revised investment

7/29/2019 Revised Investment

1/22

InvestmentAnthony Murphy

Nuffield [email protected]


2/22

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 importantelement offiscal policy.

On the supply side, long run growth is related tothe size of the capital stock, which is justcumulated investment.


3/22

Classifications of Investment Etc.

Gross fixed capital formation plus changes ininventories.

Gross investmentdepreciation = net investment

Business investment plus residential investmentplus 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


4/22

Neo-Classical Investment Model

la Jorgenson (e.g. 1979) Risk neutral firm (Fisher separation & Modigliani-

Miller theorems) maximises present value ofprofits.

Price taker if competitive firm.

Set out equations and derive demand for flow ofinvestment from demand for desired capital

stock. FOCs:MPL = w (real wage) &MPK= c = pI.(r

+ -pI/pI) (real rental / cost of capital).


5/22

The Real Rental / Cost of Capital

Real rental / cost of capital c = pI.(r + -pI/pI) is

the appropriate price of a capital good.

pI= real price of capital good; r= real interest rate;

= depreciation rate;

pI/pI= rate of appreciation of capital goodsrelative to output prices; assume approx zero.


6/22

Some Comparative Statics

Can look at effects of changes in:

Technology gains;

Real interest rates;

Tax incentives.

Cobb-Douglas example: Y = ALK1-exp(t) andMPK=(1-)Y/K.

K*= (1-)Y/c.


7/22

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

Optimal

capital stock


8/22

Technological

progress makes

more output

possible with thesame capital

stock. Desired

capital stock

increases.

Marginal productivity

of capital

Output

cK

c=slope

K

K

MPK

New

C

Old

MPK

K

K

Fig. 6.14

Output

Capital stock

Capital stock


9/22

Problems with Baseline Model

Instantaneous speed of adjustment of capitalstock unrealistic.

No role for future expectations (apart fromappreciation term pI/pI).

Note: The so called accelerator model,It=Kt+ Kt-1= Ytholds when ctis approx. constant

(i.e. when rtandpItare approx. constant) in thelong run or when credit constraints bind.

Called accelerator model cos estimated between2 and 3.


10/22

Adding Dynamics

Add ad hoc dynamics e.g. simple partialadjustment model:

Add quadratic adjustment costs and rationalexpectations ( 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 t K I K K K


11/22

Tobins q, the Stock Market and

Investment Share prices can be thought of as markets best

estimate of value of present and future profits, sothey capture future expectations.

Aside: Stock markets are forward looking. Whatabout irrational exuberance of dot-combubbles etc.?

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


12/22

The q-theory of investment

Tobins q

InvestmentI/K

01

Fig. 6.15


13/22

The Appeal of Tobins q

Simple model - (I/K)tis increasing in qt. Intuitively appealing but no formal model.

Relationship to previous models? Negativeinterest rate effects work thru stock market

valuation. Ditto effects of technology gains andtax changes.

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

etc. Tobins q is like a sufficient statistic - given q,

other information (both observed and unobserved)does not matter.


14/22

Micro Foundations of Tobins q

Can derive a Tobins q type model of investmentin an inter-temporal setting with costs ofinstalling investment e.g.

Installation costs explain why q is not alwaysequal to one. These additional costs slow theadjustment to the long run.

Diagram ofMCIandMPK.. However, in this set up, investment depends on

marginal q, as opposed to the average q proposedby Tobin.

2 212

1

( / )t t t t t

K I I K K


15/22

Micro Foundations of

Tobins q (Contd) Hayashi (1982) et. al. showed that marginal q

equals average q when:

- The firm is a price taker;- The production function displays constantreturns 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 correctlyvalues future profits.

Fi 6 17


16/22

Tobins q=1 in a world of no adjustment costs

(a)

Presentval

ueofMPK,

costof

capital

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 theinvestment rate.

Note if there were nodepreciation, the investment

rate, I/K, = K/K, the rate of

change of the capital stock.

Fig. 6.17

Investment rate (I/K)

Fi 6 17


17/22

Tobins qwhen adjustment costs are significant

(a)

Presentval

ueofMPK,

costof

capital

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



A

Fi 6 17


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Tobins q

(b)

Presentval

ueofMPK,

costof

capital

A

1

1I K( )

1q

Marginal cost

of investment

MPK1MPK2

2I K( )

2q B

With the investment ratecorresponding to the rate

at point A, in the following

period there will be more

capital and a lowerMPK.

The investment rate next

period will fall too (as will

Tobins q), ultimately

heading toward a value ofunity and no more

investment.

Fig. 6.17




19/22

Tobins q In Practise

Hayashi (1982) estimated a simple investmentequation 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 qtis about 5.

Problematic equation. Why?

Adding some dynamics helps a bit.

However, other quantity type variables matter (soq is not really akin to a sufficient statistic).

Lower correlation between (I/K)tand qtin recentyears.


20/22

Empirics (Contd)

There are a large no. ofmicro (panel data) andmacro (time series) studies of the q theory ofinvestment.

Macro studies frequently find:

- Price effects: a modest role for capital costs (qand/or its components including the real interestrate);

- Quantity effects: a substantial role for output

or cash flow variables (since, in the UK and US, alot of investment is financed from retainedearnings).


21/22

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 thefirm level;

The sensitivity of investment to cash flow andprofits, which may imply a high incidence ofcredit constraints;

The consistency of observed high hurdle ratesfor investment with the option value of waiting;

The determinants of international investment e.g.FDI.


22/22

Overview of Investment

Investment is the most volatile component ofaggregate demand.

The demand for capital depends on real interestrates, current and expected future output andtaxes.

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.

revised investment

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