investment

Tobin’s q

Inve

stm

ent

I/K

01

Fig. 6.15

The Appeal of Tobin’s q• Simple model - (I/K)t is increasing in qt.• Intuitively appealing but no formal model.• Relationship to previous models? Negative interest

rate effects work thru’ stock market valuation. Ditto effects of technology gains and tax changes.

• In addition, q should take account of uncertainty, growth in future demand, announcement effects etc.

• Tobin’s q is like a sufficient statistic - given q, other information (both observed and unobserved) does not matter.

Micro Foundations of Tobin’s q• Can derive a Tobin’s q type model of investment in

an inter-temporal setting with costs of installing investment e.g.

• Installation costs explain why q is not always equal to one. These additional costs slow the adjustment to the long run.

• Diagram of MCI and MPK..

• However, in this set up, investment depends on marginal q, as opposed to the average q proposed by Tobin.

2 212 1( / )t t t t tK I I K K

Micro Foundations of Tobin’s q (Cont’d)

• Hayashi (1982) et. al. showed that marginal q equals average q when:- The firm is a price taker;- The production function displays constant returns to scale; - Adjustment costs, per unit of I only depend on the ratio of I/K.

• Otherwise, average q will not completely capture expectations even if the stock market correctly values future profits.

Tobin’s q=1 in a world of no adjustment costs

(a)

Pre

sent

val

ue o

f M

PK

,co

st o

f ca

pita

l

1

I K( )

MPK1

MPK=Marginal return of new investment

C

If there were no costs of adjustment, the present value of the marginal cost of capital would be independent of the investment rate.

Note if there were no depreciation, the investment rate, I/K, = K/K, the rate of change of the capital stock.

Fig. 6.17

Investment rate (I/K)

Tobin’s q when adjustment costs are significant

(a)

Pre

sent

val

ue o

f M

PK

,co

st o

f ca

pita

l

1

I K( )I K( )

1q

Marginal cost of investment

MPK1

C

However the faster we try to install new capital, the more it adds to the cost of that capital. “Haste makes waste.” Hence the upward slope of the marginal cost of investment with respect to the investment rate.

Fig. 6.17

Investment rate (I/K)

MPK=Marginal return of new investment

A

Tobin’s q

(b)

Pre

sent

val

ue o

f M

PK

,co

st o

f ca

pita

l

A

1

1I K( )

1q

Marginal cost of investment

MPK1MPK2

2I K( )

2q B

With the investment rate corresponding to the rate at point A, in the following period there will be more capital and a lower MPK.

The investment rate next period will fall too (as will Tobin’s q), ultimately heading toward a value of unity and no more investment.

Fig. 6.17

Investment rate (I/K)

MPK=Marginal return of new investment

Tobin’s q In Practise • Hayashi (1982) estimated a simple investment

equation on US data for 1953 to 1976:

(I/K)t= const + 0.043qt

• R2 = 0.46, DW = 0.43 and the t stat on average qt is about 5.

• Problematic equation. Why?• Adding some dynamics helps a bit.• However, other quantity type variables matter (so q is

not really akin to a sufficient statistic).• Lower correlation between (I/K)t and qt in recent years.

Empirics (Cont’d)• There are a large no. of micro (panel data) and

macro (time series) studies of the q theory of investment.

• Macro studies frequently find:- Price effects: a modest role for capital costs (q and/or its components including the real interest rate);- Quantity effects: a substantial role for output or cash flow variables (since, in the UK and US, a lot of investment is financed from retained earnings).

Lots of Ongoing Research

• The effect of taxation on the cost of capital and q, and hence investment (e.g. event studies);

• The “excessive” lumpiness of investment at the firm level;

• The sensitivity of investment to cash flow and profits, which may imply a high incidence of credit constraints;

• The consistency of observed high hurdle rates for investment with the option value of waiting;

• The determinants of international investment e.g. FDI.

Overview of Investment

• Investment is the most volatile component of aggregate demand.

• The demand for capital depends on real interest rates, current and expected future output and taxes.

• Investment reflects the adjustment of the existing capital stock to the current demand for capital.

• Investment is a primary link from monetary policy to aggregate demand.