robert, hall - investment, interest rate and the effect of stabilazation policy
TRANSCRIPT
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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.
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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:
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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
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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-
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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-
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Brookings
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Activity,
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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).
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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."
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Brookings
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=
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.
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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.
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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
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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.
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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
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Robert E.
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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.
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Brookings
Papers on
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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.
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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
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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.
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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
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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.
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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.
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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
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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."
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82
Brookings Papers on
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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.
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Robert
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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.
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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.
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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.
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86 Brookings Papers on Economic Activity,
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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
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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