robert, hall - investment, interest rate and the effect of stabilazation policy

8/10/2019 Robert, Hall - Investment, Interest Rate and the Effect of Stabilazation Policy

1/61

ROBERT E. HALL

Massachusettsnstitute f Technology

Investment

I n t e r e s t

R a t e s

n d

t h

E f e c t s

o

Stabilization

o l i c i e s

THE RESPONSE of investment

xpenditure

o

changes

n interestrates is

at the heart

of any analysis

of

stabilization olicy.

The more

sensitive he

response, he more potent is monetarypolicy and the weaker s fiscal ex-

penditurepolicy. The stimulusof lower nterest ateson investment s one

of the

principal hannelsof monetary nfluence

n

virtually

all

macroeco-

nomic

theories.On the otherhand, he negative nfluence

f

higher

nterest

rates on investmentmay inhibit he macroeconomic ffect of expenditure

policy. The net effect of governmentexpenditureson gross national

producthas been and remains he single most important ource of dis-

agreement

over

stabilizationpolicy among economists.My purpose

here

is to examine he

empirical

videnceon

the

interest

esponse

of investment

withthehopeof narrowinghedisagreementbouttheeffectsof expendi-

ture and

monetarypolicies. Though he evidence s disappointingly eak,

it

does suggestthat

the

modem Keynesianview embodied n large-scale

macroeconometric

models-that

the

expendituremultiplier

s

around1.5

-and the

simple

monetarist

view-that

it

is essentiallyzero-are both

incorrect.

The

most

reasonablevalue lies

in the

middle, perhapsat

0.7.

Unfortunately,

he

evidence

s

probably

not

strongenough

o

convince he

firmadherent f

the

other wo positions.

Note: This research was supported by the National Science Foundation. I am

grateful to Dale W. Jorgenson and members of the Brookings panel for

helpful

comments.

61


2/61

62 BrookingsPapers on Economic Activity, 1:1977

The Empirical ssues

The interest esponseof

investment

depends undamentally n the sub-

stitutabilityof capital for other factors, and there seems to be general

agreement oday that factor substitution

an take place. In fact, the

uni-

tary-elasticity ropertyof the Cobb-Douglas

production unction s not

a

bad summary

f

the findinigs f more

generalstudies:

a

decline

of

1

per-

cent

in

theservicepriceof capitalraisesthe capital-output atio by

about

1

percent.But this is a long-run elationship,

nd t is much ess generally

agreed hatthe flow that bringsabout he change n the capital ntensity-

extra investment-is highlyresponsive

o changes n the price of capital

over the one- to three-yearhorizon of chief concern in stabilization.

Skeptics

about the

interest elasticity

of investmentpoint to

three con-

siderations hat cause the adjustment

n factor intensities o take place

slowly:

1. Lags in putting capital goods in place. It can take at least a year

to

design,order,build,

and nstall

capital

equipment fter

a

change

n

relative

factorpricesmakesnewequipment esirable.

2. The putty-clay hypothesis. Capital already in place cannot be

adapted

o

a

different apital ntensity;

actorproportions re

fixed at

the

time

the equipment s designed.Changes n factor

intensities

dictatedby

changes

n the

price

of

capital akeplace

only

as the old

capital

s

replaced.

3.

The

term

structure

of

interest rates. Stabilization policies

affect

the

short-term nterest

rate,

but

investment

respondsto the long-termrate.

Longratesrespond o shortrateswith

an

importantag.

Evidence rom a varietyof sources,

discussedbelow, seems

to

converge

on the

point

hat

ags

in the investment

rocess

are

ong enough

o limit the

immediate ffect of changes

n

the service

price of capitalon investment.

The

investment

akingplace in a given

year

is

largely

the

consequence

of

irrevocable ecisionsmade

in

earlier

years, and only a small fractioncan

be affected

by changes

n

that

year

n the financial

ttractiveness

f

invest-

ment.

This considerationmakes

expenditure

olicy stronger nd monetary

policy weaker than they would be

in

an economy with

more

flexibility

about

nvestmentn the shortrun.

Evidenceon the putty-clayhypothesis s muchmore ambiguous.The

paper containsa theoretical xpositionof the hypothesis hat emphasizes

the central

ssue

with

respect

o its

implications

or

investment

behavior:


3/61

Robert

E. Hall

63

Underputty-clay, irmsdo

not face an

economic

decisionabout

how much

output

to

produceon their existingcapitalequipment. f

there is such a

decision-for example, f

more output can be squeezed out

of existing

equipmentby operating t for longerhoursor addingmore

labor n other

ways-then the putty-clayhypothesis n its strictform is

wrong

and

the

response

of

investment o the service price of capital is

not just the

change

in

the factor

intensity of newly installed capacity

but involves

substitution etweennew

and old capitalas well. The paper

demonstrates

a

seriousproblem n the

majorexistingattempt o measure he influence

of

the putty-clay

phenomenon n the investmentequation. No definite

conclusion mergesabout he importance f putty-clay.

The questionof the

proper nterestrate for an investment

quation s

tackled only at the theoretical evel. The simple argument

hat capital is

long-lived

and

that

consequently he investmentdecisionshouldbe based

on the

long-termnterest

ate s examinedandconfirmed, utthis principle

does not imply that the

serviceprice of capitaldependson

the long rate.

Rather,the servicepriceemerges rom a comparisonof

investmentdeci-

sions made his yearon the

basisof this year's ong rate, and

those thatwill

be made nextyearon the basis of nextyear's ongrate.This comparison

involves

the

expectedchange n the long rate,

which

is measured

by

the

current hort

rate. As a matterof

theory,

t seems

quite

unambiguous

hat

an investment

heorybuilt around he

concept

of

a

service

price

of

capital

shoulduse the shortrate. The

prospect

or

empirical

onfirmation

f this

principleseems slight, in

view of the major difficultiesassociated

with

measurement f

the role of interest

atesof

any

kind.

An

Empirical

IS-LM

Framework

Generations

of

economists

have

been

taught

to

study

the

effects

of

monetary

and fiscal

policy

within Hicks'

IS-LM

framework. n the dia-

gram

below the

IS

curve traces

the combinations

f

the interest

rate and

real gross

national

product

hat

are

consistentwith the

expenditure

ide

of

the

economy.Higher

nterest atesare associatedwith

ower

evels of GNP

because

of the

negative

response

of investment.The

LM

curve describes

the alternative nterest rates and levels of GNP that clear the money

market.

Higher

evels

of

GNP

requirehigher

interestrates

to

clear

the

market

or

a

given exogenous

quantity

of

money.

Increased

government


4/61

64 BrookingsPapers onzEconomic Activity,

1:1977

expenditures

hift

the IS

curve

o the

right, ay

to

IS'.

Real

GNP rises from

Y to

Y'.

The

magnitude

f

the

increase

depends

on

the

relative

slopes

of

the two curves: t is large f theLM curve s flatandthe

IS

curve s steep

and

small

n

the

opposite

case.

An increased

money

supply

shifts

the

LM

curve

to the

right,say

to LM".

Again,

the effect on

GNP

depends

on

the

relative

slopes

of the two

curves:

monetarypolicy

s

potent

f the IS curve

is

flat

and

the LM curve s

steep.

The

centralquestion

of this

paper

can be

stated

succinctly

n

the IS-LM

framework:

ow

flat

s

the IS

curve

relative

o

the

LM

curve?

An

algebraic

development

of the

IS-LM

model

is

a

necessary

prelude

to

an

empirical

study.Startwithasimpleconsumptionunction:

C -

o

+ 61Y,

Interest

rate

LM

M

LM"?

is,

_~~~~

~ ~~~~~

/

f

t

I 5

y

yP

ytt

~~~Real

NP

where C

is

consumption

in

real terms and Y

is

real

GNP,

and thus

0,

is

the

marginal

propensity

to

consume out of

GNP. Next is the

investment

function,

I

I+

eY

Y-72y;

where

I

is real investmermtnd

r

is

the

interest

rate;

GyN

easures

he

ac-

celeratoreffect of

output

on investmentand

y2

is

the

crucial nterest

re-


5/61

Robert

E. flail

65

sponse. The expenditure ide of the economy is governedas

well by the

GNP dentity,

Y

=

C

+

I

+

GI

where

G

is

real government xpenditures.The

IS

curve is

obtained

by

solving

he

three

equations

or r

as

a

functionof Y:

r

do

+ yo+

G

-(I

-

01

-

1)

Y

72

The finalequation s the money-demandunction,

M/p

=

1'o

+ '1 Y

-

VI2

,

whereM

is the nominalmoney supply and p is the price level;

'P.

s the

incomeresponseof moneydemandand

2

iS

the nterest esponse.The LM

curve s just the money-demandunction olved or r:

r-

0

+

AY

-

M/p

'P2

The intersection f the IS andLM curves s obtainedby equating hemand

solving or Y:

Y

=o +

I,

G

+ g2

M/p,

where

pu,

s the

effectof expenditures n GNP:

1

1-01

-

7Yl

+

IP

(72/P2)'

Note

the crucial

role of the ratio

of

the two slope parameters,

2/'2.

If the

IS curve

s

steepand the LM curve s flat,

y2/'2

is small and

t,u

is

close to

the

simple Keynesian multiplier, 1/(1

-

0,

-

Yl).

With a flat IS and a

steep LM curve,

72/2

will

be large,

,t

will be small, and the interest-rate

effect

will largelyoffset he simplemultiplier ffect.

The influence

f

the realmoneysupply s described

y2:

rU=

4 l

+ (- 01 - 7')

(VP2/72)-

Again,

the ratio of the

slope parameters,

P2/Y2,

plays

a central

role,

now

in

reciprocal orm.

If

the IS curve s steep and the LM curve s

flat,

P2/y2

is

large

and

pt2

s

small. With a

flat IS and a steep LM curve, the effect

of

monetaryexpansionon GNP will be close to the extremevalue of the

crudequantity heory,

1/'P,.

How relevant s such a

simple

model

to

stabilization

olicy

n

the mod-


6/61

66

Brookings

Papers on Economic

Activity,

1:1977

em

U.S. economy? n the first

place, it takes

the real moneysupply,

M/p,

as

predetermined y monetary

policy. Unless

the monetaryauthorities

offset every movement n prices, exogeneityof M/p is realistic only if

pricesare taken

as

predetermined-that s, if the price evel does

not react

to

developments n

the economy within the

period.1This paper

is con-

cerned with the effect of

stabilizationpolicy

only for the first year after

policy actionsare taken.A good

deal of recent

research n price determi-

nation seems to

supportunresponsive rices as

a reasonable

approxima-

tion, though

herearesome

mportant issenters.

The

responsiveness f pricesto stabilization

olicy over a longerhori-

zon influences he resultsevenwhen the analysisconcernsonly the initial

year after a

policy action.

Investmentdepends on the real

interestrate

while

moneydemand

dependson the nominal

nterestrate,

and the

differ-

ence

between

hem

is

the

expectedrate of inflation rom one year to

the

next. The

assumption f

unresponsive xpectations bout he rate

of infla-

tion could be

justifiedeither as

an extensionof the rigid-price

ypothesis

to

the

second

yearor as a failureof rational

expectations.

Experiments

with a more

elaboratemodel that permitsa good deal

of

price lexibility n the firstyearand even more nthe secondsuggested hat

the

rigid-price ase enhances

the stimulus

of

monetarypolicy

by

a con-

siderablemarginand slightly

diminishes heeffectof expenditure

olicy.2

Since thefirmest

believers n the

efficacyof expenditure olicies

generally

also consider

prices rigid or

deny rationalexpectations, t seems

best

to

proceedon the

hypothesisof

unresponsive rices.

The simple

model also omits

any nfluence f interest ateson

consump-

tion, either

directly or through the effects of

wealth on

consumption.

Though the

evidence seems to

supportthe life-cycle

permanent-income

hypothesis, n

which

consumptiondependsentirely

on

a comprehensive

measureof wealth,3 here s

little evidenceabout

the

influenceof interest

rates

on that

measureof wealth.The short-run

orrelation f interest ates,

the

stock

market,andconsumptionmaynot

identify he structural

elation

1. Of

course, prices

this year react to events in

earlier years, so prices vary

over

time. Predetermineddoes

not mean

fixed over time.

2. The

model with

rationalexpectations appears

in Robert E. Hall, "The

Macro-

economic

Impact of

Changes in Income Taxes in

the Short and

Medium Runs,"

Journalof Political Economy, special issue, forthcoming.

3.

See

Robert

E.

Hall, "The Life Cycle-PermanentIncome

Hypothesis

and

the

Role of

Consumption in Aggregate

Economic Activity"

(Massachusetts Institute of

Technology, January 1977; processed).


7/61

Robert E. Hall

67

amongthem because hey all reactstrongly o othereconomiceventsand

influences.4

n any case, zero interest-elasticity f consumption s an

ap-

propriate ssumption or this paperbecauseany suchresponsewouldonly

make the IS curve latterand expenditure olicy even less effective.

The model also assumes a closed economy, or more precisely, that

importsand exportsdo not respondwithina yearto changes n GNP and

interest rates. Adding import and export equations sensitive to GNP

would change he Keynesianmultiplier nly slightly,and thus would only

slightly alterthe estimatesof the policy effects, y1 and

.

The omission

of interestratesfrom the

net demand

or

foreigngoods is more serious-

eventhe directionoi thiseffect, et alone ts magnitude, s unsettled oday.

PARAMETER ESTIMATES

Most

of the paperwill concern he numerical alues of the parameters

of

the investment

equation.

Their implications

will

be studied against

a

particular et of values of the parameters f the other equationsof the

simple IS-LM model. The appendixdiscusses he sourcesfor these esti-

mated

parameter

values.

Briefly,

the

marginalpropensity

to consume

(MPC) out

of

GNP,

01,

is taken as

0.36,

which includes he

accelerator

effects

on consumerdurables

as

well as

the

conventional

MPC

for non-

durablesandservices.Thereare

good

reasons

o think

hat

0.36

overstates

the true structural esponse

of

consumption

o

the transitory hanges

n

income broughtaboutby variousstabilization olicies.5

As

the formulas

for

1q

and

c2

show,

the

upward

bias

n

0

will

result n an

upward

bias

n

the

response

of GNP

both to expenditures

ndto

money,

but in the

light

of

the

values

of the

other

parameters,

he bias

turns

out to be

quite

small.

Thecriticalparameters f themodelapart romthose of theinvestment

equation

are

the

effectof income on

money demand,

+,

and the effectof

the interestrate

on

money demand,

q2. From

the

somewhat

mixed evi-

dence discussed n the

appendix,

settled on

the

following compromise

estimates f the

two

parameters:

-increase in real

money

demandassociatedwith an

increase

of

$1

billion

n

real

GNP

$0.135 billion;

4.

See the

discussion

of Frederic

Mishkin's paper, "What Depressed

the Con-

sumer?

The Household

Balance Sheet and the 1973-75 Recession,"

n this

issue.

5.

See Hall, "Life

Cycle-Permanent

ncome

Hypothesis."


8/61

68

Brookings

Papers on Economic

Activity,

1:1977

=

decrease n

real

money

demand associated

with an increase

of

100 basispoints n the short-termnterest ate

-

$2.0 billionl.

Finally,a previewof the conclusionsof the rest

of thepaper s

needed

to fill

in

the remaining arameters f the IS curve.Begin

with the

capital-

demandfunction

mplied by the Cobb-Douglasproduction

unction,

as

derivedby Dale W. Jorgenson:6

a

Y

K*

=

I

Kvs

whereK* is the demand orcapitalor desired apitalstock,Y is realGNP,

v is the real serviceprice of capital,and

a

is the elasticityof the produc-

tion functionwith

respect

to

capital.

At 1977

levels,

real GNP

is

about

$1,325

billion and the real

service price

is

$0.23 per

$1 of capital per

year (assumingdepreciationof 10 percent a year). The income

share

of

capital

s the

usual estimate

of

a

and is 0.31.

Then,

underthe extreme

assumption

f full

adjustment

f actual

capital

to desiredcapital

within

a

year

after a

policy is

implemented,

he

parameters

of the investment

functionare

y,

=

accelerator

effect,

-K

=

$1.36

billionof investment

per

$1

billionof

GNP;

72

=

interest-rate effect

-

av

O,(9v

r

=

$83.8

billion

per

100

basis

points.

In

the second

calculation,

have assumed hat the real service price of

capitalchangespointforpointwiththe interestrate (Ov/Or

=

1), which

is

a

close approximation.

Table

1

presents he derivedvalues of the policy effects under these

parameter alues.

The first

row

maintains

he strong(and surely incor-

rect) assumption

of full

adjustment

f

capital

in

the first

year.

In this

economy

the crude

quantity heory

holds

quite

closely.

An

increase

in

government xpenditures

f

$1

billion

raises GNP by only $0.2 billion;

6.

The initial

statement of Jorgenson's heory was made in "Capital

Theory

and

Investment Behavior,"American Economic Review, vol. 53 (May 1963), pp. 247-

59. For a complete bibliography of his later work with many collaborators, see

his

"Econometric Studies of Investment Behavior: A

Survey,"

Journal of Economic

Literature,vol. 9 (December 1971), pp. 1111-47.


9/61

Robert E.

Hall

69

Table

1.

Effects on Real

GNP of Monetary and

Expenditure

Policies

underAlternative

AssumptioIIs

of

First-YearResponse of Investment

Billions of

dollars

Effect

of

increase

of $1

billion n

Effect of increase

real

government

of $1 billion

n

Assumption boutthe

investment expenditures

real

money

supply

response n thefirst

year

,5

A2

Full response o

both

output and

interestrate

0.2

8.5

One-fourth f

bothresponses

0.6

6.1

One-halfof

outputresponseand

one-eighthof interest-rate esponse 1.4 7.8

One-eighthof

both

responses

0.8 4.4

Sources: Derived from

IS-LM model

using parameter values

developed

in the

appendix and further

explained

in

the

text.

the Keynesian

multiplier ffect is almostentirely

offset

by higher

nterest

rates

andconsequently ower

investment.Monetarypolicy is

correspond-

ingly potent:

a $1 billion increase n the money supplydepresses

nterest

ratesand

stimulates nvestment ufficientlyhatGNPrisesby $8.5

billion.

Theevidenceon lags in the investmentprocessshows thatneither he

strongaccelerator ffectnor the strong

nterest-rate ffect of the firstrow

describes he

modernAmerican

conomy.Rather,only a fractionof both

responsescan

take place within a year.

Jorgenson's nvestment unction

recognizes his

ag, and the secondrowembodieshis conclusion hat

both

responsesare

imited n the firstyearto aboutone-quarter f the full

long-

run amount

predictedby the capital-demand unction. The

interesting

featureof this

case is the continuing

ow value of the effect of an expen-

diturepolicy:

$1 billion n expenditures aises

GNP by only $0.6 billion.

The inhibiting

negative eedbackfrom

higher interestrates to lower in-

vestment s still

substantial ven whenconsiderable luggishness f invest-

ment

is

recognized.Monetarypolicy

remains

strong:

its

impact

on

real

GNP is nearlythree-fourths s large as that in

the

first

row,

even

though

the direct stimulativeeffects of lower interestrates are now

only

one-

quarter s

large.

The

paradoxemergesbecause

he

sluggishness f

invest-

mentresults

n less

"crowding

ut" as well

as

in

less

stimulation.At the

end of the

paper, I will argue

that the

empirical

evidence is

fully

com-

patiblewiththe economyof the secondrow. Note the strongdisagreement

with

the conventional iew that

$1 billion

of

expenditure

aises

GNP

by

about$1.5

billion

n

the firstyear.


10/61

70 Brcookin-gs

apers on Economic Activity,

1:1977

The third row of table 1 considers

he implicationsof the

putty-clay

model, in which the outputresponse

akes place much more quickly

han

the interest-rate esponse.The impliedeffect of an expenditurepolicy is

quite conventional:$1.4 billion

in GNP per $1 billion of expenditure.

This

follows from the high value

of the acceleratoreffect and the low

value of

the inhibiting

nterest-rate ffect. But monetarypolicy

is also

extremelypotent with the putty-clay nvestment unction: the

effect of a

monetaryexpansionof $1 billion is to raise GNP by $7.8 billion,

only

slightly ess than the $8.5 billion implied by the full-adjustment

ase

in

the firstrow. This implication

may cause some believers

n

the putty-clay

hypothesis o reconsider. t turnsout that the IS curve for row 3 is posi-

tively sloped. Recall that the slope of the IS curve is (1

-

0O

-

71) /72;

the MPC,

01,

is 0.36 and the accelerator oefficient,

i,

is 0.68

(one-half

of the extreme1.36 noted

above). Then the marginal ropensityo spend,

01

+

Yl,

is

1.04, so the pure Keynesianexpenditureprocess

is unstable

and the expendituremultiplier s effectively infinite. The

interest-rate

feedbackmakes the IS-LM

model stable but the shape

of

the

IS curve

implieshigh sensitivityof GNP to monetarypolicy. Most

economists,

n-

cluding hiswriter,will probablyrejectthe possibility hat the marginal

propensity o spend exceedsone, but this implies rejectionof

the quick

responseof investment o output

associatedwithrows

1

and3.

The last row

of table

1 shows

the implications

of

an even more

slug-

gish investment unction, in

which only one-eighthof the

long-runre-

sponse occurs n the firstyear.

As I

interpret

he

empirical

indings

rom

James

Tobin's"q theory"

of investmentbelow,

this

function

s consistent

with

them. Longer ags

make

expenditurepolicy stronger

and

monetary

policy weaker,but

it is

still striking hat

the effect of a

$1

billionexpendi-

ture

on

GNP, $0.8 billion, is

little

more than

half

its conventional

value

of

$1.5 billion,

and

monetary

policy

remains

an

extremelypotent

tool

for

stabilization ven when investment

s

this

unresponsive

o interest

rates.

The rest

of

the

paper

nvestigates

he evidence

hat

might

enableone

to

choose one of the

four

cases

of

table

1

as

the

closest

description

of

the

U.S. economy.

It

begins

with a

restatement

f

investment

heory

n a

form

amenable o

discussing

he various

competing ypotheses, speciallyputty-

clay.

After

briefly urveying

he evidenceon

long-run

actor

substitution,

t

turnsto the first majorempirical ssue, the natureof the distributedag

in

the

investment

unction.

This

part

includes an

investigation

of

the

q theory

as an

alternative

way

to

look at

lags

in investment.A

discussion


11/61

Robert E.

Hall

71

of the putty-clayhypothesis follows. The

commonsensecase for and

againstputty-clay s discussed,and the limitationson

empirical estingof

the hypothesismentioned.A detailedreviewof CharlesBischoff's nvest-

ment function s presented.The general

conclusion

s

that the evidence

favorsthe secondcase of table 1, but it is not

overwhelming nd the deter-

mined

believer

mayunderstandablyemainunswayed.

But only exception-

ally strongaccelerator ffectsseem to justify

conventional iews about

the

strength

f

expenditure

olicyas a stabilization

ool.

A Restatement f InvestmentTheory

The

usual extbookexpositionof the theoryof investment as investors

lookingdeeply nto the futureand equating he presentvalue of the future

marginalproduct

of

capital

to

its acquisition ost today. By contrast,

n

theneoclassical nvestment unctionpioneeredby

Jorgenson,whichforms

the basis of most recent empiricalwork, investorsneed look ahead only

one periodand equate he currentmarginal roductof

capital

o

its service

cost. The relationbetweenthe two versionsof the theoryis a matterof

some confusion. n particular, orgenson's elebrated

ormula or the ser-

vice

cost of

capital

as

a

functionof the

acquisition

ost,

the

depreciation

rate, and the interestrate is often thought o require

a

long-term

interest

rate

because capital

s a

long-livedasset.

I will

arguethat

this

reflectsa

misunderstanding

f the

role of

the interestrate in the formula.

Further,

Jorgenson's ormula

s

frequently

ttackedas a

very special

case that

de-

pends

on the

existence

of markets

or

second-hand

apital goods,

which

againseems to be a misunderstanding. inally,the literatureon invest-

ment

theory

reflects

a

great

deal of confusion

with

respect

o

assumptions

about

the competitiveness

f

outputmarkets.

n his

originaldevelopment

of the neoclassical

heory,Jorgenson

et

up

the

problem

as

one of maxi-

mizing

he

present

value of

the firm

subject

o

a

fixed

outputprice.

This

assumption

as been attacked

or

its

unrealism,7

ut

in

fact the

theory

can

be restated

without

t. The central

assumption

s

only

that

firms

produce

at

minimum ost.

7. For example, Dennis

Anderson,

"Models for Determining

Least-Cost

Invest-

ments in Electricity

Supply," Bell

Journal of Economics

and

Management

Science,

vol. 3 (Spring

1972),

pp.

267-99.


12/61

72

Brookings

Papers

on

EconomicActivity,

1:1977

The restatement

makes

use of

the

followingnotation:

rt

=

nominal nterestrate

Rs

t

=

presentvalue in period of one dollar received

n

1 1 1

period s:

R,,,

1+r,

*

+re+i

+r=I

P

=

price

of

one unit of

capital equipment

Ks

=

numberof units of

new

capital

nstalled n

period

s

Q=

total

output

to be

produced

n

period

s

C8(Q,,,Ko,.

,K8)

= variable costs

of

producing

in

period s, given

capital

installed

n this

and

earlier

years

M

=,

=

marginal

alue

n

period

of investment

n

period

:

M8,

t

-

OC-/dKi.

Total

cost is

just

the

presentdiscounted

alue of future

costs,including

the acquisition ost of capital,

co

E

R8,

[C8(Q8,Ko,.

.,K8)

+

p8K.].

a-

The

first-order

onditions

or

a

minimum

with

respect

to

investment

n

period t is

00

(1)

,~~~~~~Rs,M8,

t

Pt,

-*t

exactly

the

textbook

equality

of

the

present

value of the future

earnings

of

today's nvestment,

M8,t,

and

the

current

acquisition

ost of

capital,

pt.

Before

making

use

of this version

of the

cost-minimizing

ondition,

he

firmmust

form

expectations

bout

the

contribution

f

today's

nvestment

to

reducing

ost

in the

future.

In

most

cases,

there

is

a

strong

nteraction

between heproductivity f thisyear's nvestmentn futureyearswiththe

productivity

of

investment

made in other

years.

This

implies

that the

equality

of

the

present

value

of the

productivity

o

the

acquisition

ost

is

not

by

itself

enough

to determine

his

period's cost-minimizing

evel of

investment;

he

implications

of

future nvestmentmust

be

kept

in

mind

in

evaluating oday's

nvestment.

n

general,complete

nvestment

plans

for the

future

must

be

formulated

t the

same time

that current

plans

are

made.

If the interaction mongvintagesof capital s sufficientlytrong,how-

ever,

there

s

an

important xception

o

this

rule which

gives

rise to

Jor-

genson's

rentalformula

and

the

investment

principal

of

equating oday's


13/61

Robert E.

Hall

73

marginal

roductof capital

o

today'srental

price.

Consider he

first-order

condition or

nextperiod's

apital,

co

E

Rs,

tM, t+1

=R

t+,

tp

1

8=t+I

p

t+1

The problem

s to relate

M^,,

o

M,t

+,.

Jorgenson

makesthe

assumption

that

they have

a fixed

relation

attributableo

depreciation ut otherwise

unresponsive

o factor

ntensities

r other

economic

considerations:

Me = Ms,t+1/(l+3).

Here8 is

the

proportionaloss

in

efficiencyperperiodon account

of

de-

preciation.

This

assumptionmakes

it

possible

to restate the

first-order

condition or

nextperiod's

apital

as

0o

p

t+

(2)

e2+

Rs, XM

t

rl

Now consider

he

benefitsand costs

associatedwith

investing

one unit

of

capital today

instead of 1/(1 +

8) units next

period.

The benefits

are

measured ythe difference etween hebenefitsof the investmentn

period

1,

the

left-hand ide

of

equation 1,

and

the benefits

of

the

investment

n

period

t

+ 1,

the

left-hand

side

of

equation

2.

Very

conveniently,

he

difference

s

just the

currentmarginalbenefit of

capital,

M,,t.

The

costs

are

measured

y the

difference

etween he right-hand ide

of

equations

1

and

2:

Pt+?

P'

(l

+r,)

(l1+6)'

This s

the service

or

rental

cost of

capital

as derived

by

Jorgenson-"

hen

thefirst-order

onditions

or currentnvestment

an be stated

as

P t+i

Mtt

=-Pt

-(+rt)

(1+6)'

which nvolvesno

deep ook into the

future.

The

derivationof this form

of the

investment riterion

makes it

clear

that

he

servicepriceof

capital

depends

on the

short-run

interest

ate.The

8.

Jorgensonderived his

formula

in

continuous

time as

p(r

+

8)

-

dp/dt

and

then

used the

discrete

version,

pt(rt

+

8)

-

(Pt+l

Pt),

which is a close

approxima-

tion to

the

formula

given here.


14/61

74

Brookings

Papers on

EconomicActivity, 1:1977

interestrate

entersthe formula hrough he

comparisonof the

streamof

future

returns rom

an

investment

made

today

with the streamfrom an

investment ostponedone period.Theseparate valuationof each stream

involves the long-run

nterest

rate, but the

comparisondoes not. In Jor-

genson's

ramework,

usinesses

are

deciding

when to

schedule

an invest-

ment,

and his

decision

depends

on

the short-runnterest

ate.

This derivation

of Jorgenson's

ormula

also

makes

it clear

that the

dependence

n the

short-run

nterest

rate

and the

short-run hange

n

the

price

of

capital

goods

does not

rest on

any

assumption hat nvestment

an

be

or is undertaken

or the

shortrun alone.

Firms

need

not

be viewed as

buyingcapital n oneperiodandselling t on a second-handmarket n the

next period.The theory

does

not

require he existenceof a second-hand

market,

nor

does

the

lack of such

a

marketcall

into

question he

conclu-

sion that the short-run

nterestrateand the rate of inflation

n

prices

of

capitalgoods

belong

in the

formula

or the

serviceprice. As

long as the

firm aces an

open choice

about he scheduling f investment,

he formula

holds.9

The major limiting

feature

of

Jorgenson's

theory

is its

implicit assump-

tion that the relationbetweenthe productivityof differentvintagesof

capital

is

technologicallypredetermined.

n

particular,

his

assumption

rules

out the "putty-clay" ypothesis,

n which

different

intages

of

capital

are physically

distinct

and

embody

alternative

actor intensities deter-

mined

at

the

time

of installation.

Although

he

general

rule remains

valid

that

investment

hould

be

pushed

to

the

point

of

equality

of the

present

value of

the

future

marginal

alue

of the

capital

o its

acquisition

ost,

as

a

matter

of

theory

this

rule cannotbe

transformednto

a

simple

relation

between

the current

marginal

value and a

predetermined

ental cost

of

capital.'0

An

empirical

nvestment

unction

not based

on

Jorgenson's

crucial

simplifying

ssumption ppearshopelessly

complex,

so it is

useful

to in-

9. Thus,

the

formula does

require that the

firm

plans

to make

some

investment

in

both periods.

Positive

gross investment

is

an

important

assumption

of

the

theory.

It

invariably

holds

in the

aggregate,

but

this

may

conceal a

fraction of firms

who

are

at the corner solution

of zero

gross

investment.

These

firms will not respond

to

small

changes

in the short-run

nterestrate.

10. There is always a rental price for which this simple relationis true,but in the

generalputty-clay

case

it will not be a predetermined

unction

of prices and

interest

rates.It can

be derived

only by

solving the

complete

simultaneous

problemof

deter-

mining

optimal

present

and future investment.


15/61

Robert E. Hall

75

quire

how well

his formulamightapproximate

technology n which

the

assumptiondoes

not hold

literally.Recall that

the problem s to

achieve

Rt,tMt,t

+

Rt+i

tMj+i t

+

.. .

=

pt,

but that

Mt+?,t

and

the otherfuturemarginal

alues of

capital

depend

on

future

nvestment.

Again,it is known

at time t that investment

decisions

in

t

+

1 willplanto achieve

RtE+,

Mt+?

t+1+

Rt+2,

tM+2,1+1 .++

Two considerationsmakeMt+,,t+, iffer romMt+,,t n termsof expecta-

tions

formed at time t: depreciation

and obsolescence.

As long

as

these

are expected

o occur

at

constantproportional

ates n the future,

ollow-

ing Jorgenson,a

parameter,

, easily

takes

them

into account.Otherwise,

it is hardto

thinkof realisticconsiderations

hat would

lead to important

discrepancies

etween

the marginal

alues

of

presentand future

vintages

of

capital

n the same

future

year.

If

it were

known,

or

example,

hat the

relative

price

of laborwas going

to double

suddenly

ive

yearsfromtoday,

the marginal

value of today's investment

n

five

years would be

lower

than a

general

depreciation

ormula

would predict,

and

the more

elab-

orate

simultaneousmodel would

be

required.

But events

like this are

almostnever

predictable;

xpectations

or

the future

are

generally

mooth

even

though

he actuality urns

out to

have sudden

changes.

As

a

practical

matter,then,

a

model

that assumes

a

simple predetermined

elationbe-

tween the futuremarginal

alues of

different

intages

seems

a good

guide

for

investment. n

other

words,Jorgenson's

ental ormula s

a

reasonable

startingpoint

for an investment

heory

even

if

his strong

assumption

of

highsubstitutabilityfvintagesexpostis incorrect.

Long-Run

Substitutability

f

Capital

An

early point

of attack

on

Jorgenson's

nvestment

unction

focused

on

his

assumption

hat

the

underlying

demand or

capital

is

unit-elastic

with

respect

to the service

price

of

capital.

When

there

is

only

a

single

factorotherthancapital-namely, labor-this amounts o assuming hat

the

elasticity

of

substitution

etween

capital

and

labor

s

unity,

or

that the

production

unction

s

Cobb-Douglas.

RobertEisner

was

a

leading

critic


16/61

76

Rrnakinos

Panprs

on

ECrnnomiCACtivitfv

1:1977

of this aspect of Jorgenson'swork." Jorgenson

epliedthat a large

body

of

researchon production unctions supported he assumption

of

unit

elasticity.'2The controversy bbed whenCharlesBischoffpresentedevi-

dence that

the elasticityof substitution

at

the

time capital equipment

s

designed and

installed s indeed

around

one, but that capital and

labor

are

less

substitutable

fter nstallation.'3 orgensonhas

not

defendedhis

assumption of unit elasticity

of

substitution ex post againstBischoff's alter-

native

view, though

there

is

very

substantialdifference

between

the two

views

in

the

short run.'4Bischoff'sevidence

is

scrutinized ater in this

paper.

The Eisner-Jorgensonontroversy eft the impressionamong many

readers

hat an

unresolved

discrepancy

emainedbetween ime-seriesand

cross-section

vidence

on the

elasticity

of substitution.Adherentsof the

putty-clayhypothesis

hadareadyexplanationor this finding,

ince

cross-

sections

ought

o reveal

he

long-runproduction

unction

ex ante

and time

series

the short-run

unctionex

post. However,

a

recent careful

study

of

the time-series

evidence

by

Ernst

Berndtl5

casts doubt

on

the existence

of

anydiscrepancy

t all.

By improving

he

measurement f

all

the

relevant

variables, specially heservicepriceof capital,Berndtobtainsestimates

of

the

elasticity

of substitution

hat

are around

one. Errors n

variables,

not

putty-clay,may

be the

explanation

f earlier

indings

of low substitu-

tion n time-series

ata.

Later n this

paper

repeatedemphasis

s

placed on the importance

of

11. "Tax Policy

and

Investment

Behavior: Comment,"

American Economic

Review,

vol. 59

(June

1969),

pp.

379-88;

and

two papers

with

M.

I.

Nadiri,

"Invest-

ment

Behavior

and Neo-classical

Theory,"

Review of Economics

and

Statistics,

vol.

50 (August 1968), pp. 369-82,

and

"Neoclassical

Theory

of InvestmentBehavior:

A Comment,"Review of Economics and Statistics, vol. 52 (May 1970), pp. 216-22.

12. For example,

in Dale

W.

Jorgenson,

"InvestmentBehavior and

the Produc-

tion Function,"Bell

Journal

of

Economics and

Management Science,

vol.

3 (Spring

1972), pp.

220-51.

13. Charles W. Bischoff, "Hypothesis

Testing

and the

Demand for Capital

Goods,"

Review

of

Economics

and

Statistics,

vol. 51

(August 1969),

pp. 354-68;

and

Bischoff,

"The

Effect of Alternative

Lag Distributions,"

n

Gary

Fromm, ed.,

Tax Incentives

and

Capital Spending (BrookingsInstitution, 1971), pp.

61-130.

14. The

only

mention of

the

subject

in

Jorgenson'ssurvey

article

in the

Journal

of

Economic Literature

is: "An

important

secondary problem

is the time

structure

of

financial determinants

of

investment;

Bischoff

has

suggested

that

real

output

and

the cost of capital should have separate ag structures n the determinationof invest-

ment expenditures" "EconometricStudies

of InvestmentBehavior,"p. 1142).

15.

Ernst

Berndt, "Reconciling Alternative

Estimates of the Elasticity of Sub-

stitution,"Review of

Economics and Statistics,

vol. 58 (February 1976), pp. 59-68.


17/61

Robert E.

Hall 77

econometric

imultaneity n

obscuring he true relationbetween capital

and investment

n the one hand and

theirdeterminants n the other. The

joint determinationf current nvestmentand the current erviceprice of

capital s an obstacle o measurement

f the elasticity

of substitution rom

time series. The

supply functionof

capital slopes upward:both interest

rates and the acquisition

price of capitalrise if demand

rises. As in every

econometricstudy

of demand,regressionestimates

of the elasticity of

demand or capital

with respect o

the serviceprice of capital are biased

towardzero because

of the competing nfluenceof the

supply function.

Berndtattempts

o eliminate his

bias through he use of two-stage east

squares,but as usual there s a seriousquestionaboutthe true exogeneity

of the instrumentalariables.The

directionof the bias is unambiguous, o

Berndt'sevidence

strengthenshe case for a reasonably

high elasticityof

substitution etween

capitaland abor.

Today,

few believers

n

the short-run

nelasticity

of investmentwith

respect to interestrates and other

determinants f the service price of

capital place much weight on

the lack of

substitutabilityf capitaland

labor

n

the

long

run.Rather, he case against

he

flatIS

curverestson

the

three short-run onsiderationsisted at the beginningof the paper: lags

in

the investment

process, imited

factor substitutability

x

post,

and the

slow response

of

long-term

nterestrates

to

changes

n

short-term

ates.

The

purposeof

this brief consideration f

the evidenceon

long-run

ub-

stitutability s simply to guardagainst

he

revival

of the

argument

bout

limited ong-run ubstitutabilityn

view of the criticisms

f the three

points

offeredhere.

DistributedLags

n the

Investment

Function

Virtually

ll econometric tudies

of

investment

make

use of a distributed

lag

between

changes

n the determinants

f

investmentand

the

actual

n-

vestment tself.

Throughout

is

work, Jorgenson

has attributed his

lag

to

the

time required

o

plan,

build,

and install

new

capital

once

the

need for

it

is apparent.

Other nvestigators

ave attributed

he

lag

to

the

process

by

which

expectations

of future

needs for

capital

are

formed.

Until re-

cently, he distinction etween hetwosourcesof lagsseemedunimportant,

but new work on the structural

nterpretation

f

distributed-lag

mech-

anisms or

expectations

has

suggested

hat the

source

of the

lag

matters


18/61

78

BrookingsPapers on Economic Activity, 1:1977

a

great deal.16 f

policymakersntroducean investment redit

today, for

example, here

s no

reason or thoughtful

nvestors o adjust

heirexpecta-

tions

aboutthe futurecost of capital

according o a distributedag, even

though he distributed

ag is a reasonable ummary f the

predictivevalue

of

previouschanges n

the cost of capital

with respectto the futurecost.

In

contrast, here s no reason o thinkthat

the physicalprocessof invest-

ment

will take

place

at

a

different

peed

f

the

investment s

a

response

o

a

tax credit rather han any other change

in the demand or

capital. In

other words, a

distributed-lagxpectationmechanism s not

a structural

feature of the

investment quation,

whereasthe physical delivery ag is

preciselya structuraleature. Policy analysisis now seen to requirea

separationof lags relatedto expectations

rom those of the physical n-

vestment

process.

Suppose, ollowing

Jorgenson,

hat

the

process

of

designing,ordering,

and

installing apitalcan

be

described

by a

fixed

distribution f

lags.

Let

/3i

be

the fractionof

capital

that can be installed n i

quarters.

Today's

capital stock

is thus a

weightedaverage

of

targets

set in

past

quarters

n

the basisof

information vailable hen:

i-o

where

K,

is

actualcapital

and

K'*

is

the

target

or

quarter

set

in

quarter

t

-

i.

Note

that

this

hypothesis

assumes

that

capital

with short

delivery

lags

cannotsubstitute or

capital

with

longer delivery ags, else

Kt

could

be

equated

o

K'

t

in

each

quarter.Next,

suppose

hatthere

s an observed

variable,

X,,

with the

property

hatthe

target

capital

stock set this

quarter

for

some

quarter

n

the future

s

equal

to

the

expected

value of X

in

the

futurequarter:

K*t-.

=

E

(Xt).

t-i

In

Jorgenson'swork,

X

is the

nominal

value

of

output

deflated

by

the

nominal ervice

cost of

capital,

but

the

principle

discussed

here can

apply

to

a

variety

of alternativeormulations

f

the

demand

or

capital.

16. Robert

E. Lucas, Jr., "EconometricPolicy Evaluation:

A Critique," n

Karl

fBrunner nd Allan H. Meltzer, eds.,

The Phillips Curve

and Labor Markets(Amster-

dam: North-Holland,1976;distributed n the United StatesandCanadaby American

Elsevier), pp. 19-46. Lucas deals explicitly

with the problems of

naive expectations

in the investment

function in section 5.2.


19/61

Robert

E.

Hall

79

Next,

suppose hat

Xt

obeys a stationary

tochastic

process,

xt

=

Xt

+

E

1PrUt-T.

Here,

X,

is a

deterministicrend, ut

-

is a seriallyuncorrelated andom

variable,and

the

&,

are lag, weights that describe

whatever

persistence

there is in the

movementof

X,

around ts trendover time. The random

innovations,u,

cannot be forecast from their own past values, by hy-

pothesis.Under

the furtherassumption hat no other variablesknown to

investors n quarter

-

i have any bearingon the

futurevalue

of

u,,

the

best forecastof u, made in quarter

-

i is zero.Thus the expectationof

X0

formed in t

-i is

E

(Xe)

=

Xt

+

E

P

TUt-T.

Combining hephysicalandexpectationalags gives

K=

E Pi

E

(Xt)

i=O

t-i

Xt

+

E

2i

E

1'TUt-T

10 TX

i t + "O

i

i0'pu

t-0

whereBois the fractionof all investmenthatrequires0 orfewerquarters

to

complete:

0

i.=o

The final

relationship

between

today's capital

and

earlier values of the

innovation,u,

has the

following nterpretation:

he new

information hat

became available

in

quarter

t

-

0,

measured

by

ut-,

is

expected

to affect

the

demand

for

capital

in

quarter

t

by

fout,.

However, only

those

com-

ponentsof capitalthat can respondwithin

0

quarters,a fractionBO,are

actually

ffected

by

the

information,

o

the totalcontributions

Bopou-o.


20/61

80 Brookingzs

aDers

on

Economic

Activity, 1:1977

The derivation f the distributedag between

Kt

and

X,

is muchsimpli-

fiedthrough he use

of

the ag operator otation.Let

co

-0

VjB(L)

_ E

Bo'0L0.

oo

Thenthe processassumed or

X,

can be expressedas

X

=

t

+

J(L)ut,

and he derivedprocess or capital nthepresenceof delivery ags s

Kt

=

Xt

+

iPP(L)ut.

The impliedrelationbetween

X,

and

K,

is

obtainedby

eliminating

ut

by

substitutinghe firstequation

ntothe

second:

K-t

=

Xt +

VIP

xLt

X-

xt)*

Thus the

large body

of econometric

work

that

has

involved

fitting

a dis-

tributed ag between

KY

and a variable(or compositeof variables),Xr,

yields

a certain

combinationof

the

physical-lag

oefficients

and

the co-

efficientsof the

process

for

formingexpectations.

n

general,

he

lag

dis-

tributioncannot

be interpreted

s

reflecting

he

physical

lags

alone. In

this

respect, Jorgenson's

discussionof

lags

in

the investment

process

is

incomplete.

Some idea

of

the biases

involvedcan be

gained throughexplicit

solu-

tion

of the

representative

ase in which he

distribution

f

delivery

imes

s

second-orderPascal, l-

=(

1

-

p)

2is

,

and

X,

follows a first-order uto-

regressive process with serial correlation,

/:

ir

= /t.

Then the distributed

lag

is

Kt=

x

+

ff(-Xfol

which

s second-order ascal

with a declinerate

equal

to

the

product,

ip,

of the

decline

rate

of

the

physical

distributed

ag,

8,

and the serialcorrela-

tion

parameter,

,.

The

average lag

is

23f/(1

-

pt),

which understates

the averagephysical ags,2A/(1

-

fl), provided pis less than one. The

casual mpression

hat the

combination

f

a

physical ag

and an

expecta-

tional

lag

would be

longer

than

just

the

physical lag

is mistaken.

The


21/61

Robert E. Hall 81

reason s revealedclearly n the case where

X,

is not seriallycorrelated

at all

(+

=

0).

Then

earlier luctuations

n

Xt,

are irrelevant

or

predict-

ing capitalneeds in quarter , and there s no distributedag at all. On the

otherhand, there s one important ase in which the observed

distributed

lag is exactly he sameas the distribution f delivery imes-namely,

when

the

serial-correlation arameter,v,

s

one. Then

Xt

evolves

as a random

walk. The best predictor of

X,

-

X,

at time

t

-

i is just

Xt

-

Xyti,

so

static expectationsare optimal. Bischoff has pointed out

that static ex-

pectationsunderliehis interpretation f the distributedags in

his

invest-

ment

equation,but apparently onsidersstatic expectations

a naive rule

of thumband does not investigatewhetheroptimalexpectationswould be

verydifferentromstaticexpectations.'7

Many of Jorgenson'sempiricaldistributed ags are

close to second-

orderPascalwith a mean lag of abouttwo years.His implicit

estimateof

Bl>,

hen, is 0.5. The impliedestimateof

p

is

0.5/1,

which

is different

o

the extentthat

&

differs rom one. Followingare two regression

stimates

of

+

obtained romBerndt's nnualdata

on

Jorgenson's

ompositecapital-

demand ariable or the years1950 through1968:

K*=--1.2 +

1.060

KA;

(3.4) (0.039)

K*- =

5.4 + 0.928

K'i

+ 0.48 t.

(8.7) (0.165) (0.58)

=

1 in

1950.

The

numbers

n

parentheses

are

standard

errors.In the

first

regression,

only the laggedvalueof

the variable

an

explain

ts

trend,

so

the

estimated

serial-correlationarameter,

&,

exceeds one. The second regressionets

the deterministic

rend,

XT,

be a linearfunction

of

time,

which of

course

reduces

he serialcorrelation

o

a

value less

than one. The first

regression

is relevant

or

appraising

he bias in

a

capital-demand

egression

with

no

time

trend, or,

equivalently,

n a net-investment

quation

with no con-

stant.The

second

applies

when

here s

a

timetrendor

whenthe

net-invest-

ment

equation

ncludes

a

constant.

f

f

is

actually

1.060,

as

suggestedby

the

first

regression,

hen

the

value

of

fi

is

0.47

and the true mean of

the

physical-lag

distribution

is

1.79

years,

not 2

years.

The

error

is about

11

percent

and is

easily

within

the

range

of

sampling

variation.

On

the

other

17. "Effectof

Alternative

Lag Distributions."


22/61

82

Brookings Papers on

Economic

Activity.

1:1977

hand,

f the valueof

,

from he second

regression s

correct, hen the value

of

p

is 0.54 and the

true mean of the

distributions 2.34 years. Many of

Jorgenson's andothers') quationsncludedconstants, o the secondesti-

mate s probably

omewhatmorerelevant han he first.

Thesecalculations

do

suggest hat the bias in the lag

distributions n account

of the role of

the

laggedvariables n the formation f

expectationss not

one of the most

important mpirical

ssues in

investmentanalysis.Furtherrefinement f

thesecalculationss probably ot

justified n view of thepotentially erious

problems ausedby simultaneity f the

right-hand

ariables n investment

regressions, topicto

which nowturn.

IMPLICATIONS

OF

THE

ENDOGENEITY OF OUTPUT

There is

one important urther

obstacle to measurement

of the dis-

tributed ag

in

the

investment quation: he econometric

problemsposed

by

the

endogeneity

of

the major right-hand

variables

n an

investment

equation.18

ndogeneity

arisesfrom

two sources.First,

the

randomdis-

turbance

n

the investment unction

feeds back

through

he

expenditure

process to influenceoutputand the interestrate.An upwardshift in the

investment unctionraises

GNP and the interestrate

in

much the same

way

as an

increase

n

government xpenditures oes. A

regression

of

in-

vestment

on

output

and the interestrate

(or

a

service

price

of

capital

hat

depends

on

the

interest

rate)

will

tend to overstate he

positive

effect of

output

andunderstatehe

negative

ffect

of

the

interest ate.

The

second,

more

serious,

source

of

endogeneity

arises from

the

cor-

relation

of

the disturbance

n

the investment unctionwiththe

disturbances

in

the other

major

structural

quations

of the

economy.

Unmeasured

n-

fluencesassociatedwith the arrivalof favorableor unfavorable

nforma-

tion shift the

investment

unction

and

also shift

the other determinants

f

GNP

and

of the

interest

ate.

Again,

the

likely pattern

s

positive

correla-

18. Some authors

have argued

beyond the econometric

difficulty

to say that an

equation

with, for

example,output

on

the

right-hand ide is somehow

logically

defec-

tive because

output

is determined ointly

with investment;see, for

example, John

P.

Gould,

"The

Use of

Endogenous

Variables in Dynamic

Models of

Investment,"

Quarterly

Journal

of Economics, vol. 83 (November

1969), pp. 580-99.

This line of

argumentappearsto involve a misunderstanding f the notion of a structuralequa-

tion.

For a

more

complete discussion,

see Robert

E. Hall and Dale W. Jorgenson,

"Tax

Policy and Investment

Behavior:

Reply and FurtherResults,"

American

Eco-

nomic

Review, vol.

59 (June 1969), pp. 388-401.


23/61

Robert

E.

Hall

83

tion of output, the interestrate,

and

the disturbance

n

the

investment

equation.Here, too, a regressionwill

overstatethe effect of

output on

investment ndunderstatehe effectof the nterest ate.

In

principle,econometric

echniquesare available or recovering he

true

structural nvestment ag in the

presenceof the correlationof the

right-hand

ariables ndthe disturbance

n the investment quation.These

techniques

ely

on

instrumental ariables hat are independent

f

the

dis-

turbance.

However, the logic of the investment

equation-that today's

investment s

the realization f plansmade one, two, or three

years ago-

rules out the most fruitful ourceof

instruments-namely,

agged

endog-

enousvariables uch as GNP in earlierquarters.Apart romdemographic

trends and

variations n the weather,the only admissible

nstrumental

variablesfor the investmentequation

are truly exogenous

measures

of

macroeconomic olicy. Whether

uch

measureswith any power

as instru-

mentsexist s doubtful.

Though

the

prospects or estimating

he

investment quation

hrough

two-stage

east squaresare not

entirelyfavorable, he previous analysis

does

suggest a useful

test for endogeneityof the right-hand ariables

n

an investment quation.The investment quation elates nvestmento the

first

difjerences

f GNP while the correlation f GNP and the

disturbance

may generate

an

apparent

elation

between

investment

and

the

level

of

GNP.

Then

the observeddistributed

ag

between nvestmentand GNP is

useful

in the

followingrespect:

f

the sum

of

the

lag

coefficients s

zero,

then

the observed

elationactuallydepends

on the

firstdifferences f GNP

and

may actually

be

the true investment

quation.

If

the sum is

unam-

biguously

positive,

then it is

impossible

hat

the

estimated

ag

distribution

is the

true distribution.

n

otherwords,

a

finding hat the level of invest-

ment

depends

on

the level

of GNP

invalidates

any

claim

that the

relation

is an

investment equation

alone.'19

The

problems

f

endogeneity

re

further

ompounded

n

cases

in

which

separate

distributed

ags

are

fittedto the

influences

of

real

output

and of

the relativeservice cost of capital,

notably

n

the work

of

Bischoff.The

bias from

the

endogeneity

of the

right-hand

ariables

probably

s

most

severe

n the

contemporaneous art

of

the distributedags.

Then the

lag

distribution

or

output

will

exaggerate

he accelerator

ffect in

the

short

19. All of this applies as stated to net, not gross, investment.

When

the proposed

test is applied to data on gross investment later in the paper, the test is suitably

modified.


24/61

84

Brookings Papers on Economic Activity, 1:1977

run and that for the servicepricewill

understatets trueeffect n the short

run. There is a

clear bias in the regression

away from the simplermodel

in which the responses o the two variablesare equal in magnitudeand

opposite n sign.

Again, a useful test for endogeneity s based on the gen-

eral predictionof investment heorythat the

level of outputhas no influ-

ence on net

investment. f level effectsarerevealedby the regression, here

is a presumption

gainst ts

interpretation

s a

pure structural

nvestment

equation.

EMPIRICAL

EVIDENCE ON THE

DISTRIBUTED LAG

Many authorshave fitted distributed ags

between investmentand its

determinants.20

xceptfor a numberof studies

with obviouseconometric

problemsassociated

with the use of Koyck distributed ags withoutcor-

rectionfor serial

correlation,

here is remarkably lose agreement bout

the basic

featuresof the lag functions.They are smooth, hump-shaped

distributionswith an average ag

of

about two

years.

Withinthe

general

class

of flexibleaccelerator nvestment

models, this conclusionseems

to

hold overquitewidevariationsn the specification f the demand unction

for

capital and in the econometricmethod used to estimatethe

lag

dis-

tributions.2'Of course, all of this evidence is

subject to the potentially

seriousbiasfromendogeneity iscussed arlier.

Though

ome

studies

have

used

simultaneous stimation echniques,noneto my knowledgehas come

to gripswith the

basic obstacle hat the logic of the distributed-lagnvest-

ment function

makes

any lagged endogenous

variable

ineligible

as

an

instrument

nless

t

is

laggedmore

than

the

most

distantpartof

the

invest-

ment

lag

distribution.Two

features

of

investment unctionsof the

type

fitted

by Jorgensonmay

reduce this

bias,

but there

is

no

reason to

think

they eliminate t:

First, his constraint hatoutput andthe rentalprice

of

20. Many of these are summarizedby Jorgenson,

"EconometricStudies of Invest-

ment Behavior."I will not discuss the equally

large body of evidence on the lag be-

tween appropriations

r new

orders and the

determinantsof investment.

Though

this

lag is free from pure delivery lags, it includes

many of the planning stages that I

include

in

a full description

of

the investment

process. Throughout the paper, "de-

livery lags" is a short-handterm for all of the time-consumingsteps

in

investment.

21. For example, the more refinedversion of my own work

with

Jorgenson

which

used the modern Almon lag technique and made a full correctionfor serial correla-

tion certainly fits within this general summary;

see Robert E. Hall and Dale W.

Jorgenson, "Application of the Theory of

Optimum Capital Accumulation," in

Fromm, ed.,

Tax Incentives

and Capital Spending,

pp.

9-60.


25/61

Robert E. Hall 85

capital enter as a ratio offsets the positive bias associatedwith the

cor-

relationof GNP andthe disturbancewith the negativebias associated

with

the correlation f the interestrate and the disturbance. econd,his con-

straint hatthe level of the demand or capitalhas no permanent ffecton

net

investment

robably educes he bias causedby the

correlation

f

the

level of GNP withthe disturbance.The reviewbelow of

Bischoff'swork

n

which both of these constraintsare dropped suggests that they have

a

major nfluence.

In addition o the somewhatquestionable conometric videnceabout

lags

in

investment,

here

s

an

important ody

of

surveyevidencecollected

by ThomasMayer,22 hichhas beencitedextensivelyby Jorgenson.Mayer

finds hatthe average ag between he decision o undertake n investment

projectand the completionof it is abouttwenty-onemonths.To this must

be added

any lag that

occurs betweenthe

arrival

of information hat

in-

vestment

s

needed and the decisionto

carry

out

the

investment.

As Jor-

genson argues,Mayer's

evidenceseems

perfectly

consistent

with

modern

econometric indingsabout he lag distribution.

This evidenceon

lags

in

investment onfirms he view that

they

are

a

major imitationn theresponseof investment o changes n interestrates

and otherdeterminants f the service

price

of

capital,

and thus an

impor-

tant nfluence

n making,he

IS curvesteeper

han

t

would

be if

investment

respondedquickly

o its

determinants.

ny

realisticmodelfor the

analysis

of

stabilization olicies

must

incorporate

serious

consideration f these

lags.

TOBIN'S

"Q

THEORY"

OF

INVESTMENT

The

majorcompetitor

o

Jorgenson's

heoretical

ramework or invest-

menthas

been created

by

James

Tobin.23

Tobinobserves

hat

unexpected

changes

n the

demand

or

capitalgeneratediscrepancies

etween he

cur-

rentmarket

value

of

existing

nstalled

capital

and the cost

of

reproducing

22. "Plant

and Equipment Lead Times," Journal

of Business,

vol. 33 (April

1960), pp. 127-32.

23. Tobin's thinking

on

the

subject considerablypredates

Jorgenson's,of course.

Two recent fairly

complete expositions

are James Tobin, "A General

Equilibrium

Approach to Monetary Theory," Journal of Money, Credit, and Banking, vol. 1

(February 1969),

pp. 15-29, and

Tobin "Asset Markets and the Cost of

Capital"

(with William

Brainard), Cowles Foundation Discussion

Paper 427 (March

1976),

forthcoming

in a Festschrift for William

Fellner.


26/61

86 Brookings Papers on Economic Activity,

1:1977

that capital. The ratio between the two

is his famous "q."

It is essential to

understand he

relationbetween he

two theories n order o interpret he

empiricalevidence obtainedby the

disciples of the two major

figures,

especiallybecauseTobinandhis

followersgeneraliy eem to view the lags

inthe investment

rocessas extremely

engthy.So far as I know,the litera-

turedoes not contain

a reconciliation f

the two theories.

Tobin cites two reasons or q to

depart rom unity.

First, lags in de-

liveringcapitalgoodsgenerate

ransitorydepartures.

econd,

costs of

in-

vestmentthat rise

more thanproportionately o the rate

of investment

bringaboutbothtransitory nd

permanent epartures.

propose

o

ignore

thesecondconsideration. djustment osts and deliveryags are probably

best viewed as

alternative xplanations f the lagged

responseof invest-

mentto its

determinants. model

containiing oth

wouldbe

complex

and

redundant.

If

delivery ags are the

only

obstacleto instant

ulfillment f the basic

conditionthat the

presentvalue of the

future marginal

contributions

f

capitalequal ts currentacquisition

ost, then q departs

rom one

only

to

the

extent that

capitalalready n place is now expected

to yield more

or

less thanit was expected o at the time of installation.Thatis, qt

-

1 is

the

present

value

at time

t of

the extra rent attributable

o recent

unex-

pected events.This rentwill

be earned

only

over the

period

during

which

capital

cannot

be adjusted.

A

simple

model of this

process

is

the follow-

ing:

As

before, et

Ki,t

be the stock

of

capital

with

delivery

ag i,

and let

Xt

be the stock that

would be held today if there were no

delivery ag.

Suppose

hat

the excess

rent

n real terms s a

simple

multiple

of the

gap,

X(Xt

-

-

t).

Then

today's

qt

for

capital

of

type

i

is,

in

the absence

of

discounting,

W+-1

qi,t

- I

=

-

E(X

-Ki).

8t

G

Note that no excess rentsare

expected

after

+

i

-

1,

since in

t

-+

i

and

beyond,

he

capitalstock

will be

adjusted oday

to eliminate

any expected

gap. Suppose

that

capital

demand

consists

of a

deterministic

rend,

Xt,

plus a residual hat

s

approximately

random

walk.

Then

static

expecta-

tions are appropriate

or

the

residual,

and

the

expected

uture

value

of the

demands the sumof the future rendandthecurrent esidual:

E(X8)

2s

+

(Xt

-

t).

t


27/61

Robert E. Hall 87

Now the current

anld

uturevalues of

Ki,t

were based on expectationsof

Xt

formedby the sameprocess n past quarters:

Ki,8

8

+

(X8,-i-Xs_0.

Putting these into the formula for

qi,t

gives

t?i-1

qi,

t

-

1

=

Xi(Xt

-

Xt)

-

X

E

(Xs-i-

1.-0.

8-t

The

first

term

is

today'sexpectation

of

the total future

excess rent

if the

capital stock remainsat its present evel and the second adjusts or in-

vestment ommitmentsmade n the recentpastthatwill be installedwithin

the next quarters.

Taking

he

weightedaverageof the

qi,t

over the

delivery-time

istribu-

tion,

p3i,

givesthe general

ormula

or

qt:

qg

1

=

iqi,t-

1

=

(Xt

-

-t)X

(1-Bo)Xt-.

0=0

Here

y

is the firstmomentor mean lag of the

pl-distribution

nd

B0

is,

as

before, the fractionof capital with delivery ags

of

0 or less. Again,

the

second term

adjusts

or the future

nvestment

already

n

the

pipeline.

The next

step

is

to combine

his

model

of the

determination

f

qt

with

the

earliermodel

of

investment. irst,

define

X(L)

=

Xi-X

X2(I

-

Bo)LO;

thus

q-

=

X(L)

Xt

-

t)

Recall

that

K = f3(L) Xt

-

Xt) + Xt,

so there

is,

in

fact,

a relation between

Kt

and

qt

as

posited by

Tobin:

Kt

=

X(L)

q

1)

+

fct.

Tlhe

ag between

q

and

K

is

not

the distribution

f

robert, hall - investment, interest rate and the effect of stabilazation policy

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