Capital Risk and Models of Investment Behavior
Robert S. Pindyck
Sloan School of Management
Massachusetts Institute of Technology
WP#1819-86
September 1986
CAPITAL RISK AND MODELS OF INVESTMENT BEHAVIOR
by
Robert S. Pindyck
ABSTRACT
Most investment expenditures are at least partly irreversible
-- although capital in place can be sold from one firm to another,
its scrap value is often small because it has no alternative use
other than that originally intended for it. An emerging literature has shown that this makes investment decisions highly
sensitive to uncertainty over future market conditions, and in
theory changes in risk levels should strongly affect investment
spending. However, explicit measures of risk are usually missing
from empirical investment models.
This paper discusses the effects of risk on investment and
capacity choice, and explains why q theory and related investment
models, based on the rule "invest when the marginal value of a
unit of capital is at least as large as the cost of the unit," are
theoretically flawed.
It argues that the inclusion of explicit
measures of risk can
help explain
and predict investment
spending.
The results of causality tests and a set of simple
regressions are presented that strongly support this argument.
1.
Introduction.
It is obvious to any
on
critically
depend
the
decisions often
economic
Clearly a
of market risk.
extent
on projections of
not only
will depend
in business schools,
as taught
finance theory,
of corporate
Indeed, much
that
on the degree to which future demand is uncertain.
but also
market demand,
and
nature
new capital
decision to invest in
person
business
deals with methods for properly taking risk into account when making capital
budgeting decisions.
activity ignore
most
Yet
or deal
of risk,
the role
models
econometric
aggregate economic
of
only implicitly.
with it
point of this paper is that a more explicit treatment of risk
The
help to
may
and forecast economic fluctuations, and especially movements
better explain
in investment spending.
of
Consider, for example, the recessions
jumps
in
world
energy
that
prices
contributed to those recessions, and
The sharp
1980.
in 1974 and 1979-80 clearly
occured
they
and
1975
so
did
in
a
number
of ways.
First, they caused a reduction in the real national incomes of oil importing
Second, they led to
countries.
further drop
in real
"adjustment
effects"
--
inflation
and a
output resulting from the rigidities that
income and
prevented wages and non-energy prices from coming into equilibrium quickly. 1
But those energy shocks also
economic
conditions.
For
example,
would continue to rise or later
prices would
be on
caused
fall,
the marginal
long-lived the inflationary impact
1
it
greater
over future
was unclear whether energy prices
what
product of
of
uncertainty
those
the
impact
of
higher energy
various types of capital, how
shocks
would
be, etc. Other
For a discussion of these effects, see Pindyck (1980) and Pindyck and
Rotemberg (1984).
- 2 events also contributed to
ment,
especially
in
1979-82: much
uncertain economic environ-
a more
what became
volatile exchange rates, and (at
more
This increased uncertainty
least in the U.S.) more volatile interest rates.
must have
the decline
contributed to
in investment
spending that occured
during these periods. 2
This more volatile economic environment was reflected in an increase in
From 1970 to 1981, the average monthly
the volatility of U.S. stock prices.
variance of the New York Stock Exchange Index was about
as for
the period
above.
Elsewhere
more
the
volatile
argued that
I have
as large
This increase in stock market volatility can
1950-1969.
be explained in part by
2.5 times
economic
conditions described
it corresponds to an increase in the
variance of the real gross marginal return on capital. 3
Again,
this should
have affected investment spending, and economic performance in general.
follows I
In what
will focus on investment spending, and argue that a
more explicit treatment of risk
investment at
is
needed
or sectoral
the aggregate
when investment is irreversible, as most
In such
a case
the decision
to invest
to
better
level.
model
and forecast
This is particularly true
investment is,
at least
in part.
involves an additional opportunity
cost -- installing capital today forecloses the possibility of installing it
instead at
some point
in the
future (or never installing it at all).
differently, a firm has options to install capital at various
future
(options
that
can
be
exercised
at
the
cost
Put
points in the
of purchasing the
2
This point was made by Bernanke (1983), particularly with respect to
changes in oil prices.
Also, see Evans (1984) and Tatom (1984) for a
discussion of the depressive effects of increased interest rate volatility.
3See Pindyck (1984). That paper also argues that the increase in the
variance of stock returns may have been partly responsible for the decline
in real stock prices over the period 1965-81.
capital), and if the firm installs capital now, it closes those options.
uncertainty over
future market
associated with closing
these
conditions increases,
options
the opportunity cost
and
increases,
If
current investment
spending becomes less attractive.
next two
In the
sections I
decisions in more detail, and discuss
of investment.
aspect of firms' investment
explain this
the implications
for q-theory models
Section 4 presents the results of some simple (and prelimiThese results indicate that risk
nary) empirical tests.
does seem
to help
explain and predict aggregate investment spending.
2.
The Determinants of Investment Spending.
The explanation
especially
Existing
of aggregate
problematic
models
have
predicting investment.
been able
to explain
investment.
the
had,
development
at
best,
The problem
and predict
of
limited
is not
macro-econometric models.
success
simply that
in
explaining or
these models have
only a small portion of the movements in
In addition, constructed quantities that in theory
strong explanatory
of capital
in
and sectoral investment behavior remains
-- in
should have
power -- e.g. Tobin's q, or various measures of the cost
practice do
not, and
leave much
of investment spending
unexplained. 4
It is
easy to
think of reasons for the failings of these models.
example, even leaving aside
there
are
likely
to
be
problems with
formidable
their theoretical underpinnings,
estimation
problems
aggregation (across firms, and also across investment projects
4
For
resulting from
of different
See Kopcke (1985) for an overview, as well as examples and comparisons
of traditional approaches to modelling investment spending.
III
- 4 gestations).
I will not attempt to survey these
way
a
provide
general
overview
of
the
Instead I want to focus on one special
risk, and
in particular
the effects
problems here,
state
aspect of
nor in any
of investment modelling.
investment -
the role of
on investment spending of uncertainty
over future values of the marginal revenue product of capital.
Of course non-diversifiable risk plays
models of
investment, by
affecting the
a
role
cost of
in
even
capital.
the simplest
But there is an
emerging literature that suggests that risk may be a more crucial explanator
of investment.
of investment
The thrust of this literature begins with the fact that much
spending
constructed, can
is
be used
irreversible
to make
--
i.e. a
widgets, but
widget
not much else.
irreversibility, one must view an investment expenditure as
exercising of
an option
some point
in the future, or never at all.
gives up the option of waiting
and cost
for new
Given this
essentially the
(an option to productively invest).
an option is exercised, it is "dead," i.e. one cannot decide
instead at
factory, once
But once such
to exercise it
In other words, one
information (about
evolving demand
conditions), and using that information to re-evaluate the desira-
bility and/or timing of the expenditure. 5
This lost option value
investment.
5
must be
included as
part of
the cost
of the
Doing so leads to an investment rule that is different from the
This is developed in the recent papers by Bernanke (1983) and McDonald
and Siegel (1986).
Other examples of this literature include Cukierman
(1980), Brennan and Schwartz (1985), and Majd and Pindyck (1985).
In the
papers by Bernanke and Cukierman, uncertainty over future market conditions
is reduced as time passes, so that firms have an incentive to delay
investing when markets are volatile (e.g. during recessions).
In the
other papers, future market conditions are always uncertain. But as with a
call option on a dividend-paying stock, an investment expenditure should be
made only when the value of the resulting project exceeds its cost by a
positive amount, and again, increased uncertainty will increase the incentive to delay the investment.
- 5 standard rule:
"Invest when the marginal value of a unit
of capital
least as large as the purchase and installation cost of the unit."
the marginal value of
cost by
must exceed
the unit
the purchase
is at
Instead,
and installation
an amount equal to the value of keeping the firm's option to invest
alive.
To see this more clearly, consider
a
firm
that
has
degree of
some
monopoly power (i.e. faces a downward sloping demand curve), and must decide
(To keep things simple we will
how much initial output capacity to install.
investment, and assume that the firm can chose any
lumpiness in
ignore any
output capacity it wants.)
Again,
key
assumption
is
that
the firm's
although capital in place can be sold by one
irreversible --
investment is
a
firm to another, its scrap value is small because it has no
alternative use
other than that originally intended for it (e.g. to produce widgets).
Let
AV(K)
denote
the
value
to
the
firm of an incremental unit of
capacity, given that the firm already has capacity K.
practice
is
a
non-trivial
matter,
function of (unknown) future demands.
incremental
this
result, methods
calculate
unit
of
other than
AV(K). 6
We
will
capacity
instead simply assume that AV(K)
AV(K) in
because it will be a highly nonlinear
For example, if
might
discounted cash
not
Determining
future demand falls,
not be used by the firm.
flow techniques
As a
are needed to
be concerned with this problem here, and
can
indeed
be
calculated.
It
will of
course be a declining function of K.
Given that
6
the firm knows AV(K), it must now decide whether to install
As noted by McDonald and Siegel -(1985), once a unit of capital is in
place, the firm has the option of whether or not to utilize it as market
conditions evolve. Thus option pricing methods can be used to value the
unit. Implications for marginal investment decisions and capacity choice is
examined in Pindyck (1986).
- 6 Although the firm has the option to install the unit,
the incremental unit.
this option. 7
to exercise
not want
it might
or not to
Deciding whether
exercise this option is the key to the firm's investment decision.
must
value
also
option.
the
Again,
we
are
with
an
unit that
K, i.e. a
Denote by AF(K) the value of the firm's option to install
AV(K).
Note that
this incremental unit.
option
this
value
has
if
even
it is
optimal for the firm to exercise it (just as a call option on
currently not
shares of a common stock has value even if it will not
uncertainty over
greater the
Also, the
here
concerned
incremental unit of capacity, given a current capacity
has value
invest, the firm
option to
In order to determine when to exercise its
the value of this option (just
as
a
be exercised today).
future demand, the greater will be
call
option
has
greater, value the
greater the price volatility of the stock on which it is written).
Assume the
Then k is the
by k.
i.e. the price
the firm
must pay to exercise the
Suppose demand conditions are such that it is rational for the firm
option.
exercise
the
option.
instead that AF(K) >
current K
is large
In
AV(K) - k.
that
This
is the
case, AF(K) = AV(K) - k.
might be
the case,
Now suppose
for example, if
and future demand is extremely uncertain, in which case
the firm will want to hold its option
Then what
on the incre-
firm's option
of the
"exercise price"
of capital,
mental unit
to
cost of a unit of capital is constant, and denote this cost
firm's optimal
to invest,
choice of
rather than
capacity K?
exercise it.
It is the largest
level K* such that:
7
What gives a firm this option? It may be that the firm owns a patent
More generally, the firm's
technology.
on a
particular production
managerial resources and expertise, reputation and market position enable it
to productively undertake investments that indivduals or other firms
cannot undertake.
- 7 AV(K*) = k + AF(K*)
(1)
keep adding
In other words, the firm should
point where
the value
of the
cost plus the value of the
capacity until
marginal unit
option to
it reaches the
is just equal to its purchase
install the
unit (an
option that is
closed, yielding AV(K) - k, once the unit is indeed installed).
what
Now,
is
the
of
an increase in uncertainty over future
The immediate effect, whatever
demand conditions?
is to
effect
increase the
value of
the current
option to
the firm's
invest in the marginal
But this means that all else
unit, i.e. to increase AF(K).
will want to hold less capacity than it would otherwise.
it is now worth more to the firm to keep its option
an increase
in uncertainty
will reduce
capacity K,
equal, the firm
The reason is that
to invest
alive.
Thus
firms' desired capital stocks, and
have a depressive effect on investment spending.
If there is considerable uncertainty over future demand
value of
the firm's options to invest will be large, and an investment rule
that ignores this will be grossly in error.
by
McDonald
and
Siegel
(1986)
has
projects might
require that
the present
double the cost of the project.
In fact, as the important paper
shown,
uncertainty the effect can be quite large;
can have
conditions the
an
for
investment in
value of
Also, changes
even moderate levels of
an individual
the project be at least
in the
level of uncertainty
a major effect on the critical present value needed for a positive
investment decision, and thus
such changes
should have
a major
effect on
investment spending.
In most
modelling work, effects of risk are handled by assuming that a
risk premium can be added to the discount rate used to calculate the present
value
of
a
project.
That
discount
rate is typically obtained from the
- 8 Capital Asset Pricing Model (CAPM).
of financial
But as we have learned
the correct
option pricing,
from the theory
discount rate cannot be obtained
without actually solving the option valuation problem, generally will not be
constant over
time, and
will not equal the average cost of capital for the
As a result, simple cost
firm.
or adjusted)
return (simple
of
capital
based
measures,
on
rates of
to equity and debt, may be poor explanators of
investment spending.
3.
Marginal
and Investment.
In essence,
incentive to
the
q
theory
invest whenever
of
says
investment
that
firms
marginal q -- the present value of a marginal
unit of capital divided by the cost of that unit -- exceeds one.
based on
ment. 8
is that
this theory
have not
been very
failing, but
one possibility
if risk is significant, the model is theoretically flawed.
marginal q should not equal one
value of
But models
successful in explaining invest-
There may be several reasons for this
one, because
have an
Instead it
in equilibrium.
In fact
should exceed
as we have seen, investment should occur only when the present
a marginal
unit of
capital exceeds
the cost
of the
unit by an
amount equal to the value of keeping the firm's option to invest alive.
To
see
this
more
clearly,
deciding whether to invest in an
let
us
return to the problem of a firm
of capacity. Recall that
incremental unit
the optimal investment decision is to invest up to the point K* where AV(K*)
= k + AF(K*).
8
Marginal q is the
present
value
of
the
marginal
unit of
For example, Abel and Blanchard (1983) find that even when it is
properly measured, marginal q "is a significant explanator of investment,
but leaves unexplained a large, serially correlated fraction of investment." Also, see Kopcke (1985).
- 9 capital -- in my notation, AV(K )
Then
-- divided
by the
cost of
the unit, k.
clearly q = AV(K*) > 1 in equilibrium.
A correct measure for marginal q could be defined as:
*
= [AV(K
q
which will
*
*
) - AF(K*)]/k
equal 1 in equilibrium.
be observed directly, nor can it
industry-wide data.
market value of the
will be
(2)
even more
The problem is that this measure cannot
easily
Furthermore, the
firm divided
misleading.
be
use of
from
other
firm or
an average measure of q (the
replacement cost
by the
The
computed
of its capital)
reason is that the market value of the
firm will include the value of capital in place plus the value of the firm's
options to
install more
capital in the future. 9
What is needed instead is
the value of capital in place less the value of those options.
Since the q theory has
models of
detail.
(1983).
become
investment spending,
prominent
as
a
basis
for structural
it is useful to discuss it in somewhat more
I do this with reference to the recent paper by Abel
The
model
that
they
developed is one of the most sophisticated
attempts to explain investment in a q theory framework;
constructed
measure
for
and Blanchard
marginal
rather
than
it uses a carefully
average
q,
incorporates
delivery lags and costs of adjustment, and explicitly models expectations of
future values of explanatory variables.
The model
is based
on the standard discounted cash flow rule, "invest
in the marginal unit of capital
9
Assuming
given by:
the
firm
has
if
the
chosen
present
discounted
value
of the
its capacity optimally, its value is
K*
Value =f AV(K)dK + f AF(K)dK
0
K*
i.e. the value of capital in place plus the value of options to productively
install more capital in the future.
III
- 10 -
expected flow
of profits
cost of the unit."
given the
Let
resulting from
the unit is at least equal to the
t(Kt,It) be the maximum value of profits at time t,
capital stock Kt and investment level It, i.e. it is the value of
profits assuming that variable factors are used optimally.
because of
costs of
It depends on It
aT/aI < 0, and 82r/3I2 < 0, i.e. the more
adjustment;
rapidly new capital is purchased and installed, the more costly it is. Then
the present value of current and future profits is given by:
Vt
Et[j
[
(l+Rt+i)
j=0 i=O
where Et
denotes an
]It+j(Kt+jIt+j)]
expectation, and
(3)
R is the discount rate.
Maximizing
this with respect to It, subject to the condition Kt = (1-6)Kt_l + It (where
6 is the rate of depreciation), gives the following marginal condition:
(4a)
-Et(a3t/aIt) = qt '
qt = Et[ Z [
where
j=0 i=0
In other
(1+Rt+i )
](
t+j
words investment should occur up to the point where the cost of an
additional unit of capital
expected
flow
of
is just
incremental
equal
profits
to
autoregressive
representations
tations of future values.
Their
the
present
value
resulting from the unit.
Blanchard estimate both linear and quadratic
vector
(4b)
+j/aKt+j)(1-6)
t+j
of
approximations to
Rt
of the
Abel and
qt. and use
and ant/Kt to model expec-
representation
of
Rt
is based
on
a
weighted average of the rates of return on equity and debt.
If
the
correct
discount
rates
would indeed accurately represent the
firm.
The
Rt+i were known, eqns. (4a) and (4b)
optimal
investment
decision
of the
problem is that these discount rates are usually not known, and
generally will not be eual to the average cost of
capital of
the firm, or
-
some related variable.
valuing
-
Instead, these discount rates can only be determined
as part of the solution to
involves
11
the
the
firm's
firm's
optimal
options
to
investment
make
(irreversible)
investments (now or in the future), and determining
optimal
exercise
of
those
options.
problem,
This
marginal
the conditions
for the
Thus the solution to the investment
problem is more complicated than the first-order condition given by (4a) and
(4b) would suggest.
As
an
example,
consider
a
project
that
has zero systematic (non-
diversifiable) risk.
The use of a risk-free interest rate for
to
a
much
too
large
value
for qt. and might suggest that an investment
expenditure should be made, whereas in fact it should be
more, there
is no simple way to adjust R properly.
calculation
ignores
invest.
This
the
R would lead
opportunity
cost
of
delayed.
Further-
The problem is that the
exercising
the
option to
may be why Abel and Blanchard conclude that "our data are not
sympathetic to the basic restrictions imposed by the q theory, even extended
to allow for simple delivery lags."
4.
Does Risk Help Explain Investment Spending?
We
have
seen
that
when
investment
is
irreversible,
especially strong link between risk and investment spending.
uncertainty
over
future
demand
raises
that
option
alive
(by
is an
An increase in
the value of the firm's option to
invest in a marginal unit of capital, and therefore raises
keep
there
the incentive to
not investing) rather than exercising it (by
investing), so that
other
things
Furthermore, recent
studies have
equal,
investment
shown that
spending
will fall.
in theory, this effect can be
- 12 quantitatively important.l 0
But do the data support the theory?
finding a
good measure of
One possibility is to use survey data.
An alternative,
A major problem with testing the
market uncertainty.
theory is
which I pursue here, is to use
data
markets become
we would
more volatile,
on
the
and most
the case,
aggregate stock
When product
returns will
be larger.
This
during the recessions of 1975 and 1980,
for example,
dramatically during
market.
expect stock prices to also become
more volatile, so that the variance of stock
was indeed
stock
the Great
Depression.
Thus
the variance of
returns should be a reasonable measure of aggregate product
market uncertainty.
Stock returns themselves are also a
as
spending,
(1984).
was
illustrated
the
recent
aggregate investment
work of Fischer and Merton
We would expect stock returns to have predictive power because they
reflect new
information about economic variables.
imply revised exectations about
the discount
rates used
to
aggregate
future corporate
to capitalize
show that the predictive
respect
by
predictor of
power of
investment
That new information can
earnings, and
those earnings.
stock returns
spending,
but
Fischer and Merton
is strong,
with
changes in
not only with
respect
to
other
components of GNP as well.
Our concern here is whether the variance of stock returns -- my measure
of aggregate
product market
uncertainty --
also has predictive power with
respect to investment, and whether that predictive power goes beyond that of
stock
appear
returns
in
an
themselves,
empirical
as
well
investment
as other variables that would usually
equation.
Ideally,
this
should be
IOSee McDonald and Siegel (1986), Brennan and Schwartz (1985), Majd and
Pindyck (1985), and Pindyck (1986).
- 13 examined in the context
firms' optimizing
of a
structural model
decisions.
However,
different
vintages,
etc.
derived from
such a model would be quite compli-
cated, especially if it were to take account
of
of investment
Instead,
of construction
lags, capital
I conduct two related tests of an
exploratory nature.
First, I
"cause" the
test whether
real growth
and Sims (1972).
First, X
To say that "X causes
should help
should contribute
of stock
returns can
be said to
rate of investment, in the sense of Granger (1969)
to predict
values of Y, the addition of
past
Y," two
conditions should
be met.
Y, i.e. in a regression of Y against past
values
of
X
as
independent variables
significantly to the explanatory power of the regression.
Second, Y should not help to
helps to
the variance
predict X,
it is
predict X.
(If X
likely that
helps to
predict Y
and Y
one or more other variables are in
fact "causing" both X and Y.)
In each case I test the null hypothesis that one variable does not help
predict the
other.
For
example, to
test the null hypothesis that "X does
not cause Y," I regress Y against lagged values of Y and lagged values
(the
"unrestricted"
regression),
and
then
values of Y (the "restricted" regression).
determine whether
the lagged
values of
regress Y only against lagged
A
simple
X contribute
explanatory power of the first regression. 1 1
of X
If they
F
test
is
used to
significantly to the
do, I
can reject the
l1 The F-statistic is as follows:
F = (N - k)(SSRr - SSRu)/r(SSRu)
where SSRr and SSR U are
unrestricted regressions
the number of estimated
the number of parameter
F(r/N-k).
X-----l-
---^11_ ___
the sums of squared residuals in the restricted and
respectively, N is the number of observations, k is
parameters in the unrestricted regression, and r is
restrictions.
This statistic is distributed as
III
- 14 null hypothesis
and conclude that the data are consistent with X causing Y.
The null hypothesis that "Y does
not cause
X" is
then tested
in the same
manner.
A weakness of this test of causality is that a third variable, Z, might
in fact be causing Y, but might be contemporaneously correlated with X.
example, lagged
values of the variance of stock returns might be a signifi-
cant explanator of the growth of investment in
might
become
For
insignifant
when
other
a bivariate
variables
returns themselves, interest rates, etc.
regression, but
are added, such as stock
Therefore as a
second exploratory
test I also run a set of simple regressions of the growth rate of investment
against
stock
returns,
the
variance
of
stock
returns,
and
a
set of
additional explanatory variables that usually appear in empirical investment
equations.
Data.
These causality tests and multivariate regressions require a series for
the variance of stock returns.
I constructed such a series using daily data
for the total logarithmic return on the combined value-weighted New York and
American
Stock
Exchange
Index,
obtained
from the CRISP tape.
daily data I constructed non-overlapping estimates
by calculating
sum
the
of the
From this
monthly variance
the sample variance, corrected for non-trading days.
monthly
estimates
non-overlapping estimates
for
of the
each
quarter,
to
quarterly variance,
obtain
a
I then
series
denoted by VAR.
returns themselves were also summed over each quarter and then
of
The
adjusted for
inflation, to yield a quarterly series for real stock returns (RTRN).
Because the
daily stock
return data
quarter of 1962 through the 4th quarter of
were available only from the 4th
1983, and
because the causality
-
tests
and
regressions
require
15
-
lags
of
several
quarters, the sample is
limited to the 21 year period 1963-4 to 1983-4.
I test whether the variance
of
stock
returns
can
help
growth rate of real non-residential fixed investment (INGR).
the two
major components
structures
(ISGR),
equipment (IEGR).
and
of INGR,
the
the growth
growth
rate
of
rate of
real
predict the
I also examine
real investment in
investment in durable
These multivariate regressions also include the following
additional explanatory variables:
the quarterly change in the BAA corporate
bond rate (DRBAA), the change in the 3-month Treasury bill rate (DRTB3), the
change in
the rate
of inflation
Producer Price Index (DINF),
Series
for
real
and
investment
as measured
by the rate of growth of the
the
rate
and
growth
its
of
real
GNP (GNPGR).
components, GNP, the Producer Price
Index, and the interest rates were all obtained from the Citibank database.
Causality Tests.
Granger causality tests are conducted as follows.
For
each investment
series (INGR, ISGR, IEGR), we test the pair of null hypotheses: (i) VAR does
not help predict the growth rate of investment, and (ii) the growth
investment does not help predict VAR.
accept the second, then the
returns
causing
data
investment.
are
Each
rate of
If we reject the first hypothesis and
consistent
hypothesis
with
is
variance
tested
of stock
by running the
unrestricted regression,
n
Yt
=
n
a + i=l b.Y
cX
1 t-i + i=
t-i
(6)
and the restricted regression,
n
i1
i t-i
(7)
- 16 and testing
11.)
the parameter
restrictions ci
= 0
for all
i.
(See Footnote
The tests are done for the number of lags, n, equal to 4 and 6.
of these
The results
shows the R2 's for the
causality tests are summarized in Table 1, which
and
restricted
unrestricted
Observe that for every investment
the restrictions c i = 0.
F-statistic for
variable and for both 4 and 6 lags, we reject the null
does not
help predict
opposite
null
variance."
is
hypothesis "variance
the growth of investment," and we fail to reject the
hypothesis
This
and the
regressions,
at
"the
least
growth
of
investment
to
helps
predict
evidence that market risk, as
preliminary
measured by the variance of stock returns, plays
role in the
a significant
determination of investment spending.
Multivariate Regressions.
further test, I run a set of regressions similar to those used by
As a
Fischer and Merton (1984) in their
returns.
Each
stock
the predictive
returns,
of variance
lagged values
and
finally
against
lagged
and lagged
corporate bond
values of
variance, lagged stock
returns, and the lagged values of four additional variables:
the BAA
power of stock
investment variable is regressed first against lagged values
of variance, then against
real
study of
the
change in
rate, the change in the 3-month Treasury bill rate,
the change in the rate inflation, and the rate of growth of real GNP.
The results are summarized in Table 2.
of each
Note
that three
lagged values
independent variable appear in the regressions, but only the sum of
the estimated coefficients is shown
for
each
variable,
together
with an
associated t-statistic.
As one
would expect
from the results of the causality tests, variance
is highly significant when it
appears
as
the
only
independent variable.
- 17 Variance continues
to be highly significant after adding real stock returns
to the regression, and this second independent variable
cant
explanator
of
the
growth
of
total
is also
a signifi-
non-residential investment, as
Fischer and Merton found, as well as investment in equipment, but it
significant for
structures.
investment in
When
is not
the remaining explanatory
variables are added, variance continues to be significant in the regressions
for non-residential
investment and structures, but not for equipment.
only significant explanator of equipment investment
is the
(The
BAA bond rate.)
reflect the fact that the irreversibility of investment is greater
This may
for structures than for equipment.
But the importance of our risk measure is also evident
tudes of the variance coefficients.
went from about .01
regressions
in the
3, 6, and
The quarterly variance of stock returns
1960's to
9
we
see
about .02
around 5 percent real
in the
mid-1970's.
From
that this implies an approximately 4.5
percentage point decline in the growth rate of
drop from
from the magni-
investment in structures (a
growth during the 1960's to only slightly
positive real growth), a 2.5 percentage
point drop
in the
growth rate of
investment in equipment, and a 3 percentage point drop in the growth rate of
total investment.
5. Conclusions.
I argued in the beginning of this paper that there are good theoretical
reasons to
expect market
risk to have a major role in the determination of
investment spending.
This idea is not new; it has been elaborated upon in a
number
during
of
articles
the
past
few years.
missing from most empirical work on investment.
However, it seems to be
This may be a reflection of
III
- 18 -
the
fact
that
most
theoretical
uncertainty are quite complicated,
models
so
of irreversible investment under
that
their
translation
into well-
specified empirical models represents a formidable task.
This paper
has not attempted to make that translation.
sought and found only a rough empirical verification
risk.
The
for the
importance of
tests and regressions reported in the previous section should be
viewed as exploratory, and limited in their implications.
are based
Instead I have
on highly
For example, they
aggregated data, and what is probably a very imperfect
measure of market risk.
Nonetheless,
regarding the
these
effects of
findings
support
recent
theoretical
risk on irreversible investment, and they suggest
that the explicit inclusion of market risk measures can improve
to explain
and predict
results
investment spending.
our ability
The development of structural
models that include such measures should be an important research priority.
-
19
-
Table 1 - Causality Tests
(Quarterly Data: 1963-4 to 1983-4)
n
n
Regression of:
Yt = a +
biYt-i +
i=1
No.
Lag (n)
Regression Pair
Y
X
CiXt-i
i=1
2 2
R/Ru
F(HO
1
2
4
4
INGR
VAR
VAR
INGR
.355/.495
.298/.356
4.98
1.63
3
4
4
4
ISGR
VAR
VAR
ISGR
.201/.326
.298/.347
3.33
1.38
5
6
4
4
IEGR
VAR
VAR
IEGR
.277/.442
.298/.337
5.33
1.09
7
8
6
-6
INGR
VAR
VAR
INGR
.388/.548
.299/.410
3.87
2.05
9
10
6
6
ISGR
VAR
VAR
ISGR
.225/.361
.299/.404
2.35
1.94
11
12
6
6
IEGR
VAR
VAR
IEGR
.304/.473
.299/.388
3.52
1.58
#F(4/75) for n = 4, F(6/66) for n = 6.
,ignificant at 5% level.
Significant at 1% level.
b=0)
III
- 20 -
Table 2 - Variance of Stock Returns as a Predictor of Investment
(Quarterly Data, 1963-4 to 1983-4)
Indep.
Var.
INGR
Reg. No.
1
CONST
INGR
2
INGR
Dependent Variable
ISGR
ISGR
ISGR
3
.0314 .0264 .0199
(7.72) (6.30) (2.38)
4
5
6
.0261 .0228 .0190
(5.36) (4.28) (1.75)
IEGR
7
IEGR
8
IEGR
9
.0349 .0291 .0201
(6.96) (5.67) (2.01)
i VARi -6.307 -5.306 -3.282
-6.262 -5.470 -4.786 -6.478 -5.378 -2.563
=1
-(-5.98)
(-4.92)(-2.32) (-4.98)(-4.20)(-2.59) (-4.99)(-4.08)(-1.51)
i RTRN
i=1
-1
i DRBAA
i=1
.1738 .1229
(3.46) (1.91)
.0769 .0887
(1.22) (1.05)
.2150 .1388
(3.49) (1.80)
-.0308
(-2.93)
- .0056
(-0.41)
(-3.25)
i
- .0409
j DRTB3
=1
-
.0167
(2.44)
iDINF-i
-.2827
(-0.41)
(-1.05)
.1495
(0.18)
.3505
(0.66)
.0816
(0.18)
.5428
(0.86)
.0222 .0187 .0108
(2.95) (2.59) (1.46)
.0226 .0202
.0126
(2.51) (2.20) (1.32)
.0215 .0174 .0096
(2.33) (1.97) (1.11)
.425
.501
.627
.320
.335
.477
.350
.442
.596
SER
.0204
.0194
.0184
.0244
.0247
.0239
.0252
.0238
.0216
DW
1.40
1.53
1.84
1.65
1.67
1.88
1.60
1.78
2.19
i11
jGNPGR
i=1
RHO
Variables:
Note:
.0199
.0144
(1.76)
(2.23)
-.9405
INGR = Quarterly growth rate of real business fixed
investment.
ISGR = Growth rate of real investment in structures.
IEGR = Growth rate of real investment in durable equipment.
VAR = Quarterly variance of real return on NYSE Index.
RTRN = Real return on NYSE Index.
DRBAA = Change in BAA corporate bond rate.
DRTB3 = Change in 3-month Treasury bill rate.
DINF = Change in inflation rate, as measured by PPI.
GNPGR = Quarterly growth rate of real GNP.
t-statistics in parentheses.
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