The Cost of Business Cycles under Endogenous Growth
Author(s): Gadi Barlevy
Source: The American Economic Review , Sep., 2004, Vol. 94, No. 4 (Sep., 2004), pp. 964990
Published by: American Economic Association
Stable URL: http://www.jstor.com/stable/3592801
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide
range of content in a trusted digital archive. We use information technology and tools to increase productivity and
facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
https://about.jstor.org/terms
is collaborating with JSTOR to digitize, preserve and extend access to The American Economic
Review
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
The Cost of Business Cycles Under Endogenous Growth
By GADI BARLEVY*
Robert E. Lucas, Jr. argued that the welfare gains from reducing aggregate consumption volatility are negligible. Subsequent work that revisited his calculation continued to find small welfare benefits, further reinforcing the perception that business
cycles do not matter. This paper argues instead that fluctuations can affect welfare,
by affecting the growth rate of consumption. I show that fluctuations can reduce
growth starting from a given initial consumption, which can imply substantial
welfare effects as Lucas himself observed. Empirical evidence suggests the welfare
effects are likely to be substantial, about two orders of magnitude greater than
Lucas' original estimates. (JEL D60, E32, E63, 040)
In his famous monograph, Robert E. Lucas,
discounts future utility. Suppose this consumer
is given a consumption stream
Jr. (1987) argued that business cycles in the
post-War United States involved at most negli-
Ct = A'(1 + 8,)Co
gible welfare losses, thereby challenging the
(1)
presumption that stabilizing the cyclical fluctuations that persisted during this period would
where A is a constant greater than one and st is
an independently and identically distributed
have been highly desirable. His argument can
be stated as follows. Consider a representative
(i.i.d.) random variable with mean zero. That is,
average consumption starts out at C0 and grows
risk aversion (CRRA) utility function over conat rate A, so that average consumption after t
sumption streams {Ctj o0, i.e.,
periods will equal AtCo. Actual consumption
will deviate from this average by a factor of 1 +
00 c1- 1
et. Using per capita consumption growth from
consumer with a conventional constant relative
the post-War era, we can estimate A and the
U({Ct})= E 8tvariance
' of st. To determine the costs of fluct=0
tuations, Lucas asked what constant fraction of
where y > 0 measures relative risk each
aversion
and
year's consumption
the consumer would
<3 < 1 denotes the rate at which
be willing
the to
agent
give up to avoid fluctuations, i.e.,
to replace st with zero in each and every period.
For reasonable values of y, the answer turns out
* Economic Research Department, Federal
Bank
to Reserve
be astonishingly
small, less than one-tenth of
of Chicago, 230 South LaSalle Street, Chicago,
1 percent.IL
By 60604,
contrast, Lucas calculated that a
and National Bureau of Economic Research (e-mail:
consumer would sacrifice as much as 20 percent
gbarlevy@frbchi.org). I have benefited from comments on
this and an earlier version of the paper by Fernando Alvarez,
of his consumption each year when y = 1 to
Marco Bassetto, Jeff Campbell, Larry Christiano, Elhanan increase the average growth rate A by 1 percentHelpman, Zvi Hercowitz, Sam Kortum, Robert Lucas, Alex age point. Thus, Lucas concluded that growth
Monge, Assaf Razin, Helene Rey, and seminar participants
matters, but business cycles, at least of the magat Northwestern, Wisconsin, Harvard, Columbia GSB,
nitude
that prevailed in the United States over
NYU, Princeton, Maryland, Ohio State, the Chicago Fed,
the Canadian Macro Study Group, the Society of Economic the post-War period, do not.
Dynamics, and the National Bureau of Economic Research,
Although the calculation above abstracts
as well as two anonymous referees. I am also grateful to
Valerie Ramey for supplying me with the data and the
from several important considerations, its im-
plication that consumption volatility at busi-
original code from her paper. The views expressed here do
not necessarily reflect the position of the Federal Reserve ness-cycle frequencies does not matter much for
Bank of Chicago or the Federal Reserve System.
welfare has proven to be quite robust. For
964
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
example, Ay?e imrohoroglu (1989), Andrew
Atkeson and Christopher Phelan (1994), Per
Krusell and Anthony Smith (1999), Paul
In
965
I
C,
I"
I
I
I
I
Beaudry and Carmen Pages (2001), and Kjetil
I
I
I
I
Storesletten et al. (2001), depart from the representative agent setting and calibrate income
streams to individual-level data, assuming only
I
I
I
I
I~~~~~~~~~~~~~~~~~~~~~~
imperfect insurance arrangements across
agents. Since agents can still save against future
income shocks, the implied costs of business
cycles in these papers are small, typically less
than 1 percent of consumption per year, and in
some cases are even negative. Maurice Obstfeld
(1994) maintains a representative agent framework but allows shocks to be persistent rather
than i.i.d., and again finds relatively small costs.
Lastly, Obstfeld (1994), John Campbell and
John Cochrane (1995), James Pemberton
(1996), James Dolmas (1998), Fernando Al-
I
I
I
I
I
(a) Increased girowth from reduced volatility of investmnent
I
I
(a Icrasd roth~o rduedvoatliy f ,"' ten
I
I
In
C,
In C, II~~,"
I,
,"
,"
t
,'
_s
t;77~~~~~~
,
t~~~~~
varez and Urban Jermann (1999), Thomas Tal-
larini (2000), and Christopher Otrok (2001)
examine departures from CRRA utility. With
the exception of Campbell and Cochrane and
Tallarini, whose findings are challenged in
some of the other papers, these experiments
(b)
Increased
FIGURE
again tend to find small costs of fluctuations at
growt
1.
CO
GROWTH
business-cycle frequencies for reasonable pa-
rameter configurations. Thus, it appears that there
is limited scope for generating large costs of busi- The
notion
ness cycles from aversion to consumption risk.1 large
welf
The results above would seem to deny that growth
ha
business cycles can ever matter much for wel- cluding
E
al.
(1999
fare. Nevertheless, this paper argues that cycles et
can be associated with considerable welfare
Maury
(2
costs, about two orders of magnitude greater
than those Lucas originally computed. These
costs are not due to consumption volatility per
se, as maintained in previous work, but to the
fact that cyclical fluctuations can affect the
economy's long-run growth rate. The motivation for examining growth effects comes from
Lucas' original insight that changes in growth
rates can have large welfare effects: even if
aggregate fluctuations have a modest effect on
the rate at which an economy grows, they could
in principle have a significant effect on welfare.
1 Lucas (2003) surveys the literature on the costs of
consumption risk over the business cycle that emerged since
his original monograph and reaches a similar conclusion.
Pommeret
to
generat
of
the
ma
ence.
The
r
models
do
type
impli
efits
from
much
an
a
sumption
level
of
co
illustrated
dashed
line
the
models
run
growth
that
are
al
in
equilibr
creases
inv
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
966
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
raise
welfare if they help agents to coordinate
consumption will indeed grow at a faster
rate.
But since such investment takes resources
onaway
an equally productive but less volatile techfrom consumption, average initial consumption
nology). Thus, this paper does not set out to
advocate
will fall, as illustrated in the bottom panel
of in favor of stabilization; rather, its
Figure 1. Clearly, the welfare implications
purpose
of ais to offer a rationale for why business
cycles matter. Documenting a large cost of cygiven change in the growth rate will be different
cles isthe
an important result in its own right given
under these two scenarios. Not surprisingly,
benefits from reoptimizing between present
the grave
and importance people often seem to attach the
to economic fluctuations despite previous
future consumption are much smaller than
benefits of being able to achieve more
results
rapid
that suggest they should not, and it opens
the door to a role for stabilization, at least in
growth.
This paper reformulates the endogenous
growth models above in a way that does give
rise to the growth effect illustrated in the top
panel of Figure 1. It does this by introducing
diminishing returns to investment, which im-
plies that the growth rate will be a concave
some scenarios, that previous calculations
would deny. The basic insights developed here
can and should be used to explore environments
where policy can play a beneficial role in order
to determine whether stabilization policy is ultimately desirable.
function of the level of investment. As a result,
The paper is organized as follows. Section I
even if eliminating fluctuations had no effect on
average investment, and thus no effect on aver-
develops an endogenous growth model that allows for diminishing returns to investment. Section II quantifies the cost of fluctuations implied
by the model using data on growth. Section III
age initial consumption, it would still lead to
more rapid growth by making investment less
volatile. Intuitively, eliminating fluctuations reallocates investment from periods of high investment to periods of low investment. Since
the marginal return to investment is higher
when there is less investment, this allows agents
to achieve more growth from the same re-
sources. The first part of the paper formalizes
this argument using a familiar model of endogenous growth.
In the remainder of the paper, I assemble
various pieces of evidence on the extent of
diminishing returns to investment. These suggest that eliminating fluctuations will increase
the growth rate of per capita consumption from
2 percent to between 2.35 and 2.40 percent if we
held average investment fixed. For y = 1, this
implies a cost of cycles of 7-8 percent of consumption per year, and the cost only rises when
I turn to an alternative set of preferences that
can better replicate the volatility of aggregate
investment over the cycle. While this suggests
business cycles are quite costly, it need not
examines whether such a cost can be reconciled
with other macroeconomic time series. Section
IV calibrates the model to gauge whether agents
would ever respond to macroeconomic shocks
in a way that implies such a large cost, as
opposed to trying to offset such shocks. Section
V concludes.
I. Endogenous Growth with Diminishing
Returns to Investment
To study the effects of economic fluctuations
on growth and welfare, I need a model in which
the growth rate is determined endogenously.
Towards this end, I use a stochastic AK growth
model. This specification has become a staple
for modeling endogenous growth under uncertainty, and using it facilitates comparison with
the previous literature. The first to analyze this
model were David Levhari and T. N. Srinivasan
(1969), who used it to study savings decisions
under uncertainty. They in turn solved an
follow from this result that stabilization is de-
infinite-horizon version of a problem that was
sirable. This largely depends on the source of
aggregate shocks. For example, if cycles are due
to productivity shocks, policy makers will only
end up making agents worse off by attempting
to offset such shocks with countercyclical policy (although policy makers can still potentially
originally studied by Edmund Phelps (1962).
Hayne Leland (1974) subsequently reinterpreted this model in terms of long-run economic
growth. Many authors have since used variations of this basic model to study endogenous
growth in the face of aggregate uncertainty.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
967
The economy consists of a representative agent
x, Prob(At+ 1 - x A,) is weakly decreasing in
who derives utility only from consumption. To
At. Thus, a higher realization of productivity
simplify the exposition, I focus on the planning
today is associated with a weakly higher exproblem for this economy. One can show that the
pected productivity next period. This assumpallocation of resources that solves this problem
tion ensures the agent will be better off at higher
coincides with the equilibrium allocation in a delevels of aggregate productivity. Note that it
centralized market economy. Time is discrete, and
includes the case where At is i.i.d. I further
the agent discounts the future at rate /3. For now,
assume that the values of At are such that exI assume per-period utility is isoelastic in conpected discounted utility is well-defined, i.e.,
sumption, i.e., for a given consumption stream
the growth rate cannot exceed the discount rate,
{Ct} t=, the utility of the agent is equal to
and the planning problem has an interior solution. Finally, I assume the initial distribution
over A, corresponds to the invariant distribution
l- C y-- 1
of the Markov chain (which implicitly assumes
(2)
=E t t
t=0
such a distribution exists and is unique). I evaluate welfare using this distribution throughout
In evaluating the benefits of growth,
the paper, i.e.,Lucas
the expected utility of the agent
(1987) considered the case where
y = prior
1, toi.e.,
is calculated
the resolution of uncerlog utility, a value that falls within
the
range
ofof productivity Ao.
tainty
over the
initial level
estimates for intertemporal elasticity
substiSince of
output
is proportional to capital, the
tution found in the literature, e.g.,time
Larry
path ofEpstein
output (as well as consumption)
and Stanley Zin (1991). I similarlydepends
useonthis
caseof the capital stock Kt.
the evolution
as my benchmark for calculating
the
of
At date
0, thecost
agent is endowed
with some initial
fluctuations. However, below I argue
that
this
amount of
capital Ko.
For any date t, if the agent
specification for utility does abegins
poor
job
the period
withof
Kt units of capital, a fracmatching certain empirical regularities,
which
motion 8 will
depreciate
over the period, so only
tivates me to eventually turn to a(1more
general
- 8)Kt units
remain by the start of the next
formulation that includes (2) as a period.
special
case.
The agent
can add to this stock by setting
The agent has access to a production
aside sometechnolof the output from the current period
ogy that converts inputs into consumption.
The with his existing capiand converting it, together
only input for producing consumption
goods
tal, into capital
for useis
in the subsequent period.
capital. Production is linear in capital,
where
the new capital is charThe technology
for producing
amount that can be produced from
a aunit
acterized by
function of
(D(It, Kt) that depends on
capital fluctuates stochastically over
time,
i.e.,
the amount
of output
set aside for investment It
and the existing stock of capital K,. The function
(3)
Y, = A,K,
I( ?, ? ) is assumed to be homogeneous of degree
1 and increasing in its first argument. Hence, we
where At follows a Markov process. Thus, the
can rewrite this production function as
source of fluctuations in this economy are
shocks to productivity. However, as noted by
Jonathan Eaton (1981), we could reinterpret
these shocks as government policy shocks; sup-
pose aggregate productivity is constant over
time, but there is a government that collects a
random fraction r of income in taxes that it uses
to finance contemporaneous purchases that do
not affect the agent's utility. This leaves the agent
with an income of Yt = (1 - T)AKt AtK,.
In what follows, it will prove necessary to
impose some regularity conditions on the
Markov process At. First, I require that for any
(1i,, K,) = 4) Kt
Kt
where ('(') > 0. The stock of capital available
for production in period t + 1 is thus
Kt+l= (1
- 8)K,.
Repeated substitution of the above equation
yields the capital stock at date t as a function of
the initial capital stock Ko:
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
968
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
where A, 1 + (isAs) - 8 is the growt
(4) Kt= i 1 + &K -8 Ko.
c,A,
of the capital stock, t - c - 1 is the
deviation of consumption from its trend, and
The original Levhari and Srinivasan Co
(1969)
= coAoKo is the initial level of consumption. Note
model is a special case of this model where
the that if the growth rate of capital
As were
function 4(() is equal to the identity function
and constant, (5) would simplify to
8 = 1. While several authors have by now
At(l +
deE?)Co, precisely the form Lucas posited. But (5) emerges endogenously as an
parted from the assumption of full depreciation,
the assumption that 4(() is linear is still commonoptimal response to the underlying economic
environment
rather than as an exogenous
place. But following Hirofumi Uzawa (1969),
it is
quite natural to allow (.) to be concave, implying
specification.
diminishing returns to investment. Formally,Following
conLucas, I measure the cost of ag-
cavity in >() implies that holding capitalgregate
fixed,fluctuations as the additional fraction of
consumption per period the agent would require
less to the stock of capital. This concavity can be in the stochastic environment so that his ex ante
interpreted as convex adjustment costs, since in- utility (i.e., prior to the realization of {At)t=) is
creasingly more capital is required to absorb new the same as his utility if we were to move him
investment goods. As I discuss in more detail to an environment with the same initial cap-
each additional unit of investment will contribute
ital stock but where productivity is constant
and equal to the unconditional average productivity in the stochastic environment. This
measures how much better off the agent
of the period. Out of this output, the agent would be if the technology were equally
chooses to consume an amount C, and uses the
productive on average but did not fluctuate
remainder It = Yt -Ct to invest in capital for over time. For notational convenience, let an
below, empirical evidence suggests there is indeed
some curvature in 4(') in practice.2
To summarize, output in period t is produced
using all of the capital available at the beginning
the next period. Define ct = C/Yt as the fraction
asterisk denote the value of a variable in the
of output the agent consumes and it = IlYt =
counterfactually stable environment. Thus,
1 - ct as the fraction he sets aside for investment. Using this notation, we can rewrite the
agent's consumption stream in a form reminiscent of Lucas' original specification:
productivity A* is constant for all dates t and
(5) Ct = ctAtKt
hypothetical in the sense that it cannot be
avoided by stabilization policy. Although the
t
= ctAt[n(l + (isAs)- )]Ko
s=O
t
[n AS(l + et)Co
s=0
is equal to E[A] A*.
A few remarks about the interpretation of this
cost are in order. If At reflects exogenous technology shocks, the cost of fluctuations is purely
government can replicate the effects of productivity shocks on the agent through taxes and
subsidies, the original allocation is Pareto optimal, and any self-financing scheme that fools
him into different consumption and savings
choices will only lower his welfare. Hence, the
cost of cycles should not be viewed as the gains
from pursuing a feasible stabilization policy.
By contrast, if fluctuations in At reflect spu-
riousto
fiscal
policy shocks, the cost of cycles
2 As an aside, diminishing returns also serve
dampen
be avoided
simply by eliminating arbithe response of investment to changes incan
A. This
helps to
address a common critique of AK growthtrary
models,
namely
policy
variability, in which case the cost
that policy changes that ought to affect investment have
of cycles is also the value to stabilization.
little effect on growth empirically. While some have argued
However, for this logic to go through, it is
that policy changes have no effect at all on long-run growth,
important
that fluctuations be spurious rather
Ellen McGrattan (1998) argues that these effects
are apparent in longer time series.
than an optimal response to some other un-
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
969
derlying shock.3 For example, we would not
PROPOSITION: Suppose Prob(At,+1 - x At)
It
want local governments to smooth expendiis weakly decreasing in At. Then itAt = t is
tures on snow removal over the year. AlKt
though smoothing these expenditures would
increasing in At.
eliminate one source of volatility, it would
prevent resources from being allocated to ad- To understand the welfare implications of
dress underlying weather shocks that are seacyclical fluctuations, it will help to work
sonal in and of themselves.
Since the utility of the agent depends on the
consumption stream he faces, we first need to
solve for the optimal consumption in each environment. The representative agent must solve
through the different ways in which shifting
from stochastic productivity {At) to a constant
productivity A* induces the agent to change his
consumption. First, eliminating fluctuations induces the agent to choose a consumption path
that does not fluctuate around its trend. For-
V(K,, Ao)-maxEo, ,B-'
Ct
t=
X
C1_7
cy
O
mally, when A* is constant for all t, the agent
will choose to consume a constant fraction c* of
output. But this implies the deviation from trend
consumption in (5) will equal
s.t. l. K,+= g) +1- K,
,= -1A = 1=0.
c*A* c*A*
2. A0, K0, and the law of motion for A,.
Since the agent is risk-averse, elim
from trend makes him better off. But
An important result from solving the ations
above
when
problem is that when At fluctuates over time,
theLucas (1987) computes the implied welagent will choose to vary his investmentfare
rategain assuming that all observed fluctua-
tions
in consumption growth reflect deviations
ItKt with At. Consequently, the growth rate
t =
from trend, the welfare gains from eliminating
1 + O(I/Kt) - 8 = 1 + (itAt) - 8 will
fluctuate over time. Establishing this result re- such deviations turn out to be negligible for
quires additional technical assumptions, namely reasonable utility specifications.5 Simply put,
that Q(.) is strictly concave and that it satisfies deviations from trend per capita consumption
the boundary conditions limxo +'(x) = oo and over the post-War period are not large enough
limx, o '(x) = 0. Under these assumptions, we to generate significant costs of cyclical fluctuahave the following proposition, whose proof is tions for reasonable degrees of risk aversion.
Second, since the agent will choose to set
contained in an Appendix:4
aside a constant fraction i* of his income for
investment when productivity is stable, eliminating fluctuations in aggregate productivity induces the agent to choose a consumption path
3 Arbitrary fluctuations are not limited to capricious
policy-making. Sunspots and coordination failures can also with a deterministic trend rather than a stochaslead to spurious volatility in productivity. Examples include tic trend. Thus, stabilization eliminates both
Jess Benhabib and Roger Farmer (1994), who generate fluctuations around trend consumption as well
sunspots in models with increasing returns to scale, and
Andrei Shleifer (1986) who generates sunspots from coor-
as fluctuations in trend consumption. Once
dination failures.
4 The fact that At is increasing in At implies trend growth
in investment and output are higher when these variables are consumption and output growth can still be positively corabove their trend. That is, if we decompose Y, and I, in the related given they share a common trend.
same way as consumption so that es is the deviation of
5 Lucas' calculation assumes deviations from trend are
output from trend and 't is the deviation of investment from
i.i.d., while the model allows deviations to be serially cortrend, then sE and etl are both positively correlated with A,. related. More persistent shocks would generate larger costs.
This will not necessarily be true for consumption, i.e., the e, But as I discuss below, allowing for more persistent shocks
term in (5) may be negatively correlated with A,, as I in fact to the level of consumption does not lead to substantial costs
find empirically. Even when this correlation is negative, of fluctuations.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
970
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
again, this will make the agent better off 1
given
+ 4(i*A*) - 6 = 1 + O(E[itA]) - 6
his aversion to risk. But since fluctuations in
trend consumption are permanent, they reduce
> 1 + E[[(itAt)] - S.
welfare by more than stationary fluctuations
around trend. Still, when Obstfeld (1994) cal-Thus, merely eliminating volatility in investculates the implied welfare gain under the asment will lead to more rapid growth, even if the
sumption that all observed fluctuations in
average amount of resources set aside for investment remains unchanged. If we then allow
consumption growth represent i.i.d. permanent
shocks to trend, he again finds relatively small
the agent to freely choose his investment optiwelfare costs. Somewhat larger costs can arise
mally and he chooses some i* + E[itAt]/A*, the
if we assumed persistent rather than i.i.d. shocks
long-run growth rate will change further. The
to trend, as is allowed under the more general
direction of the change depends on whether the
Markov structure of At. But empirically, conagent desires higher or lower investment in the
sumption growth exhibits fairly low persistence,
absence of shocks. Both scenarios are possible
as documented among others by Lawrence
for different parameter values. The effect of
Christiano et al. (1991).6 This reaffirms Lucas'
eliminating fluctuations in At on growth can
original observation that the volatility of per
thus be decomposed into two parts: the part due
capita consumption over the cycle is so small
to eliminating the volatility of investment
around
is
its original average, and the part due to
changes in average investment in response to
moving to a more stable environment.
To see why it is important to distinguish
that the gain from smoothing consumption
negligible.
Lastly, eliminating fluctuations in productivity in this environment can induce the agent to
maintain a differently sloped consumption profile from the one in the stochastic environment.
between these two effects, note that by forcing
the agent to keep the average investment-capital
ratio unchanged, we leave his expected initial
in the consumption profile that are due to consumption unchanged, since
Here, we need to distinguish between changes
changes in the volatility of investment and those
that are due to changes in the level of investment. To separate the two, suppose we were to
eliminate fluctuations in At but force the agent
c*A*K* = (A* - i*A*)K*
= E(ctAtKo).
to save a constant fraction i* such that the
average investment-to-capital ratio is the same
Thus, eliminating fluctuations and forcing the
as in the stochastic environment, i.e. i* =
agent to maintain the same average investment
E[itAt]IA*. Since 4(() is concave and the prop- allows him to attain a consumption path that
osition above implies irAt will have a nondegen- starts at the same level on average but grows
erate distribution, average growth must rise,
more rapidly. Lucas (1987) provides some calsince
culations on just how much the agent would be
6 Ravi Bansal and Amir Yaron (2001) argue instead that
consumption growth is persistent. They assume consumption growth follows an ARMA process g,+ 1 = pgt + 7t o7t,_ 1 where rt is i.i.d. If co is close to p, it will be hard to
distinguish this process from white noise even when p is
large, which could lead us to erroneously infer growth is not
highly autocorrelated if we fail to take into account the
moving-average term. Bansal and Yaron estimate p = 0.95
and X = 0.85 from dividend growth (which is the same as
consumption growth in their model), and use this to argue
willing to sacrifice to achieve this scenario. For
y = 1, he reports the agent would be willing to
sacrifice 20 percent of consumption each year to
increase the growth rate of consumption by 1
percentage point. By contrast, if the growth rate
is higher because the average investment rate
i*A* is higher, initial consumption will be
lower, since C* = (A* - i*A*)KIo is decreasing
in i*A*. The two ways of affecting the growth
rate are thus associated with different welfare
the costs of business cycles are large. However, ARMA
effects for a given change in the average growth
rate. In fact, the agent might very well prefer an
models for consumption growth data, such as Arthur Lewbel (1994), fail to find high values of p.
would imply slower growth, although he would
average investment rate i*A* < E(itAt) that
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
971
never be happier with slower growth starting
consumption growth during the post-War pefrom the same initial consumption.7
riod to predict the same counterfactual growth
rate.
Since previous authors assume 0(') is linear,
they only allow fluctuations to affect growth
In computing the cost of fluctuations, recall
through changes in the level of investment.that
Notcycles affect growth in two ways: they
surprisingly, they have tended to find only small
make investment fluctuate around its average
costs; if eliminating fluctuations increases
level, and they can change the average level of
investment
itself. For the model above, elimigrowth by increasing investment, the gain
the
agent reaps from more rapid consumption
nating the volatility of investment while holding
growth will be largely offset by the loss
he
average
investment fixed provides a lower
incurs from a lower initial consumption.
To on the cost of business cycles. This is
bound
generate more substantial welfare gains ofbecause
the investment is Pareto optimal, so allowmagnitude suggested by Lucas' calculationsing
onagents to also change the level investment
the value of growth, it is necessary that cycles
can only make them better off. In what follows,
I abstract from the effects of fluctuations on the
retard growth for a fixed average investment,
which is precisely what happens under diminaverage level of investment. As long as investishing returns. In the next several sections,
I is socially efficient, this approach provides
ment
examine whether empirically plausible degrees
a lower bound on the cost of cycles. If investof diminishing returns can indeed lead ment
to a is inefficient, my approach could potensignificant growth effect and hence to a large
tially overstate (or understate) the true cost of
cost of business cycles.
aggregate fluctuations. However, the welfare
effects of changing average investment are typII. Quantitative Analysis: Evidence fromically much smaller than the effects of reducing
Growth Data
growth for a given initial level of consumption,
so it seems unlikely that abstracting from them
Since the cost of fluctuations above stems
will significantly overstate the true cost of cyfrom the effects of fluctuations on growth, it is cles. Moreover, there is some evidence (which I
natural to begin with evidence on growth rates cite below) that macroeconomic volatility does
in order to quantify this cost. In this section, I not appear to be related to the level of investpursue two different approaches to exploiting ment, suggesting these effects are likely to be of
such data to gauge the effects of fluctuations on minor significance in any event.
growth. First, I consider a reduced-form approach that uses empirical variation in volatility
and growth to predict the counterfactual growth
rate in the United States if aggregate volatility
were set to zero. This approach does not require
directly estimating returns to investment. Second, I make explicit use of estimates of diminishing returns together with the distribution of
A. Reduced-Form Estimates
Suppose we had cross-section or time-series
data on growth rates, investment, and macroeconomic volatility. We could use this data to
estimate average growth as a function of volatility and other variables, i.e., to estimate
(6)
7 A similar distinction arises in models where growth is
driven by learing-by-doing rather than factor accumulation, e.g., Garey Ramey and Valerie Ramey (1991). In these
models, eliminating fluctuations can simultaneously raise
both current output and future output growth. The inherent
trade-off in these models is not between present and future
consumption, but between present leisure and present (and
future) consumption. Once again, we would want to distinguish between changes in the growth rate due to changes in
the level of output, which require sacrificing initial leisure,
and those due to changes in the volatility of output, which
do not.
E[A] =f(X, o)
where E[A] denotes average growth over a
given time period, a is a measure of aggregate
volatility over this same period, and X denotes
other variables that affect average growth. If X
includes the average level of investment over
the relevant time period, we can use the functionf( *, ) to project average growth to the case
where a = 0 but average investment is held fixed.
Conveniently, previous authors have already
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
THE AMERICAN ECONOMIC REVIEW
972
SEPTEMBER 2004
mate that an agent would sacrifice approxicarried out such an exercise. For example,
Ramey and Ramey (1995) estimate a mately
linear20 percent of consumption for a 1 point
specification of (6) using cross-country
increase
data.
in growth when y = 1, we obtain a cost
That is, they estimate a model of the form
of aggregate fluctuations of at least 10 percent
(7) Alnyit = do-'i + OXi + Eit
eit - N(0, o2)
where Alnyit denotes the growth rate of real
GDP per capita in country i and year t, the
vector Xi is a set of country-specific explanatory
variables (including average investment), and
the error term eit is distributed normally with a
variance of specific to each country.8 This spec-
ification assumes that in any given year, the
growth rate in each country varies from its
of consumption per year, over two orders of
magnitude greater than Lucas' original estimate. It is also noteworthy that Ramey and
Ramey find that controlling for the investmentto-output ratio has no effect on the point estimate for ,L; the negative correlation between
growth and volatility does not operate through
differences in average investment shares. This
accords with additional evidence they present
that the investment share of output does not
vary systematically with the volatility of GDP
growth across countries. Thus, macroeconomic
volatility appears to affect growth directly
historical mean by a normally distributed error
term et, where the historical mean iLo-, + OXi
depends linearly on the standard deviation of
rather than through its effect on investment.
the error term for the country in question.9 If the
tin and Carol Ann Rogers (2000) consider the
relationship between growth and volatility
across European regions. They estimate A, at
-0.274, compared with Ramey and Ramey's
growth rate is concave in investment as in the
previous section, /L should be negative.
The model in (7) can be estimated by maxi-
mum likelihood. Ramey and Ramey estimate
Ramey and Ramey's results have been subsequently extended. For example, Philipe Mar-
estimates of -0.211 for the OECD sample. This
would suggest an even larger growth effect of
almost seven-tenths of a percentage point.10
subset of 24 OECD countries using observa- To gauge the plausibility of cross-country or
tions between 1952 and 1988. They find that
cross-regional variation in growth rates, I next
after conditioning on average investment,
compare the estimates above to estimates for a
growth and volatility are indeed negatively resimilar exercise from time-series data using
lated, i.e., ,L is significantly different from zero
only U.S. data. Previous authors, including Vicat conventional significance levels. Their point
tor Zamowitz and Geoffrey Moore (1986) and
Ramey and Ramey (1991), have already demestimate for /L varies across samples and spec(7) for a sample of 92 countries using observations between 1962 and 1985, as well as a
ifications between -0.1 and -0.9, although esonstrated that the level and the volatility of
timates appear clustered around -0.2. Since the
output growth in the United States are negastandard deviation of per capita output growth
tively related over time. However, these studies
in the United States is 2.5 percent, using the
only report raw correlations rather than point
point estimate of -0.2 suggests that eliminating
estimates for ,L, and neither controls for average
investment. I therefore reexamine the timeaggregate shocks altogether should increase the
growth rate by half a percentage point, from 2.0
series data to derive estimates that are compato 2.5 percent per year. Applying Lucas' esti'0 Martin and Rogers' methodology is not identical to
Ramey and Ramey's. For example, they regress average
8 Although the relevant growth rate for calculating the
growth on the unconditional standard deviation of output
welfare cost of fluctuations involves the growth rate of
growth rather than use (0.2). But the explanatory variables
consumption, the two series grow at the same rate in the
account for such a small share of the variation in growth that
long run in the model constructed above. Thus, the fact that
this is insignificant. Martin and Rogers also do not control
Ramey and Ramey use the growth rate of output per capita
for average investment. But as noted above, average investdoes not pose a problem for my analysis.
ment is uncorrelated with volatility across countries, sug-
9 Ramey and Ramey experimented with a nonlinear
gesting that omitting this variable may not be of much
specification, but found it provided a worse fit.
consequence either.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
973
BARLEVY: THE COST OF BUSINESS CYCLES
TABLE
rable to the above specification. Following
1 THE RELATIONSHIP BETWEEN GROWTH AND
VOLATILITY IN U.S. TIME-SERIES DATA
Ramey and Ramey (1991), I divide the data into
(Dependent variable: real per capita GDP growth)
distinct four-year episodes between presidential
elections. This identification assumes elections
United States 12 four-year panels
play an important role in generating changes in
Intercept 0.0065
macroeconomic policy, which in turn affects the
(0.0055)
level of aggregate volatility.l I apply this time- Average I/Y 0.0132
(0.0292)
series data to estimate the same model as in (7).
IL
-0.3484
That is, I assume that the growth rate each
(0.22
quarter is a deviation from the mean growth rate
over the relevant four-year period, where the
deviation is drawn from a normal distribution
with standard deviation oi specific to that period. Using quarterly data from 1953:1-2000:4
on output and gross domestic investment from
publicly available Bureau of Economic Analysis (BEA) sources (and converted to per capita
Log-likelihood 651.99
Number of panels 12
Number of observations 192
Data sources: U.S. quarterly real GD
mestic investment (in 1996 chained do
BEA estimates for 1953:1-2000:4. Re
U.S. population, where population ea
polated geometrically from annual po
from the U.S. Census Bureau for Ju
Panels correspond to presidential term
levels using Census Bureau population figures),
I constructed a panel data set of 12 four-year
periods, with each panel consisting of 16 quar- sists of 16 quarterly observations. JL
terly observations. In contrast with the cross- on the standard deviation term in eq
The method of estimation is maximum
country data, there is now no need to introduce
additional control variables such as measures of
in parentheses denote asymptotic stan
human capital, which are unlikely to have much
explanatory power for a single country within a and nine-tenths of a percen
relatively short time horizon.
holding average investment fi
The results for the 12 four-year panels are
B. Estimates Based on Dimini
reported in Table 1. The parameter of interest ,L
is the coefficient on the standard deviation of
As an alternative approach, w
on growth rates together with
esis that /L > 0. Its point value is -0.348, which minishing returns to predict t
also falls within the range from cross-country factual rate at which the econo
data in Ramey and Ramey (1995). I experi- we stabilized investment at its mean. To be
output growth. The point estimate of Lt is negative, although we cannot reject the null hypoth-
mented with dropping observations to gauge the more precise, suppose 4(') is given by
robustness of the point estimate of ,u. For all of
the subsamples I considered, the point estimate
l' (Ii K)
\ I K)
for /t remained clustered around -0.2 or -0.3. (8)
Thus, several different sources of variation that
can be used to estimate a reduced-form relationwhere ? E (0, 1] governs the extent of diminship-countries, regions, and time periods-all ishing returns to investment. Suppose further
suggest that eliminating volatility in the United that we know the distribution of trend per capita
States should increase growth by between half consumption growth, At = 1 + (itAt) - 8.
Kw K
By inverting the function 4() in (8), we
can compute the implied growth rate if we
1 I also experimented with accounting for the two pres- were to stabilize investment at its mean value.
idential successions that occurred between elections during Specifically,
this period, but this change proved unimportant. I likewise
considered grouping observations by presidential adminis(9) 1 + (E[itA,]) - 8
trations rather than by terms. However, a likelihood ratio
test overwhelmingly rejected this specification in favor of
= 1 + (E[(At - 1 +
one that allows volatility to differ across terms.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
8)1/]) - 8.
974
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
Thus, if we estimate 4t together with the distrielasticity above unity. While
bution of the permanent part of consumption
yields values above 1, it typica
growth, we can directly compute whatto
themuch higher values than th
Abel. The highest estimate Abe
growth rate would be in the absence of fluctuations if we were to hold average investment
implies a value of 4, of 0.12, s
fixed.
large degree of diminishing ret
More recently, Janice Eber
Turning first to t, note that the first-order
mates the elasticity of investm
condition of the agent's maximization problem,
which is derived in the Appendix, can be reto q using micro data from sev
written as
tries. In contrast to previous w
for several different specificat
-E[VK(Kt,, At+, )]--1
tionship between investment a
(10) '(itAt) = (C)
the isoelastic specification i
United States, she estimates
The expression inside the brackets
investment
is the ratio with
of
respect to q a
the marginal value of a unit of capital
the curvature
relative to parameter 4F =
the value of an additional unit of investment.
ison, when she estimates the sa
This ratio is commonly referred to as marginalshe computes a point elasticity
q.12 For the isoelastic function, we obtain themeans. This suggests that inferr
following relationship between the investmentof investment with respect to
to-capital ratio and q:
sion of the level of the invest
ratio on the level of q may un
/I\
1
value of i, implying the adjust
(11) In - = constant + In q.
\K/ 1 4'
tion 4(') exhibits less curvatu
gested by earlier estimates.
Hence, we can recover the curvature
parameter
Since some
of the applications
i from the elasticity of the
investment-toform
approach above make use
variation,
it isof
not
obvious that
capital ratio with respect to
q. Estimates
this
elasticity abound in the literature.
However,
attention to
Eberly's estimates
most of these estimates areAfter
based all,
on appealing
estimating
to cross-cou
(11) in levels rather thanestimate
logs. While
a level of volatilit
the effect
sumes that allof
countries
face the same investspecification implies the elasticity
investment
with respect to q will not
ment
betechnology
constant
4(() but for
not theall
same degree of
values of q, we can still underlying
estimate
volatility.
the
Thus,
point
rather than limit
attention
data to to
U.S. q
firms,
we should use evelasticity for investment with
respect
at the
sample mean. In an early contribution,
Andrew
idence on the elasticity
of investment in other
B. Abel (1980) reports a range
0.50estimate for
countries tobetween
obtain a more precise
and 1.14 for this point elasticity.
bethe curvatureEstimates
parameter 4t. Although
Eberly's
low 1 are problematic, since
point
they
estimates
imply
vary across
a negthe 11 OECD counative value for 4. However,
such
low
values
tries in
her sample,
they
are remarkably consishave been dismissed on the
grounds
that
meatent.
Weighting by
the number
of observations
surement error in q wouldin bias
the estimated
each country,
the average elasticity of investelasticity towards 0. For example,
Jason
Cumment with respect
to q across
all 11 countries is
mins et al. (1999) argue that
1.36,properly
an estimate that
instrulies inside the 95-percent
interval
for 10 out of the
11 OECD
menting for q routinelyconfidence
yields
estimates
of
countries in the sample, including the United
States. This suggests a still higher value for 4q of
0.26.
12 Since the production technologies are all homogeIn sum, micro data on investment and q sugneous of degree 1, marginal q in this economy is equal to
gest that (1982).
, - 0.18-0.26.
this
average q, as shown in Fumio Hayashi
TheInterestingly,
latter
measure is the one frequently used
in is
empirical
work.
range
consistent with
estimates
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
that are ob-
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
975
tained from aggregate data. In a recent paper,
the years 1951-1998. I constructed the likeliChristiano and Jonas Fisher (1998) use a methodhood function recursively following James
of-moments approach to estimate various paramHamilton (1994). In estimating the likelihood
eter values for a related model from aggregate
function, I restricted the unconditional expected
data, where one of the parameters corresponds growth
to
rate E[A,], evaluated at the invariant
distribution of the estimated transition matrix P,
the elasticity of investment with respect to q.13
Their estimate of the elasticity of investment with
to equal 2.0 percent per year. This accords with
respect to q is 1.31, which implies 4t = 0.24. conventional estimates for the growth rate of
Armed with a range of estimates for 4, I next
per capita consumption based on even longer
turn to the task of recovering the distributionhorizons
of
than my sample period. This restricAt from consumption data. Recall that consumption is not too stringent, since consumption
tion growth in the model is given by
grows at roughly this rate over my sample period. However, because of the finite length of
A In C = In A, + A ln(l + E,).
the sample, there is potential for the maximum
likelihood estimate to force transient phenomHence, we can use consumption growth A Inena
C, into estimates of long-run trends. Table
to recover the distribution of trend consumption
2 reports the maximum likelihood estimates for
growth At. Specifically, assuming productivity
all the parameters for the case of N = 2 and N =
A, follows a Markov process, we can estimate
3, respectively. The estimates reveal substantial
the distribution of A, using maximum likelivariation in the growth of trend consumption
over time, ranging between -0.7 and 4.3 perhood. Let P = [p,j] be an N X N matrix that
denotes the transition probabilities between the
cent per year. There is no conflict between the
N values At can assume. For the model to accord
finding of a negative growth rate in the data and
with observed consumption growth, I need to
the fact that the isoelastic specification implies
introduce an additional noise term; otherwise,
+(x) > 0, since growth can be negative if the
consumption growth can assume at most depreciation
N2
rate 6 exceeds O(iA). The fact that
values. I therefore assume that measured conestimates for A ln(l + e) are negative imply
sumption growth is given by
that trend consumption grows more rapidly
when consumption is below trend, i.e., the level
A In Ct = In A, + A ln(l + e,) + mt
of consumption falls when aggregate productivity is high. As noted earlier, this pattern is not
where r,t N(0, o2) is assumed to reflect mearuled out by the model. By contrast, the model
surement error. The parameters of the model
does imply that output and investment grow
that need to be estimated are a set of trend
more rapidly when they are above trend. Estigrowth rates {In hj 1f 1, a set of first differences mating a similar decomposition for these two
in consumption levels {A ln(l + ej+ l)} 2, series confirms this prediction, but I omit these
the transition matrix P, and the variance term results for the sake of brevity.
o2. Using the estimated transition matrix P, we
Using the invariant distribution for A, in Tacan solve for the invariant distribution over the ble 2, and assuming 8 = 0.1 as is standard in the
N possible states of the world. With this distri- literature, the implied growth rate (9) in the
bution and the estimates for In At, I can then two-regime model is given by
compute expression (9) for a given 4.
1 + (0.37(0.0957)1'"
For my estimation, I use annual consumption (12)
data from the Bureau of Economic Analysis
(BEA), divided by population estimates ob-
+ 0.63(0.1341)-)i - 0.1
tained from the Census Bureau. The data spans
and in the three-regime model it is given by
13 It should be noted that Christiano and Fisher allow for
preferences that exhibit habit formation rather than the
CRRA utility considered so far. However, I will introduce
habit formation in Section V.
(13) 1 + (0.29(0.0930)1/'
+ 0.42(0.1227)1'/ + 0.29(0.1429)1/*) - 0.1.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
976
SEPTEMBER 2004
THE AMERICAN ECONOMIC REVIEW
TABLE 2-MAXIMUM LIKELIHOOD ESTIMATES FOR MARKOV MODEL OF CONSUMPTION GROWTH
Two-regime model
Three-regime model
Coefficient Standard errors
Coefficient Standard errors
Poi
Pio
In
In
0.5369 0.1543 Poi 0.1110 0.1356
0.3117 0.1113 P02 0.3936 0.1326
Pio 0.2308 0.1057
P12 0.1812 0.1086
P20 0.1730 0.1317
P21 0.4724 0.1892
Ao
A1
-0.0043
0.0341
-
In
0.0066
Ao
In
-0.0070
A1
In
0.0227
A2
0.0033
0.0429
0.0039
A ln(l + S01) -0.0250 0.0049 A ln(l + sol) -0.0174 0.0045
A ln(l + 812) -0.0201 0.0031
02
0.00024
0.00009
o2
0.00010
0.00003
Implied invariant distribution Implied invariant distribution
State
Prob
State
Prob
0
0.37
0
0.29
1
0.63
1
0.42
2
0.29
Data
sources:
Real
consumption
p
denotes
the
transition
rate
betw
estimation
constrains
the
average
regime
model.
In
Asij
denotes
the
the
variance
of
the
measurement
transition
score method.
matrix
pij.
Standard
er
Figure 2 plots these two values against 4I. In theregime models produce similar growth effects,
relevant range for ?, the estimates largely coin- with the three-regime model suggesting a
cide with those obtained from the reduced-form
slightly larger effect. These estimates predict
approach above. For example, for Abel's largest that stabilizing investment at its mean will inestimate for ? of 0.12, stabilizing investment at crease growth by three to nine-tenths of a perits average value will raise the growth rate from centage point, which coincides with the range
2.00 to 2.74 and 2.86 percent, respectively. from the reduced-form approach above. Thus,
When ? = 0.18 as in Eberly's estimate for U.S.
the two approaches to using growth data are
data, the implied growth rate from stabilizing fairly consistent, both suggesting a cost of cyinvestment at its average value is 2.53 and 2.60 cles of at least 7 percent of consumption per
percent per year, respectively, which coincides year if not more.
with the lower range of the estimates obtained
from the reduced-form approach. Christiano III. Reconciling Growth and Other Macro Time
and Fisher's estimate for 4' of 0.24 implies a
more modest increase in growth to 2.40 and
2.43 percent per year, respectively. Finally, for
Series
The previous section found evidence of di-
t = 0.26, which corresponds to the estimate
minishing returns that imply large costs of busi-
from averaging all 11 OECD countries in Eberly's
sample, the implied growth effect is 2.36 and
2.40 percent per year, respectively. Thus, for the
range of estimates of the investment elasticity
reported in the literature, the two- and three-
ness cycles. However, for reasons that will be
discussed momentarily, very sharp diminishing
returns can make it difficult to reconcile the
model with certain macro data. For this reason,
I now examine whether the growth effects
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
977
BARLEVY: THE COST OF BUSINESS CYCLES
VOL. 94 NO. 4
E(x)
2-Regime Model
3.2
...... 3-Regime Model
3.1
3.0
.Abel (1980)
2.9
I
2.8
2.7
2.6
(1997)- U.S. only
2.5
2.4
(1997) - 11 OECD countries
2.3
2.2
4. )
I
I)~~~
I
'I-
~v
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
FIGURE 2. PREDICTED GROWTH RATE AFTER STABILIZATION AS A FUNCTION
OF DIMINISHING RETURNS
thatconsisthe ratio of investment at its peak to its
estimated from growth data alone are
trough
is given by
tent with other macro series, specifically
investment and q. The results raise doubts that diminishing returns are so strong as to imply that
iloAo Al - 1 + 5 1/
stabilization will raise growth by half
a per(14)
ioAo AOo- 1 + &
centage point or more, but an increase of 0.35-
0.40 percentage points is on the whole quite
Since A1 > Ao by our earlier proposition, the
ratio on the right-hand side of (14) shoots off to
Consider the consequences of diminishing
plausible.
returns to investment for investment itself. Di-
infinity as I --> 0. Thus, under rapidly dimin-
minishing returns implies that each additional
unit of investment contributes less to the capital
stock. Since growth is driven by capital accu-
ishing returns to investment, iA at its peak
would have to be orders of magnitude larger
than at its trough to account for variation in
mulation, it follows that for more rapidly diminishing returns, a larger increase in investment is
observed growth rates. The estimates for ,
ment to accord with the fluctuations in the
estimated in Table 2.
above that yield sizable growth effects would
required to raise the growth rate by a given not be as credible if they also require implausiamount. Diminishing returns to investment may bly volatile investment to account for the varitherefore require very large swings in invest- ation in A we observe empirically and which is
Using the estimates for Ao and A1 in Table
growth rate that we observe over the cycle.
2 and setting 8 = 0.10, we can compute for any
Formally, consider the version of the model
4 the ratio of investment rates implied by (14).
with two different productivity levels. Recall
value is plotted against ? in Figure 3. For
that the growth rate A is equal to 1 + 4(iA) - This
8.
? = 0.12, the highest value implied by Abel's
Suppose once again that 0(iA) = (iA)'. Let iA1I
original estimates, investment at its peak must
denote the investment-to-capital ratio when probe a whopping 16 times as large as at its trough
ductivity assumes its higher value, and let A1
to accord with the variation in growth rates A in
denote the corresponding growth rate. Simi-
the data. At , = 0.18, which corresponds to
larly, define ioAo and Ao when productivity asEberly's estimate for U.S. firms, the required
sumes its lower value. A little algebra shows
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
THE AMERICAN ECONOMIC REVIEW
978
17 16 -
SEPTEMBER 2004
Abel (1980)
15 14 -
13 12 -
11 10 98-
7-
(1997)- U.S. only
6-
Christiano and Fisher (1998)
5-
, Eberly (1997) - 11 OECD countries
4-
32-
10
0.00
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
0.50
FIGURE 3. INVESTMENT VOLATILITY REQUIRED TO MATCH GROW
FUNCTION OF DIMINISHING RETURNS
ratio falls considerably to 6.52. For Christiano
share of output i has ranged between 10 and 15
percent, suggesting il/io 0 1.5. As for the ratio
implied ratio is just slightly above 4. Finally, for A,/Ao, I make use of the fact that the capital-toi = 0.26, the value implied by averaging over output ratio in the model corresponds to aggre-
and Fisher's (1998) estimate of t = 0.24, the
all 11 OECD countries in Eberly's sample, the gate productivity. Empirically, available
ratio falls to 3.66.
estimates of aggregate productivity are based on
Clearly, for the smaller estimates of 4I that production functions that utilize both capital
can be found in the literature, e.g., 0.12 or 0.18, and labor, so for the sake of comparability we
it would take an absurdly large increase in in- need to modify the model to incorporate labor.
vestment to raise the growth rate from -0.43 to The problem with introducing labor is that if
3.41 percent. But for the larger estimates of 4 production is linear in capital, production would
that can be gleaned from the literature, e.g., 0.24 exhibit increasing returns to scale, in which case
or 0.26, a much smaller increase in investment the decision problem for a price-taking firm is
is required. Nevertheless, the increase is far not well defined. However, following Paul Rofrom negligible: at its peak, the investment-to- mer (1986), we can assume increasing returns to
capital ratio would have to be over three times scale are external to any individual firm. That is,
as large as at its trough. While we can safelyeach firm i uses capital Kit and labor Nit, but the
dismiss some of the larger estimates of dimin- productivity of labor in firm i depends on the
ishing returns, the question remains as to aggregate capital stock Kt = 2i K,t. Output of
whether the more modest estimates of diminish-
firm i is then
ing returns (and the more modest growth effects
they imply) can still be reconciled with aggregate investment.
Yi, = Zt(KtNit),'Kil,-
To address this question, let us decompose where Zt denotes the level of productivity (comilA1
the ratio - into the product of il/io, which
corresponds to the volatility of the investmentto-output ratio, and A /Ao, which corresponds to
the volatility of the output-to-capital ratio. For
most of the post-War period, the investment
mon to all firms) and a = 0.67 corresponds to
the labor share of output. Each firm's technology exhibits constant returns to scale in its own
inputs, so the firm's problem is well-defined.
One can show that aggregate output Yt = i2 Yit
across all firms is linear in the aggregate capital
This content downloaded from
fff:ffff:ffff:ffff:ffff:ffff:ffff:ffff on Thu, 01 Jan 1976 12:34:56 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
979
stock, where the coefficient on capital A incorbe higher than even the largest estimates in the
porates productivity and labor, i.e.,
empirical literature, implying even more modest
diminishing returns to investment and a smaller
Yt = (ZtN-)K, =AK,.
growth effect. Alternatively, the estimates of 4
might be correct, but the volatility of investment
Empirically, both Zt and Nt exhibit a standard
reported above is somehow mismeasured and
deviation on the order of 5-6 percent.'4 actual
To
investment is significantly more volatile.
convert this into ratios Z,/ZO and N,/No, set To distinguish between these two hypotheses,
_ 0.633 I turn to data on aggregate q. To see why this
data can be useful, note that upon rearranging
equation
we can
relate investment,
and similarly set N, (1
+ (11),
x)N
and
No = aggregate q, and qi with the following equation:
0.633 -
Z, = (1 + x)Z and Zo = (I - 0.3
1- 0.367x N. This parameterization en-
sures that at the ergodic distribution
in Table
io A Io q o 1-)
(15) will iOA0\
qo 9 Z and the
2, the average value of Zt
equal
average value of N, will equal N. A simple
computation reveals that the standard deviation
Equation (15) reveals that the extent of diminof Zt or Nt in percentage terms, denoted sd, is
ishing returns to investment, as captured by i,
.633
also determines how responsive investment is to
equal to .367 x. Hence, these two ratios are
q. As such, q data provide an independent set of
given by
observations that can confirm or deny either of
/0.367
Z1 N 1 + .633 sd
Zo No 10.633
-
sd
1 0.367 sd
For a standard deviation of 6 percent, we
approximate the ratio Al/Ao as
these hypotheses. Specifically, if i is indeed
much larger than 0.26, we should observe that a
similarly high value of 4q is needed to reconcile
investment with data on q. Alternatively, if in-
vestment is more volatile than my estimates
would suggest, it should similarly be the case
that we need a greater degree of investment
volatility than I estimate in order to be consis-
tent with q data when ' = 0.26.
Turning to the data, one of the first to esti-
A1 ZIN1
-== (1.14)167
Ao
ZoNo
1.24.
mate q from aggregate data was Lawrence H.
Summers (1981). He constructed two series
from 1931 to 1978, one equal to the value of
equity divided by the value of physical capital,
Multiplying together, the investment-to-capital
ratio at its peak is 1.5 X 1.24 = 1.86 as large as
at its trough, clearly short of the value required
to accord with fluctuations in the growth rate A
when 4i = 0.26. There are two ways to interpret
this finding. One is that the true value of t must
and another which amends this ratio to account
for taxes and depreciation allowances. Restricting attention to the post-War period, the average
value of his measure of regular q is 0.96 with a
standard deviation of 24 percent, while the average value of the tax-adjusted q series over the
same period is 1.92 with a standard deviation of
38 percent. However, the data used in construct14 See, for example, Robert King and Sergio Rebelo ing these series has been subsequently revised.
(1999). Note that according to the model, the standard Olivier Blanchard et al. (1993) reconstruct the
Solow residual is equal to In Z + a In K and thus is an series for standard q in light of these revisions,
imperfect measure of total factor productivity Z (or whatand extend the original series up to 1990. The
ever this term represents, e.g., utilization, cyclical markups,
etc.). However, since capital does not move much over the average of their q series falls to 0.64, and the
cycle, the Solow residual should still provide a good ap-
proximation for the variance of Z.
implied standard deviation rises slightly to
29 percent. Ben Bernanke et al. (1988) also
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
THE AMERICAN ECONOMIC REVIEW
980
7 -
SEPTEMBER 2004
i,A, X, -i1+ 618/
i1A1
? ioAo Ao -1++J
iAo
6
5
4
3
2
1
0
0.00 0.05
0.10 0.15 0.20 0.25 0.30 0.35
0.40 0.45 0.50
FIGURE 4. INVESTMENT VOLATILITY REQUIRED TO MATCH q D
Notes: Solid lines show peak-to-trough investment required to match a gi
peak-to-trough investment required to match growth data.
construct a quarterly series of tax-adjusted q for
Why Their
mightavermy estimate for -the period between 1947 and 1983.
i0A0
One obvious
culprit is with
my estimatean
for A,/Ao,
age for tax-adjusted q is equal
to 1.41,
based on assumptions
regarding exannual standard deviation ofwhich
37was
percent.
Thus,
ternal returns
to scale that were motivated
while Summers' original series
overstate
the by
than empirical of
considerations.
level of q, their measures oftheoretical
the rather
volatility
However,
it is unlikely that better
measurement
aggregate q are confirmed in
subsequent
studA would yieldwe
more can
volatile investment-toies. Assuming a two-regime of
model,
once
again translate the standard deviation
capital ratios. In theof
end, q
A isinto
just the a
ratio of
output to
capital, and
since capital is relatively
value for the ratio qllqo. By the
same
argument
stablefor
over the
volatility
of A should
as above, a standard deviation
qcycle,
ofthe28
perequal the volatility
of output. But
cent implies ql/qo = 1.92. If approximately
the standard
deviation were instead equal to 38
output
percent,
is no more volatile
as than
in already
theimplied
tax-adjusted series, the ratiobywill
my estimate
equal
for A /Ao.
2.56.
For each of these two values,
A more
Figure
likely candidate
4 traces
is my estimate for
out the implied investment
(15) inil/io.volatility
One reason to suspectin
that aggregate
vestment ti.
is mismeasured
is that when 4(') is
against the curvature parameter
Regardless
concave,
the amount
output It set
aside for
of whether ql/qo is equal to
1.92
orof2.56,
no
value of t? can reconcile our the
measure
ultimate production
of of
investcapital goods is not
the we
same aspush
the grossdown
change in the
ment volatility and q. Even if
tfstock of
goods
Kt+1ratio
- (1 - 8)Kt;
to its lowest possible value capital
of 0,
the
of more pre-
investment from peak to trough
wouldimplies
stillthat
have
cisely, concavity
the former is more
volatile
latter.cases
The implied peak-toto be at least as large as ql/q0,
yetthan
in the
both
the latter is greater than my estimate
trough ratio ofof
3.66 1.86
concernsfor
the variation in the
investment volatility. Thus, amount
there
of resources
is a fundaset aside for the production
mental inconsistency between
investof measured
capital goods. But
the way investment is
ment and q, which supports the
measured
hypothesis
in the aggregatethat
statistics is based on
thevolatility
value of all finalis
investment
goods promy estimate of investment
too
small.
duced, which corresponds more closely to the
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
981
change in the stock of capital goods. In particthis value, investment at its peak must be 2.69
ular, many adjustment costs associated with inas large as at its trough, which is indeed greater
vestment, e.g., transport, installation, and
than my estimates. When ql/qo is equal to 2.56,
servicing, are categorized as intermediate conin line with the volatility of tax-adjusted q, the
sumption (i.e., as an operating expense), and
corresponding value of 4 is 0.26, precisely the
their value is assigned to the market value ofsame as the value implied by averaging the
whatever final good the firm that undertakes
elasticity of investment with respect to q across
these activities ultimately produces rather than
all 11 OECD countries in the Eberly (1997)
be counted as investment. Thus, some of the
sample, and which recall implies investment at
activities that would be counted as investment
its peak is 3.66 times as large as at its trough.
in the model and which we know are cyclically
Thus, the largest point estimates for i among
sensitive are not reflected in the aggregate acthose in the previous section can in fact be
counts. Another problem is that not all investreconciled with q (especially tax-adjusted q),
ment that takes place in a given year contributes
and the requirement that investment at its peak
immediately to production and hence to the
be over three times as large as its trough seems
contemporaneous growth rate A. For example,
reasonable in light of the fact that q is so
new construction will count towards investment
volatile.
before it is leased out and used for productive In sum, very large degrees of diminishing
purposes. This intuition suggests investment returns
in
(and correspondingly large growth efequipment should be a better indicator of the
fects) are hard to reconcile with data on either
part of investment that contributes to conteminvestment or q. But more modest degrees of
poraneous growth. In fact, if we consider the
diminishing returns, e.g., a value of ? of 0.26,
share of equipment investment in output, it does
do not require absurdly large investment volaappear more volatile; the implied ratio for il/io
tility, and can certainly be reconciled with q
is about 1.75, implying the investment-to-capital
data. Although it is still hard to reconcile a
ratio is about 2.2 times as large at its peak than
value of ? of 0.26 with investment data, the
at its trough. This is still too small relative to the
discrepancy is moderate, and the fact that it is
degree required to reconcile with growth data
just as hard to reconcile investment with other
when p = 0.26, but the discrepancy is indeed
macro time series such as q suggests it may be
smaller.
a poor counterpart for investment in the model.
In the absence of a way to reliably measureTrying to reconcile the model with other macro
investment, I follow an alternative route of usvariables thus confirms that stabilizing investing q data to proxy for how volatile investment
ment at its mean can raise growth by 0.35-0.40
ought to be. The idea is to infer the extent of
percentage points, but not by as much as 0.50investment volatility that is necessary to recon0.90 percentage points as suggested in the precile q, which drives investment, and A, which vious
is
section. However, recall that even this
the outcome of investment. Formally, I solve for
more modest increase will matter tremendously
the value of 4 for which the volatility of investfor welfare: agents would be willing to sacrifice
ment implied by data on A is the same as theat least 7-8 percent of consumption per year to
volatility of investment implied by data on q,
eliminate fluctuations and the drag they induce
and then use this measure of my volatility as on
an growth.
indicator of how volatile investment would appear if we could measure it accurately. Figure 4
IV. Calibrating the Model
illustrates this graphically by superimposing the
curve that traces out the degree of investment
volatility required to accord with growth data,The previous section demonstrated that a
the same curve as is depicted in Figure 3. When
growth effect of 0.35-0.40 percentage points
q1/qo is equal to 1.92, the value of q for which
requires large, but not implausibly large, volaboth q and A imply the same investment volatility in the investment-to-capital ratio iA. This
tility corresponds to 0.34, slightly higher than
ratio is a composite of two terms: i, an endog-
the estimates for ? from the micro literature. At
enous decision variable, and A, an exogenous
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
982
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
the discount rate f3 and the inverse
shock variable. As noted in the previous ters:
section,
empirical considerations suggest that inintertemporal
pracelasticity of substitution y. Foltice, At is not inordinately volatile inlowing
and of
Lucas, I set 3 to 0.95 and y to 1. On the
itself. Thus, for cycles to have a pronounced
production side, I maintain the isoelastic form
effect on long-run growth, it must be the
for case
Q(.) in (8), which requires me to assign a
to t. While the previous section suggests
that the endogenous choice variable i is value
sufficiently volatile to generate enough variation
q is approximately
in
0.26, the model itself sug-
the investment-to-capital ratio iA. But
intugests
a way of estimating this parameter. As
itively, if investment volatility is really asnoted
costly
by Jones et al. (1999), if we set , = 1 and
as my estimates suggest, agents would presumcalibrate {At} to match the empirical average
ably have an incentive to avoid varyinggrowth
it overrate, the consumption share of output
time. This raises the question of whether
willitbeisroughly one-third. But empirically, conpossible to generate empirically plausible
vola- accounts for about two-thirds of outsumption
tility in the investment-to-capital ratioput.
in reJones et al. argue that this discrepancy can
sponse to moderate fluctuations in the
be resolved by counting a fraction of investment
exogenous driving process At. In this section I in the model as consumption, under the pretext
argue that this is possible, but only if we redressthat investments in human capital such as eduthe model's well-known failure in replicating cation and health care expenditures are counted
asset prices.
as private consumption in national income accounts. However, between 1951 and 1998, total
Formally, given a process {At}, we can solve
the agent's problem and derive the optimal path
expenditures for these two categories account
for it. This allows us to derive the process for
for at most 20 percent of consumption, and in
the growth rate At = 1 + (itAt) - 8 for a given
earlier years account for only 6 percent of total
process of exogenous shocks. My approach is to
consumption, far less than the 50 percent share
needed to reconcile with the data.15 An alternacalibrate {At} so that the implied growth rates
match up with the estimates in Table 2. Once
tive interpretation is that constant returns to
this is done, I can check what part of the variinvestment provide overly powerful incentives
ation in iA is due to exogenous productivity
for agents to invest. This suggests we can use
shocks and what part is due to investment dethe fact that consumption accounts for two
thirds of income to determine the extent of
cisions. To accord with empirical observations,
the bulk of this volatility must be due to variadiminishing returns. Formally, I calibrate i to
tion in i. To gauge this, I consider the ratio of
match a consumption share of output of 0.67.
the standard deviation of iA to the standard
This yields a value of $ = 0.226, within the
deviation of A implied by my calibration; the
upper range of estimates for I described above.
larger this ratio, the more the volatility of the
I focus on this value of qi, although none of my
investment-to-capital ratio is due to fluctuations
conclusions would change much if I were to set
in i. This particular metric is the usual one used
f to 0.26; on the contrary, a higher value of f
to evaluate the success of real-business-cycle
would make it easier to induce agents to vary i
over time.
models, since it corresponds to the volatility of
investment relative to the volatility output. ThatFinally, I turn to the Markov process At. For
is, since I = iAK and Y = AK, the volatility ofsimplicity, I assume At follows a two-state
investment for a fixed capital stock corresponds
Markov process, where the transition probabilities between the two states are taken from the
to the volatility of iA, while the volatility of
output corresponds to the volatility of A.
Since the household problem must be solved
numerically, I must first assign values to the key 15 Alternatively, some human capital expenditures might
not
preference and technology parameters. I begin
be counted in either GDP or investment, in which case
the measured investment share would be smaller than its
my analysis using the standard CRRA utility
true value. Jones et al. (1999) explore this possibility in
described in Section I, although as anticipatedsubsequent work, but they find that only a negligible fracabove I will subsequently generalize this function of such expenditures is likely to be missing from GDP
when returns to investment are assumed constant.
tion. The CRRA utility involves two parame-
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
983
two-regime model in Table 2. Since the optimal
in the standard real-business-cycle model, asset
policy assigns a unique it to each realizationprices
of are far too smooth in comparison with the
At, this ensures that the growth rate At follows
data.a Formally, let qo denote the value of qt
two-state Markov process. Thus, calibrating the
when A, = Ao and similarly for ql. For the
process involves assigning two values, CRRA
Ao utility above with y = 1, the ratio of q
and A1, so that the growth rates Al and across
Ao the two regimes in the model is given by
coincide with the estimates in Table 2. Note
that by defining A1 = (1 + x)A and Ao =
ql Al Co
(16)
o Ao C1'
1 - 0.367 xA, we can equivalently view this
/ 0.633 \
problem as assigning a value to A and x, where
Since -_ 1of
and At
consumption
is not very
A measures the unconditional mean
and x
Ao
governs the unconditional variance
will
volatile as longof
as AtAt.
itself isInot
too volatile, q
make use of this interpretation
below.
will hardly
vary over the cycle, and thus neither
I briefly discuss how to solve
the
will investment.
But asagent's
we know from the preoptimization problem in the Appendix.
The
calvious section, q empirically
is highly
volatile. It
ibration implies that the value
ofsurprising
x needed
is hardly
that a modelto
which does a
match observed fluctuations
in consumption
notoriously
poor job of accounting for the volgrowth is 0.362. This corresponds
to
a fails
standard
atility of asset
prices
to generate plausible
deviation for A of 47.8 percent,
investment
or volatility
alternatively
when investment inherto a ratio A /Ao of 3.63, much
than
entlylarger
responds to these
prices. what
above discussion suggests
that if we
I computed above as reasonableThevariation
in At.
This confirms the concern raised
beginmodify the in
modelthe
so that more
reasonable proning of this section: since volatile
investment
is
ductivity shocks
can generate larger movements
so costly, agents will try not to
over
time,
in q,vary
we might i
be able
to induce
agents to vary
so the only way to generate enough
volatility
investment even
when productivityin
shocks are
the investment-to-capital ratio
= qiA
is to
reasonablyI/K
small. Since
is intimately
related
allow for very large fluctuations
init seems
A. natural
Indeed,
to asset prices,
to turn to recent
along the optimal path, the investment
share
of the
literature that has attempted
to reconcile
output it only varies betweentraditional
0.292
and 0.358.
real-business-cycle
model If
with asset
we compare the standard deviation
of iAt
to (1998),
the Urban
data, e.g., Christiano
and Fisher
standard deviation of At, theJermann
fact (1998),
that
is Boldrin
not et al.
and it
Michele
very volatile implies the standard
deviation
offinance
(2001). Building
on insights from the
iA is only 9.8 percent larger literature,
than they
the
standard
suggest
replacing (2) with a
deviation of A, while empirically
more generalthe
functionstandard
known as habit-formation
deviation of investment is 2.5-3
utility, times as large
as that of output.
To appreciate why the model has such diffi(Ct - bCt- )1
culty in inducing agents to vary
over time,
(17) iU({Ct})
= E t _
recall that the first-order condition (10)t=0is
given t=o
by
'- 1
for some b > 0. Note that the CRRA utility is
just a special case of this function where b = 0.
Kt ve of ei
But if we allow b to be sufficiently different
from 0, marginal utility will be quite volatile
even when consumption is relatively smooth.
where q is the ratio of the market value of equity
to the replacement value of physical capital.This
As translates into a relatively volatile series
such, the model implies that the volatility for
of q, which provides strong incentives to vary
investment will be intimately related to the investment
volover time. In fact, all three papers
atility of asset prices. But it is well known above
that find that in the absence of diminishing
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
984
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
returns, investment proves to be too volatile
special case of (17) where b = 0, I maintain the
same values for A and r as before to keep the
asset prices, and some friction in the investment
nonstochastic steady-state growth rate ungood sector such as adjustment costs must
be
changed.
I then set the remaining parameter, x,
introduced to moderate the volatility of investto match the variability of the growth rate as
ment. Jermann (1998) provides a particularly
reported in Table 2. In contrast to the case of
nice intuition for why business-cycle models
CRRA utility, the optimal it will now depend on
when b is set to accord with observations on
the level of habit Ct_ . Since the latter state
that are capable of matching asset prices require
both habit formation and adjustment costs:
variable is continuous, the growth rate At will no
"With no habit formation, marginal rateslonger
of
follow a two-state Markov process. I
substitution are not very volatile, since people
therefore calibrate x to yield a standard deviado not care very much about consumption voltion for the growth rate reported in Table
atility; with no adjustment costs, they choose
2, which is equal to 1.85 percentage points, so
consumption streams to get rid of volatilitythat
of the volatility of the growth rate A in the
marginal rates of substitution. They havemodel
to
accords with my previous specification.
both care, and be prevented from doing any-To solve the model for (17), I resort to a
thing about it."16
linear approximation of the intertemporal Euler
This motivates me to recalibrate the model
equation to handle the additional state variable
above with (17) instead of (2) to see if allowing
that is due to the habit term. I provide a brief
for habit persistence can allow us to generatediscussion
a
of my approach in the Appendix.
large growth effect with more modest fluctuaThere are two parameters, b and x, that must be
calibrated, and these are chosen to match the
tions in At. In assigning preference parameters,
I continue to set 8 = 0.95. In accordance with
ratio of investment volatility to output volatility
some of the authors above, I continue to set yand
= the volatility of the growth rate A, respec1. As for the habit parameter b, I choose it tively.
so
These values are given by b = 0.725 and
x = 0.165. How reasonable are these values?
that along the equilibrium path, investment will
be 2.5 times as volatile as output, in line with
Turning first to x, allowing for habit formation
lowers the standard deviation of A necessary to
the estimate provided in Jermann (1998). I then
examine whether the requisite ratio of b is conmatch the volatility of the growth rate by more
sistent with the estimates of this parameter than
in
half. The implied standard deviation for A
previous work.
is now equal to 21.6 percent, or alternatively the
Turning to the technology parameters, the
ratio AI/Ao is equal to 1.63. This is still quite
intertemporal Euler equation, which is provided
high when compared to total factor productivexplicitly in the Appendix, reveals that the nonity, but can presumably be brought down by
stochastic steady state of the economy is indeappealing to more habit persistence and to
pendent of b.17 Since CRRA utility is just
somewhat
a
larger values of qp as some of the
above empirical work would suggest.
As for b, this estimate is consistent with what
previous researchers have argued is necessary to
16 An alternative modification of the RBC model that
also generates more volatile asset prices is the generalizawith data on the equity premium. For
tion to a multicountry setting, as in Marianne Baxter accord
and
example, Boldrin et al. (2001) estimate b =
Mario Crucini (1993). In this case, asset prices are volatile
not because marginal rates of substitution are volatile, but
0.73 in calibrating their RBC model to accord
because dividends are. Specifically, production will tend to
be concentrated in the country with the highest productivity,
so owning equity in a country-specific technology will yield
low dividends when that country is not the leader. Givendifference
the
between them. If utility is logarithmic in the ratio
implied volatility of asset prices, Baxter and Crucini simiof consumption to habit, the steady-state growth rate is
larly need to introduce adjustment costs for investment again
not
independent of habit. Since Carroll et al. assume
to be too volatile.
greater curvature in utility than the log case, they find that
17 Christopher Carroll et al. (2000) examine a related
habit affects growth. If I were to use their preferences,
model in which growth does depend on the degree of habit.
agents would have even greater incentive to invest in
But they use a different specification where agents care
growth, requiring a smaller value of q to match the conabout the ratio between consumption and habit, not the
sumption share of output.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
985
with the empirical equity premium. Christiano
than under the CRRA preferences with the same
and Fisher (1998) estimate a somewhat lower
y. Intuitively, habit formation implies that
value of b = 0.6, while Jermann (1998) estiagents care even more about growth, since what
mates a somewhat higher value of b = 0.82.
they care about is how much more they con-
Thus, if we were to impose the same preference
sume relative to past consumption. To compute
parameters that previous researchers have arthe lower bound on the cost of cycles described
gued can help to explain asset price volatility,
above, consider how much an agent would be
we can generate empirically plausible investwilling to sacrifice to increase the growth rate
ment volatility even with relatively small flucby 0.35 percentage points in the absence of
tuations in At. In other words, introducing habit
fluctuations, as the above calibration suggests
formation leads agents to vary i much morewould
in
happen. That is, given two consumption
response to A, so that much less variation in A
is
streams
Ct = AtCo and C$ = (A + .0035)tCo, by
necessary to explain why growth rates varywhat
as constant scaling factor should we adjust
much as they do over time.
the first consumption stream to deliver the same
Why does habit formation lead agents to vary
utility as C'? For A = 1.02 and y = 1, the
investment so much despite the presencescaling
of
factor AL solves the equation
diminishing returns? Consider a negative pro-
ductivity shock which lowers households' (18)
in-
comes. Consumers are reluctant to decrease
their consumption immediately-habit format0
/ln((1 + X.) /1.0200 3
tion implies they will want to do it gradually.
(1 + i) X 1.0235
Thus, on impact, households will try to sell off
t = I
their assets to finance consumption. This causes
asset prices to fall, which signals to firms that
1.0200 -b
they should cut back on accumulating capital.
1.0235 - = 0.
Eventually, if the recession continues, consumers will get habituated to low consumption, they
will not be as driven to get rid of their assets,When b = 0, which corresponds to the CRRA
and investment will begin to recover. This over- case, -L = 0.075, i.e., an individual would sacshooting explains why investment is so volatile. rifice 7.5 percent of his consumption each year
By contrast, under the standard CRRA utility, for consumption to grow more rapidly. When
households do not need to let their consumptionb = 0.7, the corresponding ,u is given by 0.083,
fall gradually, so there is no equivalent drop in or 8.3 percent per year. Allowing for habit formation therefore serves to increase the cost of
asset prices and investment.
To summarize, if we modify the endogenousbusiness cycles in several ways: it makes agents
growth model to allow for more volatile asset care more about consumption risk; it necessiprices, it is possible to reconcile the presence oftates greater diminishing returns to investment,
diminishing returns to investment with the factwhich implies fluctuations lower average
that agents choose to vary investment as muchgrowth by a larger amount; and it causes agents
as we observe in the data. Essentially, we need to care more about the growth rate, and thus to
to introduce an additional motive to smooth
suffer more from the effects of fluctuations on
consumption that offsets the incentive for growth.
agents to smooth investment. Such motives are
Finally, I should point out that the large cost
not altogether implausible given the large pre- of business cycles with habit formation and
mium on risky equity, which suggests that in endogenous growth is not just due to the fact
practice agents are averse to too much con- that agents are more averse to consumption
sumption volatility. However, since we do this
by modifying preferences, we need to confirm
such a growth effect is still costly to the agent.
It turns out that a one-percentage-point reduction in growth is actually more costly under (17)
volatility. As discussed in the introduction, previous work such as Otrok (2001) has argued that
even with nonseparable preferences such as
(17), the cost of consumption volatility should
be viewed as small. This is because Otrok and
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
986
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
thevolafluctuations in trend growth that we observe
others compute the value of eliminating the
the cycle.
tility of per capita consumption that we over
actually
observe over the cycle, which is quite small.
TheBy
key feature that leads to such large costs
contrast, the cost of cycles that is due of
to business
their
cycles is that the growth rate is
concave
effects on growth depends on the much
largerin whatever input determines long-run
counterfactual volatility of per capita consumpgrowth. In the AK growth model where growth
tion that would prevail if agents were to
is driven
keep by capital accumulation, adjustment
investment constant over time (since if thecosts
costinofthe installation of capital will naturally
cycles were less than this cost, agents would
in- to such curvature, and a variety of
give rise
deed choose perfectly smooth investmentempirical
paths). evidence suggests this curvature is
Thus, endogenous growth is indispensable
substantial.
for
In models where growth is driven
generating such large costs of business cycles.
by other sources, this curvature must reflect
other considerations. For example, in a previous
V. Conclusion
version of this paper, I argued there is similar
evidence of substantial diminishing returns to
This paper considers a cost of aggregate R&D,
fluc- which would likewise suggest that stabituations that is due not to consumption volatillizing R&D at its average will lead to higher
ity, but to the effects of fluctuations on growth.
long-run growth. Thus, large costs are likely to
In a sense, it closes a circle that began arise
within a variety of endogenous growth models,
Lucas (1987), who argued that growth matters
although the fact that the rate of growth is not
for welfare while business cycles do not;
if efficient in some of these models realways
business cycles can affect the rate of economic
quires further work to determine the welfare
growth, they can matter after all. My analysis
effects of changes in the level of investment.
suggests that eliminating fluctuations can inLastly, while the arguments presented here
crease the growth rate by 0.35-0.40 percentage
suggest that business cycles may be quite
points without affecting average initialcostly,
con- it bears repeating that it does not immesumption. This implies a welfare cost 100 times
diately follow from this that stabilization policy
larger than what Lucas originally computed
is inherently desirable or could avoid these un-
based on the cost of consumption risk alone.
derlying costs. This conclusion hinges on the
The remaining sections of the paper confirm
precise nature and source of aggregate fluctuathat the large cost of cycles is internally consistions, and the degree to which government poltent. That is, even though investment volatility
icy can truly eliminate them. This paper opens
is inherently costly, agents can be induced
theto
door to large welfare effects of fluctuations,
vary investment in response to moderate exogand the growth channel it explores should be
enous shocks. Moreover, as long as diminishing
used to study the role of policy in the variety
returns are not too large, empirically plausible
of models that have been devised to explain
variation in investment can be reconciled with
business-cycle fluctuations.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
987
BARLEVY: THE COST OF BUSINESS CYCLES
APPENDIX
PROOF OF PROPOSITION:
We can rewrite the agent's problem recursively as
V(Kt, A,) =c,
max{1
+ fE[V(K,+1, A+ )lAj]}
)1--A'
=
max
1
-
+
pE[V((1
c,e[0,1]
where
recall
}
it
+
(it
=
1
a(A,)KJ -7
V(K,, At) =a(A)K
It is easy to confirm that this multiplicatively separable function conforms to the Bellman equation.
Ignoring the constant term in the utility function, we can rewrite the above Bellman equation as
(c,A,)'- '
a(A,) = max t + 13E[a(At+ 1i)|A][((l - ct)A,) + 1 - 8]1'c,e[0,1] I -
Note that for any function V( , * ) which is increasing in both arguments, the expression
f(ctAtKt) I-
max I + + 3E[V((4((1 - ct)At) + 1 - 8)Kt, At+ I )A
must be increasing in At and Kt given that Prob(At+ 1 < xjAt) is weakly decreasing in At. The standard
fixed-point argument establishes that the solution to the Bellman equation V( ? , ) is increasing in
a(A) K -
both arguments. Hence, if V(K, A) 1 , it follows that a(A) is increasing in A. This in t
implies that the conditional expectation E[a(At+ 1)At] is increasing in At.
Using the first-order condition of the Bellman equation, we have
(ctAt)-' = 3E[a(At+,)IA,][((1 - c,)At) + 1 - 6]-Y'((1 - c,)A,).
We can rearrange this equation to obtain
'(itA) = 1E[a(A,+ )IA,t] A,( - i) )
Let x = iA. Then we can rewrite the first-order condition as
4'(x) = k(A)(A-x )
where k(A) is a positive constant and k(A) <0. Since '(x) is decreasing in x and ( - 6
is increasing in x, there exists at most one x which solves this equation. Existence then follows from
the limit conditions limx,o '(x) = oo and limx_o '(x) = 0. If we rewrite this equilibrium
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
THE AMERICAN ECONOMIC REVIEW
988
SEPTEMBER 2004
condition asf '(x) - kA)( - )= 0, the fact that fx < 0 and fA> 0 imply t
A rises, x must also rise to maintain f = 0, which establishes the claim.
Solving the Modelfor CRRA Utility.-From the proof of the proposition above, we know t
a(A) K -
value function V(K, A) has the form . Substituting into the Bellman equation yields t
following equation, one for each possible realization of At:
a(A) (c(A)AK) 1- E[a(A,+ )lAt = A](A)]A) + K]
g1-/ -' -Y [(I([1 - c(A)]A) + 1 - )K]-
Taking the first order with respect to c(A) on the right-hand side of the above
Euler equation for c(A):
(c(A)A)-' = PE[a(A,+ )IAj][E((1 - c(A))A) + 1 - 8]- Y'((1 - c(A
Thus, we have two nonlinear equations for each pair of variables c(A), a(A
amounts to solving this system of nonlinear equations, with two equations fo
assume.
Intertemporal Euler Equation Under Habit.-The intertemporal Eu
utility function U({ Ct) is given by
UC,,= AtE, A- Uct +
where Uc.t denotes the marginal utility of U with respect to Ct and At denotes the Lagrange multiplier
on the constraint Kt = (I + f(I) - 6)K. For (17)we have
Uc,t = (Ct - bCt)-Y - b(Cet+ l- bCt,+)-7
while adjustment costs imply that
At+ 1 4'(ItKt) 1t+ I 'it+,
Define
c = - Then we can rewrite the Euler equation as
tK
Et[v(ct-1, C, ct+l, ct+2, A -, At, At+1)] = 0
where the function v can be obtained by substitution. The deterministic steady state is the constant
value c which solves
v(c, c, , , A, A, A) = 0
and one can show that if we set ct_ 1 = c t = c+1 = t + 2, the coefficient b drops out. To solve for
the nonsteady-state dynamics, I use a linear approximation of v(.) at the deterministic steady state
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
VOL. 94 NO. 4
BARLEVY: THE COST OF BUSINESS CYCLES
989
by evaluating the relevant derivatives of v with respect to each of its arguments, and then
to derive a linear approximation of the policy rule which is given by ct+ t = ca't + aA
for some coefficients ao, a,, and a2 that I need to solve for.
REFERENCES
of Habit: a Consumption-Based Explanation
of Aggregate Stock Market Behavior." National Bureau of Economic Research (CamAbel, Andrew B. "Empirical Investment Equations: An Integrative Framework." Carnegiebridge, MA) Working Paper No. 4995,
Rochester Conference Series on Public
January 1995.
Policy, 1980, 12, pp. 39-91.
Carroll, Christopher; Overland, Jody and Weil,
David. "Saving and Growth with Habit ForAlvarez, Fernando and Jermann, Urban. "Using
Asset Prices to Measure the Cost of Business
mation." American Economic Review, June
Cycles." Mimeo, The Wharton School, 1999.
2000, 90(3), pp. 341-55.
Atkeson, Andrew and Phelan, Christopher. "Re- Christiano, Lawrence; Eichenbaum, Martin and
considering the Costs of Business Cycles
Marshall, David. "The Permanent Income Hywith Incomplete Markets," in S. Fischer and
pothesis Revisited." Econometrica, March
J. Rotemberg, eds., NBER macroeconomics
1991, 59(2), pp. 397-423.
annual. Cambridge, MA: MIT Press, 1994, Christiano, Lawrence and Fisher, Jonas. "Stock
pp. 187-207.
Market and Investment Good Prices: Impli-
Bansal, Ravi and Yaron, Amir. "Growth Rate
cations for Macroeconomics" Mimeo, Northwestern University, 1998.
Cummins, Jason; Hassett, Kevin and Oliner, Ste2001.
phen. "Investment Behavior, Observable ExBaxter, Marianne and Crucini, Mario. "Explain- pectations, and Internal Funds." Federal
ing Saving-Investment Correlations." Ameri- Reserve System Discussion Paper No. 99/27,
1999.
can Economic Review, June 1993, 83(3), pp.
416-36.
Dolmas, Jim. "Risk Preferences and the Welfare
Beaudry, Paul and Pages, Carmen. "The Cost of
Cost of Business Cycles." Review of EcoBusiness Cycles and the Stabilization Value
nomic Dynamics, July 1998, 1(3), pp. 646-76.
Eaton, Jonathan. "Fiscal Policy, Inflation, and
of Unemployment Insurance." European
the Accumulation of Risky Capital." Review
Economic Review, August 2001, 45(8), pp.
Dynamics and the Costs of Economic Fluctuations." Mimeo, The Wharton School,
1545-72.
of Economic Studies, July 1981, 48(3), pp.
Benhabib, Jess and Farmer, Roger. "Indetermi- 435-45.
Eberly, Janice. "International Evidence on Innacy and Increasing Returns." Journal of
Economic Theory, June 1994, 63(1), pp. 19- vestment and Fundamentals." European Eco41.
nomic Review, June 1997, 41(6), pp. 1055-
Bernanke, Ben; Bohn, Henning and Reiss, Peter. 78.
"Alternative Non-nested Specification TestsEpaulard, Anne and Pommeret, Aude. "Recurof Time-Series Investment Models." Journal
sive Utility, Growth, and the Welfare Cost of
of Econometrics, March 1988, 37(3), pp.
293-326.
Volatility." Review of Economic Dynamics,
July 2003, 6(2), pp. 672-84.
Blanchard, Olivier; Rhee, Changyong and SumEpstein, Larry and Zin, Stanley. "Substitution,
mers, Lawrence H. "The Stock Market, Profit,Risk Aversion, and the Temporal Behavior of
and Investment." Quarterly Journal of Eco- Consumption and Asset Returns: An Empirnomics, February 1993, 108(1), pp. 115-36.ical Analysis." Journal of Political Economy,
Boldrin, Michele; Christiano, Lawrence and
April 1991, 99(2), pp. 263-86.
Fisher, Jonas. "Habit Persistence, Asset Re- Hamilton, James. Time series analysis. Princeton, NJ: Princeton University Press, 1994.
turns, and the Business Cycle." American
Economic Review, March 2001, 91(1), pp. Hayashi, Fumio. "Tobin's Marginal q and Aver149-66.
age q: A Neoclassical Interpretation." EconoCampbell, John and Cochrane, John. "By Force
metrica, January 1982, 50(1), pp. 213-24.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms
990
THE AMERICAN ECONOMIC REVIEW
SEPTEMBER 2004
imrohoroglu, Ay?e. "Cost of Business Cycles
tutability." European Economic Review,
August 1994, 38(7), pp. 1471-86.
with Indivisibilities and Liquidity Constraints." Journal of Political Economy,
Otrok,
De- Christopher. "On Measuring the Welfare
cember 1989, 97(6), pp. 1364-83.
Cost of Business Cycles." Journal of MoneJermann, Urban. "Asset Pricing in Production
tary Economics, February 2001, 47(1), pp.
61-92.
Economies." Journal of Monetary EconomPemberton, James. "Growth Trends, Cyclical
ics, April 1998, 41(2), pp. 257-75.
Jones, Larry; Manuelli, Rodolfo and Stacchetti,
Fluctuations, and Welfare with Non-Expected
Utility
Ennio. "Technology (and Policy) Shocks
in Preferences." Economics Letters, March
Models of Endogenous Growth." Mimeo,
1996, 50(3), pp. 387-92.
Phelps, Edmund. "The Accumulation of Risky
Northwestern University, 1999.
King, Robert and Rebelo, Sergio. "Resuscitating
Capital: A Sequential Utility Analysis."
Real Business Cycles," in John B. TaylorEconometrica,
and
October 1962, 30(4), pp.
729-43.
Michael Woodford, eds., Handbook of macroeconomics, Vol. IB. Amsterdam: NorthRamey, Garey and Ramey, Valerie. "Technology
Commitment and the Cost of Economic FlucHolland, 1999, pp. 927-1007.
Krusell, Per and Smith, Anthony. "On the Welfare Effects of Eliminating Business Cycles."
tuations." National Bureau of Economic Re-
Leland, Hayne. "Optimal Growth in a Stochastic
Environment." Review of Economic Studies,
Between Volatility and Growth." American
Economic Review, December 1995, 85(5),
pp. 1138-51.
Review of Economic Dynamics, January
1999, 2(1), pp. 245-72.
search (Cambridge, MA) Working Paper No.
3755, June 1991.
. "Cross-Country Evidence on the Link
January 1974, 41(1), pp. 75-86.
Levhari, David and Srinivasan, T. N. "Optimal Romer, Paul. "Increasing Returns and Long-Run
Savings Under Uncertainty." Review of EcoGrowth." Journal of Political Economy, Ocnomic Studies, April 1969, 36(1), pp. 153-63.
tober 1986, 94(5), pp. 1002-37.
Lewbel, Arthur. "Aggregation and Simple DyShleifer, Andrei. "Implementation Cycles."
namics." American Economic Review, SepJournal of Political Economy, December
tember 1994, 84(4), pp. 905-18.
1986, 94(6), pp. 1163-90.
Lucas, Robert E., Jr. Models of business cycles. Storesletten, Kjetil; Telmer, Chris and Yaron,
Oxford: Basil Blackwell, 1987.
Amir. "The Welfare Cost of Business Cycles
. "Macroeconomic Priorities." AmeriRevisited: Finite Lives and Cyclical Variacan Economic Review. March 2003, 93(1),tion in Idiosyncratic Risk." European Ecopp. 1-14.
nomic Review, June 2001, 45(7), pp. 131139.
Martin, Philipe and Rogers, Carol Ann. "LongTerm Growth and Short-Term Economic InSummers, Lawrence H. "Taxation and Corporate
stability." European Economic Review,
Investment: A q-Theory Approach." BrookFebruary 2000, 44(2), pp. 359-81.
ings Papers on Economic Activity, 1981, 1,
Matheron, Julien and Maury, Tristan-Pierre.
pp. 67-121.
"The Welfare Cost of Fluctuations in AK
Tallarini, Thomas. "Risk Sensitive Real BusiGrowth Models." Mimeo, University of ness Cycles." Journal of Monetary EconomParis, 2000.
ics, June 2000, 45(3), pp. 507-32.
McGrattan, Ellen. "A Defense of AK Growth
Uzawa, Hirofumi. "Time Preference and the
Penrose Effect in a Two-Class Model of EcoModels." Federal Reserve Bank of Minneapolis Quarterly, Fall 1998, 22(4), pp. 13-27.
nomic Growth." Journal of Political EconMendoza, Enrique. "Terms-of-Trade Unceromy, July-August 1969, 77(4), pp. 628-52.
tainty and Economic Growth." Journal of Zarnowitz, Victor and Moore, Geoffrey. "Major
Development Economics, December 1997,
Changes in Cyclical Behavior." in R. Gor54(2), pp. 323-56.
don, ed., The American business cycle: ConObstfeld, Maurice. "Evaluating Risky Consumptinuity and change. Chicago: University of
tion Paths: The Role of Intertemporal SubstiChicago Press, 1986, pp. 735-79.
This content downloaded from
202.65.183.201 on Wed, 09 Sep 2020 02:20:30 UTC
All use subject to https://about.jstor.org/terms