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ALFRED
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WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
DYNAMIC GENERAL EQUILffiRIUM MODELS WITH
IMPERFECTLY COMPETITIVE PRODUCT MARKETS
Rotemberg
Massachusetts Institute of Technology
Julio J.
Michael Woodford
University of Chicago
WP#3623-93-EFA
October 1993
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
DYNAMIC GENERAL EQUILffiRIUM MODELS WITH
IMPERFECTLY COMPETITIVE PRODUCT MARKETS
Rotemberg
Massachusetts Institute of Technology
Julio J.
Michael Woodford
University of Chicago
WP#3623-93-EFA
October 1993
^
M.I.T.
OCT
LIBRARIES
2 5 1993
RECEIVED
Dynamic General Equilibrium Models with Imperfectly
Competitive Product Markets
Julio J.
*
Michael Woodford
Rotemberg
Massachusetts Institute of Technology
October
University of Chicago
13, 1993
Abstract
This paper discusses the consequences of introducing imperfectly competitive product markets into an otherwise standard neoclassical growth model.
competition
for the
We
pay particular attention to the consequences of imperfect
explanation of fluctuations in aggregate economic activity. Market structures considered
include monopolistic competition, the "customer mjirket" model of Phelps and Winter, and the implicit
collusion
model of Rotemberg and Saloner. Empirical evidence relevant to the numerical calibration of im-
perfectly competitive models
is
reviewed.
The paper then analyzes
the effects of imperfect competition upon
the economy's response to several kinds of real shocks, including technology shocks, shocks to the level of gov-
ernment purchases, and shocks that change individual producers' degree of market power.
It
also discusses
the role of imperfect competition in allowing for fluctuations due solely to self-fulfilling expectations.
•
We
wish to thank David Backus, Roland Benabou and participants at the Frontiers of Business Cycle Research for comments,
and Martin Uribe for research iissistcince and the NSF for research support.
Stephcinie Schmitt-Grohe
In this
paper we discuss the consequences of introducing imperfectly competitive product markets
otherwise standard neoclassical growth models.
We
in
are particularly interested in the effects of imperfect
competition on the way the economy responds at business cycle frequencies to various shocks. The literature
on equilibrium modeling of aggregate fluctuations has mainly assumed perfectly competitive
that represents an obvious starting point for analysis,
we argue
firms.
While
that there are important reasons for allowing
competition to be imperfect.
One
reason
technologies.
is
'
that imperfect competition makes equilibrium possible in the presence of increasing returns
This increased
modeling fluctuations,
on increasing returns
necessary
is
if
in particular for
is
the specification of technology
flexibility in
may be
of great importance in
understanding cyclical variations in productivity. Empirical evidence
discussed in section 3 below.
We
argue below that not only
one wishes to assume increasing returns, but that conversely
if
is
imperfect competition
market power
is
important one
virtually required to postulate increasing returns, in order to account for the absence of significant pure
profits in
economies
like
that of the U.S. Increasing returns
may
also
make
possible
new sources
of aggregate
fluctuations - in particular, fluctuations due solely to self-fulfilling expectations.
Allowing
for
market power (and hence prices higher than marginal cost) and increasing returns may
have important consequences for the interpretation of business cycles, although we do not argue for a
particular theory of the cycle in this paper.
In the real business cycle literature, technology shocks have
usually been assigned a dominsint role as the source of fluctuations.
But the existence of market power
and increasing returns implies that the Solow residual, interpreted
the
in
RBC
literature as a
measure of
exogenous technology shocks, contains an endogenous component. As Hall (1988, 1990) has emphasized
endogenous component may be unrelated to true changes
complete dynamic model that increases
result in a positive
in
when they
a fraction of the increase in output which
technology. For example,
government purchases
Solow residual, as well as an increase
firms are perfectly competitive
in
in
in the
in fact
output and hours. Thus,
'
of Baxter
and King (1990).
increasing returns are importeint.
We
if
one assumes that
random
technical progress
eff"ect
upon production
possibilities.
if the increasing returns are external, rather than internal to the
beUeve, however, that there is much more reeison to believe that internal
Increasing returns are compatible with competitive firms
model
a
generated by increased government purchases, or other
types of shocks that raise equilibrium output other than through an
firm, as in the
in
presence of imperfect competition
are not, one can be led to attribute to
is
we show below
this
Various empirical puzzles regeirding the behavior of Solow residuals suggest that this endogeneity
important, as we discuss
Section
in
4.
Imperfect competition also changes the predicted effects of technology shocks
by Hornstein (1993), the ability of increases
reduced
Hence
further in section 5 below.
shocks
in productivity to
will
if
imperfect competition
have to be assigned a major role
The hypothesis
stimulate increased employment
is
important,
it
seems
the gap between price and marginal cost.
the level of labor input that firms
Thus changes
of employment.
demand
We
increased.
is
structure
-
in the
We show
markup
is
also consistent with variations over
show that an increase
The
at a given real wage.
in this
effect
gap results
in
a reduction
upon labor demand
is
thus
upon labor
of price over marginal cost are potentially an important determinant
that fluctuations in these markups, of a size that
of the source of
for
discuss this
Imperfect competition
is
not implausibly large given
^
data on the U.S. economy, can generate employment variations of the size observed.
One view
greatly
likely that other types of
similar to an adverse technology shock, while there need not be so large an offsetting wealth effect
supply.
is
does introduce new potential sources of employment fluctuations as well as
implies not only that price generally differs from marginal cost, but
in
it
We
As shown
the explanation of business cycle variations in employment.
in
providing a channel through which the importance of other shocks
in
occur.
of imperfect competition does not in itself point one towards ciny particular alternative
However,
source of shocks.
time
when they
the case of even rather moderate degrees of market power and increasing returns.
in
may be
markup
fluctuations
is
that they result from exogenous changes in market
example, in the context of the model of monopolistic competition developed
in Sections 1-2
below, variations in the degree of substitutability between the differentiated goods. Under this view, imperfect
in
competition introduces a new source of shocks. But
it is
also possible for
markups
response to aggregate shocks with no direct relation to market structure.
markup
we
will
We
variation
become an additional channel through which such shocks
show, this chzinnel
may be
it
is
In that case, the effects of
Ccin affect
aggregate activity. As
particularly important in understanding cyclical variations in
discuss several theories of endogenous veiriation in
theories in which
to vary endogenously
possible for the
markup
to
fall
markups
when
in
there
Section
is
7,
employment.
giving peirticular attention to
an increase
in
aggregate demand.
We
it is worth pointing out that the assumption that producers have marl<et power
product markets is an essential element in models of nominal price rigidity. Such price rigidity enhances the role of
monetary policy shodcs as a source of aggregate fluctuations. For examples of completely specified dynamic model, see Hairauil
^In addition to the channels discussed below,
in their
and Portier (1992) and Yun (1993).
then illustrate the potential importance of allowing for endogenous
theories affect the response of equilibrium
Finally, the
employment
to changes in
all.
In
of "sunspot" variables.
This equilibrium
Among
these equilibria there
expectations.
The
may
is
exist "sunspot" equilibria in
necessarily independent
of this paper
is
to
exist several
which fluctuations
result
quantitative plausibility of this possibility has been analyzed
by Benhabib and Farmer (1992), Gali (1992), and Farmer and
aim
in the
But the introduction of imperfect competition implies that rational expectations
self-fulfilling shifts in
further
these
government purchases.
no longer correspond to the solution of a planning problem, and indeed there can
distinct equilibria.
A
how
standard real business cycle models, there exists a unique equilibrium
(which corresponds to the solution to a planning problem).
from
variation by showing
assumption of imperfect competition can lead to equilibrium aggregate fluctuations
absence of any shocks at
equilibria
markup
Guo
(1993).
show how existing empirical studies using data
at various levels of
aggregation can be used to obtain estimates of the departures from perfect competition and from constant
returns.
While our survey of
this literature
is
far
from complete, we show how existing evidence bears upon
the calibration of certain of the key parajiieters of imperfectly competitive models.
Finally, the
is
easy.
It is
paper shows that incorporating imperfect competition into equilibrium business cycle theory
true that, because the resulting allocation
not Pareto optimjJ,
is
the equilibrium by considering the solution to a planning problem.
computation of dynamic general equiUbrium models, that make use of
it is
not possible to compute
However, familiar methods
ein
for the
Euler equation characterization of
equilibrium (as discussed in detail in the next chapter) can also be applied
when markets
are not perfectly
competitive.
Our paper proceeds
as follows. In section
1,
we
which firms are monopolistic competitors and there
show
that,
under quite general conditions, firms
mcirkup over marginal cost.
We
returns. In section 2
we embed
and discuss the way
in
3 provides a brief
first
is
will
develop a basic imperfectly competitive model,
no intertemporal aspect to
their pricing problem.
in
We
choose to charge a price which represents a constant
cdso discuss the connections
between imperfect competition and increasing
model of firm behavior
a complete dynamic general equilibrium model,
this
in
which the resulting model generalizes a standard real business cycle model. Section
overview on the microeconomic evidence on the importance of imperfect competition.
then discuss the numerical solution of the response to shocks. In section
4,
We
numerical results are presented for
shocks to the level of government purchases while section 5 concentrates on technology shocks. These sections
illustrate the
importance of taking account of imperfect competition. They also show how a comparison of
the U.S. data and the model's responses can be used to obtEiin estimates of the quantitative importance of
Section 6 shows that for some parameter values (involving a
the departures from imperfect competition.
sufficiently large degree of imperfect
competition and increasing returns), the equilibrium response to shocks
becomes indeterminate. This opens up a new potential source of aggregate fluctuations, namely, fluctuations
due solely to
to
self-fulfilling
may
expectations, that
occur even
in the
absence of any stochastic disturbances
economic "fundamentals".
Sections 7 and 8 then discuss models with
markup
power (here modeled
of exogenous variations in the degree of market
substitutability of diflferentiated products) in a
variations. In section
as
model of the kind treated
7,
we consider
the consequences
due to exogenous changes
in sections 4
and
5.
We
in
the
show that
shocks of this kind can produce an overall pattern of co- movement of aggregate variables that captures several
features of observed aggregate fluctuations,
in
employment.
We
estimate the size of
and that they are
markup
in particular able to
produce large movements
fluctuations that would be required to account for observed
business cycle variations in employment in the U.S., and compare this with independent calculations of
the degree of cyclical variation in markups in the U.S. economy. In section
endogenous variations
detail, the
used
the
in
our
eff"ects
in
markups occur
in
response to other kinds of shocks.
we discuss models
We
in
which
develop two models
in
"customer markets" model of Phelps and Winter (1970), and the model of oligopolistic collusion
own previous work.
In this section
we
eJso illustrate the predictions of these
of changes in the level of government purchases.
shocks other than technology shocks to produce variations
model of Gali (1992),
In the context of this
at
8,
in
two models regarding
Here we particularly emphasize the
in
labor demand.
We
ability of
also briefly discuss the
which the equilibrium markup depends on the composition of aggregate demand.
model we discuss the
possibility of aggregate fluctuations in the absence of
any shock
all.
1
We
The Behavior
of Monopolistically Competitive Firms
suppose that there exists a continuum of potentially producible differentiated goods indexed by the
positive real line.
At any point
in time,
only the subset whose index runs from zero to
/(
is
actually produced.
These goods are bought by consumers, the government and
both as materials that are used
in
firms.
The
latter
buy the
goods
difTerentiated
current production and in the form of investment goods that increase
the capital stock available for future production.
To
simplify the model, and to
standard perfectly competitive model, we assume that
all
make
it
comparable to the
of these ultimate demeinders are interested in a
single "composite good". In other words, the utility of consumers, the productivity of materials inputs,
the addition to the capital of firms depends only
An
purchased.
upon the number of units of the composite good that are
agent whose purchases of individual differentiated goods are described by a vector Bt obtains
Q, units of the composite good, where Qt
is
given by
Q,
We
assume that the aggregator
=
f,iB,)
(1.1)
an increasing, concave, symmetric and homogeneous degree one
/( is
By asymmetric function we mean
function of the measure Bt-
that
its
value
is
unchanged
quantities purchased of any of the individual goods, so that the value Q, depends only
quantities purchased of individual goods, and not
is
the
same
for all of the
differentiated
it;
and
upon the
identities of the
purposes mentioned above; we allow, however,
if
one exchanges the
upon the
distribution of
goods purchased. The aggregator
for variation over time, as the set of
goods being produced changes. The producer of eeich of the differentiated goods
sets a price for
the collection of these prices describes a price vector P( conformable with the vector of goods purchases.
Consider an agent (be
The agent
it
a consumer, government or firm) wishing to buy G» units of the composite good.
will distribute its
purchases over the vjtfious differentiated goods so as to minimize the total cost
<
P(,B(
to
Gt times a homogeneous degree zero vector-valued function of the price vector:
>
of obtaining Gt- Because /<
homogeneous of degree one,
is
Bt
Hence
for
a given vector of prices F(,
allows us to aggregate the
all
demands of
all
Furthermore, because
/<
depend only upon the price
is
p{
for the
demand
equal
G,A,(P,)
).
This
i
must
types to obtain
=
QtAtiPt)
composite good
for all
purposes.
symmetric, the component AJ(P() indicating purchases of goods
charged
is
agents will choose sczJar multiples of the same vector A(P,
Bt
where Qt denotes total demand
=
this cost- minimizing
for that
good and the
6
overall distribution of prices charged.
We
will
We
be concerned here only with symmetric equilibria.
possible exception of firm
in
j)
charge a price of P( at
the form Dt(p\/pt)/U, where Dt
of goods produced at date
t
will
thus consider situations where
while firm
j
charges
p\. In this
a decreasing function, the seime for
is
all
:',
degree zero. (The normdization by
/(
and
denotes the number
It
A
simply for convenience.) The demand for firm
is
firms (with the
case A\{Pt) can be written
Dt depends only on the ratio of the two prices because
t.
all
homogeneous of
is
i's
product
is
then
given by
u
By
Pt
we mean that each firm
monopolistic competition
charged by other firms, and chooses
indicated by (1.2).
We
^
its
D((l)
=
1
for all
<.
continuum
We
own
i
takes as given aggregate
price, p\, taking into
/(
in
each period that ft{M)
uniform measure).
case, the
furthermore assume that Dt
similarly independent oft.
The
latter
is
Then
assume that
goods
for
cire
each
t,
+
pD'{p)
common
is
It
1,
for all
is
a vector
and that the value D[{1) < —1
is
than one. Finally, we
it is
positive.
This implies the existence of a downward sloping
The
elasticity of
result of these assumptions
demand.
It is
is
that,
worth stressing that we
have obtained this result without having to make global assumptions on preferences, as
Stiglitz (1977).
is
symmetric, one must have
elasticity of substitution is greater
symmetric equilibrium, firms face a time-invariant
and
M
goods, remains the same as additional
all
marginal revenue curve for each producer of a differentiated good.
in Dixit
sales
Dt-
where
i,
its
a monotonically decreasing function of the relative price p over
the entire range of relative prices for which
at a
=
on
the price
assumption means that the degree of substitutability between different
added, and the
D{p)
effect of p\
demand curve
since /(
differentiable at
differentiated goods, evaluated in the case of equal purchases of
differentiated
demand Q, and
account the
are therefore interested in the properties of the
Let us assume as a normalization of
of ones (or, in the
Pt
is
done
for
instance
^
an obvious one, given that we eventually wish to assume the existence of a continuum of goods
an intervzd [0, /i] on the real line. In the continuum limit, the price charged for an individual
good obviously has no effect upon any agent's intertemporal allocation of total expenditure, and so has no effect upon the
equilibrium processes {pt.Qi}. Even in the case of a finite number of goods, we can define equilibrium in this way, just as
one can define VValrasian equilibrium for an economy with a finite number of traders. However, the equilibrium concept only
becomes compelling as a formal representation of the outcome of competition in the limit of an infinite number of traders. For
rigorous development of this equilibrium concept for the finite case, see Benassy (1991, sec. 6.4) and references cited therein.
It has become common in the Uterature in macroeconomics and international trade to assume a continuum of differentiated
goods, especieilly when, as here, one wishes to treat the number of goods as an endogenous variable.
•'This equilibrium concept
is
in each period, identified with
*In their model ft{Bt)
elasticity of substitution
is
equeil to It~
equal to
1/(7.
'-'
'"'
[52 li C"!)'""]
This means that Dt(p)
that the condition of decreasing marginal revenue
is
is
< a <
where
equal p~ '
satisfied for all p.
1.
They thus assume a
globally constant
so that DJ(1) = -\/a for all t. We also observe
However, a globally constant elasticity of substitution
,
We now
economy with imperfectly competitive
specification that
to
When
turn to a discussion of the technology with which firms produce output.
is
standard
in
firms,
it
considering an
no longer meikes sense to assume the kind of technology
the real business cycle literature. First of
all, it is
common
in that literature
assume a production function using only capital and labor inputs, ignoring produced materials. In the
case of perfectly competitive firms, this involves no loss of generality, as the output measure that one
concerned with
is
total value
added (the
total
is
product net of the value of materials inputs), and this can
indeed be expressed as a function of capital and labor inputs. Suppose that the production function for good
i
is
given by
= G{Ki,z,Hi,Mi)
q\
where
z,
is
an index of labor augmenting technical progress at
capital services, //J the hours employed,
equilibrium, the price of materials
In
is
the
(1.3)
while
t,
^j
denotes the output,
and A// the materials inputs of firm
same
in
as the price for output, so that value
an equilibrium with perfect competition, this
F{Ki,z,Hi)
i
period
added
t.
is
A'J
the level of
In a
symmetric
given by
q\
— A/,'.
will necessarily equal
= m^[G(Ki,ztHi,Mi) -
M']
(1.4)
This follows from profit maximization by price-taking firms. Thus there exists a pseudo-production function
for value
added with only capital and labor inputs as
its
arguments. Furthermore, by the envelope theorem,
the derivatives of
F
must be equated
to their prices (deflated by the price of output) in equilibrium.
with respect to
equilibrium conditions
if
its
two arguments
one simply treats
F
equcil the
as the true production function.
being done in the reed business cycle literature (as in other
But with imperfect competition,
choose
its
(1.4) is
margined products of those two factors, that
no longer
common growth
A
correct.
Thus one obtains
This
is
implicitly
correct
what
is
models).
monopolistically competitive firm
will
materials inputs so as to maximize
^G{I<i,ztHi,Mi)-Mi
(1.5)
Pt
given the relation (1.2) between
its
sales
and
its price.
Because
p\ is
not independent of the quantity sold,
materials inputs are not chosen as in (1.4), even though in a symmetric equilibrium p\
of this kind
ceise of
is
nowhere essential to our conclusions, which depend only on the assumption that the
is independent of scale.
uniform prices
=
pt-
elasticity of
If (1.3) is a
demand
in the
smooth
in
neoclassical production function, the first-order condition for choice of materials inputs implies that
a symmetric equilibrium,
GM{Ki,ztHiMi) =
so that the use of materials inputs depends
solve this equation for
economy's true production
in
to
which
Suppose that
inefficient point
inside will
it is
This complication can be avoided
if
equilibrium).
on
(1.3) takes the
=
In this case firm
i
will
follows, insofar as
it
seems
realistic to
materials are relatively small; but
With imperfect competition,
for this
reason even
in
in
added
as a
degree of market
in the
be strictly inside
mm
its
production
far as
^
materials inputs
ViKi,z,Hi) M/i
-
SAf
SM
in
i
the value of gross output (in a symmetric
M/ = sm?!
of market power, and there exists a production function for value added that
We
for value
given preferences over consumption and
always choose materials inputs
of market power, namely V{K],ZtHl).
still
form
corresponds to the share of materials costs
1
it
changes
will
we can
depend upon the degree of market power.
1
< 5m <
economy
course,
would not represent the
one assumes a fixed-coefficient technology as
q,
Here
in the case of
the presence of imperfect competition the
and the degree
are concerned.
fact that this function
would also change
(and not simply at an
possibilities frontier
leisure),
it
Of
and so obtain an expression
But apart from the
possibilities,
+ D'{l)-']-'
upon the degree of mzirket power.
as a function of (A'J, 2t//^J),
A/,'
function of those two inputs alone.
power. In general,
[l
will in fact
is
regardless of the degree
independent of the degree
assume a production function of
this
form
in
assume that opportunities to substitute capitsJ or labor inputs
so doing
we neglect
effects that
may
materials inputs matter also for another reason and they continue to matter
With imperfect competition,
materials inputs affect the size of the wedge between the marginal product of labor and the wage.
cost, this
wedge
is
for
actually be of importance.
the case of a fixed-coefficients production function.
given degree of market power
what
(i.e.,
a given slope Z?'(l)), and hence a given
greater the larger the share of materials.
markup
For a
of price over marginal
Hence taking account of materials inputs
is
important when we wish to calibrate our model on the basis of evidence about typical degrees of market
power.
'For further development of this point, see Basu (1992).
To
see this, note that in the case of the fixed-coefficients production function, capital
are chosen to
and labor inputs
maximize
%\-WtHi-rtKi-SMqi
Pt
where Wt represents the wage deflated by the price of the composite good and
same way, again given
deflated in the
(Because the present paper
(1.2).
is
rt
the rental price of capital
concerned solely with imperfectly
competitive product markets, we assume that firms are price-takers in factor markets.)
equilibrium, the
first
order conditions for factor
[1
[1
We assume
+
+
D'{1)-'
D'{1)-'
SM]ztV2{Kt, ztHi)
so that a symmetric equilibrium of this kind
the moment.)
is
1
+
is
has an
We now
librium.
(We
SM]r,
(1.6a)
- SM]wt
(1.66)
eJso defer discussion of second order conditions
The wedge between marginal products and
a monotonic function of (1
sm >
[1
-
^
£>'(!)
possible.
1-SM +
This
=
[1
that
SM <
for
symmetric
demands take the forms
- SMmKlz,H\) =
-
In a
eff"ect
— sm)D'{1),
higher
factor prices
is
observed to be
D'{1)-
when the
latter
is
a smaller negative quantity. Hence
equivalent to making each firm's degree of meirket power higher.
consider the relation between price and marginal cost in a monopolistically competitive equi-
In period
(,
each firm's margined cost of production (using the composite good as numeraire)
IS
Comparing
this
with (1.6b), we observe that each firm's markup (ratio of price to marginal cost)
7
Note thai
in
this
= [1-H£''(1)"']-'>1
simple model, the markup
is
a constant, regardless of any changes that
will
equal
(1.7)
may occur
in
equilibrium output due to technology shocks or for other reasons. This conclusion depends crucially on the
homogeneity of the aggregator function / as well as upon the assumption of monopolistically competitive
10
behavior on the part of firms. Without homogeneity, each firm's
But abandoning homogeneity
itself.
makes the aggregation of
jJso
cated. For this reason, our entire analysis
from monopolistic competition
If
sm >
0,
closely related.
is
The former can be thought
do consider departures
/.
markups.
in
markup
7,
although the two are
of as the ratio between the price of value
added (the difference
between the price of output and the cost of materials) and
price to marginal cost 7 because firms
We
larger than the individueil firm's
is
/i
output
demands more compli-
endogenous variations
in
level of
different buyers'
conducted with a homogeneous
which result
in section 8
the inefficiency wedge
markup can depend on the
mark up
marginal cost. This
its
is
larger than the ratio of
their materials inputs as well. For a given value of
s,^/, // is
a monotonically increasing function of 7, given by
,= i\:il-h
This relation
is
is
important when we consider below the
(1.8)
effects of variations in
market power. (Recall that
a parameter of the production technology, rather than an endogenous variable.)
It is
also important for
understanding the relation between different measures of the degree of market power found
literature, as
We now
we discuss further
in
We
in the
empirical
in section 3.
discuss the relationship between the inefficiency
degree of returns to scale.
s,m
mentioned
earlier that imperfect
wedge introduced by market power and the
competition makes equilibrium possible even
the case of an increasing returns technology, so that we have more flexibility in the specification of V. In
fact,
once we have assumed market power, assuming increasing returns
not only possible but also more
{V homogeneous
In the case of a constant returns production function
reasonable.
is
of degree one), Euler's
theorem together with (1.6a)-(1.6b) implies that
q\
Hence
^i
>
I
- Mi =
+
fi{r,Ki
w,Hi)
implies pure profits (the value of output exceeds the
sum
(1.9)
of materials costs, capital costs, and
labor costs). Yet studies of U.S. industry generally find evidence of httle
discuss this further in section 3.)
Hence
we must conclude that there do not
if
market power
is
if
any pure
profits
on average. (We
significant (as evidence discussed below suggests),
exist constant returns.
Let us use as a measure of returns to scale in the production of value added the quantity
,
^ V,{Kl,ZtHi)Ki + VM<lztHl)z,Ht
11
Here increasing, decreasing or constant returns correspond to
Note that
this
a purely local measure that
is
homogeneous of some degree, then
that this
the
is
ry'
is
may
t]\
greater than, less than, or equal to one.
differentiated goods being
produced remains
fixed;
run returns to scale in a growing economy with growth in the
the production of value added rather than of gross output.
A
in
the factors employed while
has no implication regarding the long
it
number
well as in the total quantity of fcictors employed. Finally, note that this
in
of types of goods being produced as
is
a measure of increasing returns
rtKi
=
in
standard (local) measure of increasing returns
the production of gross output would instead be the ratio of average to marginal cost for firm
Pt
is
a constant and corresponds to that degree of homogeneity. Note also
a measure of the short run returns to scale associated with changes
number of
V
vary over time as production varies; in the case that
i,
i.e.,
+ w,Hi + Ml
- sm) + SM
- Sm) + SM
r;|/i-'(l
/i-l(l
Note that
if
s^ >
0,
the measure
t}\
will
be larger than
though the two coincide when there are no
pj,
^
intermediate inputs.
Abandoning the assumption
of short run constant returns
{rj
=
1),
we
find instead of (1.9) the
more
general result
r,\{qi
Hence zero pure
Thus
profits
- Mi) =
ti{r,K\
on average are consistent with
/i
>
+
wtHi)
1 if
the average returns to scale are
increasing returns (in the sense just explained) are required.
Note that
»?
>
1
also
r]
=
fx
means p >
>
1,
1.
so
that there are also increasing returns in the production of gross output, of a magnitude
p\
The
intuition
is
simple.
= [fi-^(l-SM) +
With increasing
own average
^One reason
if
its
own marginal
we emphasize the measure
a production function for vaiue added, and so
specifying
ri
price exceeds marginal cost. It
there are also external returns to scale the firm will
costs exceed
ihat
if
is
important that these
be internal to the firm, rather than due to externalities of the kind postulated by Baxter
and King (1990). Even
its
=7
returns, average cost exceeds marginal cost so that price can
be equal to average cost and profits be zero even
incre2ising returns
SM]~^
rather than
t)
positive profits unless
cost.
is that most studies in the real business cycle literature simply assume
these authors calibrate the degree of increasing returns they are in fact
here
when
make
p.
12
.
The
existence of increasing returns of this size
economic principles,
profits.
This
is
furthermore not merely fortuitous, but follows from
Chamberlin (1933) pointed out.
as
any period
If in
consistent with profit-maximization, assuming that the
is
fi,
then there are non-zero pure
number
of differentiated goods being
^
t]\
produced, and the identities of their producers, cainnot change. (Negative short-run profits are possible
is
assumed that
it
paid in advance.)
not possible to simply shut
is
But
demand
for
each good
/,
depends upon the number of goods sold
— D'(l)
remains the same after
that produces an additional product earns the
existing products.
ail
their optimal
at zero cost, perhaps because fixed costs have been
does not make sense that such a situation should persist.
it
assumed that the aggregator
of
down
The reason
is
same
that his optimal
markup does not change
either.
changes.
I,
7,
With
in
return to the level zero, due to adjustment in the
A
it
markup
is
is
the
same
rccisonable to
number
assumption, an entrepreneur
as that of
profits in the
assume that
of produced goods
—
mm
all
existing firms and
production of existing
profits should correspondingly
in the
long run, profits
/,
simple specification for the production function (1.3) that maJces this possible
9(
we have
on the new product as the profits earned on
profits
Hence sustained positive
some producers. Hence
Recall that
such a way that the elasticity
this
goods give entrepreneurs a reason to introduce new goods. Sustained negative
eventually \eaA to exit of
if it
is
F{Ki,ztHt)-^ A/'i
1 - SAf
Sm
(111;
.
where
is
F
is
assumed
to be
homogeneous degree one, and
a production function in which marginal cost
the existence of the fixed costs;
cycle literature in a
way that
it
is
4"
>
independent of scale, but average cost
generalizes the specification that
again using Euler's theorem, where
long run
if Y,' in
V,'
is
standard
in the
is
'
This
decreasing due to
equilibrium business
In the case of production
given by
denotes value added in industry
i
in
period
each industry tends toward a particular value, namely
be brought about by having the right number of differentiated goods
'
is
new parameter.
involves the introduction of only one
function specification (1.11), the index of increasing returns
in the
indicates the presence of fixed costs.
7,
4>/(/j
i.
Profits
—
1).
become zero
This
in
turn can
relative to the aggregate quantity of
Alternative specifications are possible. In particular, one can assume that the fixed costs take the form of some fixed
of labor, or capital. The current specification assumes that both labor and capital can be used as fixed costs and that
amount
the proportions in which they are employed for this purpose
depend on factor
13
prices.
capital
and labor inputs used
in
production; specifically,
we
require that in the long run
(1.12)
where
and Ht denote aggregate quantities of capital and labor inputs respectively. This condition requires
A'l
that the steady state
number
of effective labor inputs
of differentiated goods grows at the
and aggregate output.
same
rate as the capital stock, the quantity
*
Let us now collect our equations describing aggregates in a symmetric equilibrium.
added
is
determined by aggregate factor inputs through the relation
y,
(This
is
Aggregate value
=
F(A-,,z, //,)-*/.
of course the output concept for which
(1.13)
we have aggregate
data.)
Aggregate factor demands are
related to factor prices through the relations
Fi(K,,z,H,)
ZtF2{I<„z,H,)
where the inefficiency wedge
fi is
=
=
(1.14a)
tirt
(1.146)
fiWt
determined by (1.7)-(1.8). Because our interest in this paper
is
the short
in
run effects of shocks, we will treat both of the processes {z(} cuid {/(} as exogenous, even though we recognize
that in the long run macroeconomic conditions
literature
may
affect
both techniced progress
reasons stressed in the
on endogenous growth) and the number of differentiated products that are produced
sketched above).
Our
(for
reasons
specification of these exogenous processes, however, will be such as to imply that our
equilibria will involve only transitory deviations
from a scale of operations at which (1.12) holds.
These equations jointly describe the production side of our model. Note that
$ =
(for
in the case that
/j
=
1
and
these are the equilibrium conditions of a standard real business cycle model. Hence our specification
nests a standard competitive
model
as a limiting catse.
^ In this formulation, the output of each fimi stays constant in the steiuly state, the entire growth in output is accounled for
by growth in firms. An alternative formulation that preserves a constant steady state markup and degree of increasing returns
is to assume as we did in Rotemberg and Woodford (1992) that
(j(
=
.
rrun
\
L
Mn
F[h",,z,H',)-i,
1
- »M
,
'M
.
has the same steady state growth rate as zi and hence the same growth rate as A'l and Qi. hi this case, an
equilibrium with a constemt steady slate markup has no growth in the number of firms. The entire growth in output is rellected
in growth in each firm's output. One could probably also construct intermediate models with constant steady stale markups
where the number of firms as well aa output per firm grow over time.
and that
il>i
14
A
Complete Dynamic Equilibrium Model with Monopolistic
Competition
2
The economy
also contains a large
number
of identical infinite-lived households. At time
the representative
t,
household seeks to maximize
oo
E,\j20'N, + rU(Ct + r,ht+r)}
T
where Et takes expectations at time
of
members per household
period
the
t,
and
number
h,
in
period
t, /?
t, C(
denotes a constant positive discount factor,
denotes per capita consumption by the
denotes per capita hours worked by
of households at one,
we can use Nt
aggregate consumption, and so on.
argument, and decresising
in its
We
members
make assumptions about
assume, as usueJ, that u
demand
clciss
is
members
of the household in
t.
=
By normalizing
NtC, lo denote
a concave function, increasing
of utility functions
directly,
it
is
in its first
further specialized below.)
turns out to be more convenient
functions for consumption and leisure. These Frisch
functions depend on the marginal utility of wealth Aj which
A,
Assuming that households can
denotes the number
also to represent the totzd population, Ct
second zirgument. (The
the Frisch
A^(
of the household in period
Rather than make assumptions about the par2imeters of u
to
(2.1)
=
=
demand
given by
is
Ui(c,,/»,)
(2.2)
freely sell their labor services for the real
wage
w,, they
must
satisfy tiie first
order condition
— — Wt — U2iCt,ht)
"2(Ct,/»()
(ii.i)
7
A,
ui(c,,/i,
where the second equality follows from the definition
(2.3),
we can
solve for
One advantage
C(
and
/i,
of using the Frisch
expectations) on current choices
tiie
as functions of Aj
is
demand
Combining
(2.2).
and
ly,
(2.2) with the
second equality of
which gives the Frisch demand curves
c,
=
c{wt,X,)
(2.4a)
ht
=
h{ivt,Xt)
(2.46)
functions
is
that the effects of
captured by the marginal
condition for market clearing in the labor market
utility of
all
future variables (and their
wealth A(. In terms of these functions,
is
Ht=Nth{w,,Xt)
15
{2.b)
while that for the product market
is
y,
= Ntc(wuXt) +
[Kt+i
-
(1
-
S)Kt]
where G( represents government purchases of produced goods, and
<
the capital stock, satisfying
6
<
+
Gt
(2.6)
6 is the constant rate of depreciation of
Equation (2.6) with Yi representing value added
1.
is
the standard
GNP
accounting identity, except that we do not count value added by the government sector as part of either Gt
or
y'l
at
/
This equation says that one unit of the composite good at
.
+
It
1.
t
can be used to obtciin one unit of capital
follows that the purchase price of capital, just like that of materials,
equal to one.
is
We
assume
that households, like firms, have access to a complete set of frictionless securities markets. As a result,
tiie
expected returns to capital must satisfy the asset-pricing equation
Substituting (1.14a),
we obtain
l
A
= ^£;,|(^)[£il£l±i:ii±i^f±il + (l_6)]}
rational expectations equilibrium
that satisfy (1.13), (1.14b) and (2.5)
the response of this
Plosser,
model
-
is
a set of stochastic processes
(2.7),
to changes in
Zj
for the
(2.7)
endogenous variables
given the exogenous processes {Gt,zt,Nt,It}-
^
{Yt, A'l, //,
We
analyze
and government purchases using essentially the method of King,
and Rebelo (1988a). This involves restricting our attention to the case of small stationary
ations of the endogenous variables around a steady state growth path. Let us
first
exogenous variables, the equilibrium requires that variables such as {Yt,Wt,
in
for
...}
transformed (detrended) variables can exist
As
in
their
growth
in
the
exhibit trend growth as well.
if
the equilibrium conditions
terms of these transformed variables do not involve any of the trending exogenous variables
opposed to
fluctu-
consider the conditions
under which stationary solutions to these equations are possible. Given the existence of trend growth
However, a stationary solution
,
(;(
or
A^i
as
rates).
King, Plosser and Rebelo (1988a), this requires only that there exists a
homogeneous of degree zero
in
(w,X'^), and c(w,X)
is
<r
homogeneous of degree one
>
in
such that h{w, A)
is
(iv,X~^). Given these
'The variables I'l, Ht,uji, ,\t must be measurable with respect to information available at time (, while Ai must be measuiable
with respect to information available at time t— I. Information available at time ( consists of the realizations at time t or eailier
of the variables Gt,Zt,Ni, It- In section 6, we allow the information set to also contain "sunspot" variables.
16
w,, A,
j
conditions, there exists an equilibrium in which the detrended endogenous state variables
V -
^'
^*
v -
w -
ZtNt
Wi
-
—
At
,
=
^'
Nt
Zt-iN,
A,(z<)
Zt
are stationary, given stationary processes for the exogenous
^t
/=.
random
It
J
and a constant population growth rate so that -jf^
=
variables
^t
z
y'^
in all periods.
The equilibrium conditions
in
terms of the stationary variables become
y:
= F{{yl)-'Kt,Ht)-^i,
F^r^^Htj
Ht
c(u;„ A,)
1
=
(^)
=,iwt
(2.10)
= H{wt,\t)
+ [i^Kt+i -
/?^.{(7.%x)-^
(2.9)
-
(2.11)
G,
=
^^((^'V')"!^^'-^^'^'^^)
+
(1
6){'(tr'K,]
+
[
(2.12)
V".
(1
-
S)]
(2.13)
}
These equilibrium conditions involve only the detrended state variables, and so admit a stationary solution
terms of those variables.
in
'°
Like King, Plosser and Rebelo, we furthermore seek to characterize such a stationary equilibrium only
the case of small fluctuations of the detrended state variables around their steady state values,
in
constant values that they take
in
a deterministic equilibrium growth path
in
the case that
7,*
,
constant. This steady state can be found by solving the 5 equations (2.9)-(2.13) for the five
H
,
w, A and K. Since these solutions vary continuously with
(1.12) holds
and
profits are zero.
Given a steady
state,
At
this solution,
/<I>
equals
(/i
/,
—
we
ccin
l)Y
/,
j.e.,tiie
and G\ are
unknowns
V',
then find a value for / for which
.
we approximate a stationary equilibrium involving small fluctuations around
it
by
the solution to a log-linear approximation to the equilibrium conditions. This linearization uses derivatives
'"Note that equilibrium conditions
in
terms of stationary variables
multiple steady state equilibria.
17
ceir
be obtained with this technique even
if
the model has
evaluated at the steady-state values of the state variables.
the notation Vi for log(y(/V'), Wt for log{wt/w),
log-linear
^'
In writing the log-linear equations,
and so on, where the
Y,w
denote steady state values. The
approximation to the Frisch consumption demand and labor supply functions
where the coefficients represent the
we use
(2.4)
can be written
Ct
= (Cmm + (cx>^t
(2.14a)
Ht
=
(2.146)
CHwrbt
+ fHX>^t
elasticities of the Frisch
specification of preferences affects our equilibrium conditions
and so we calibrate the model by specifying numerical values
Thus the only way
demands.
is
in the values
in
which the
implied for these elasticities,
for these elasticities directly.
Our homogeneity
assumptions furthermore imply that
(Hw -<^eHX
=
(cw - fftcx
=
^
The
fCu
=
(2.Sa)
1
(2.86)
i^^
(2.8c)
three restrictions (2.8a), (2.86) and (2.8c) imply that there are only
.
To
(ex, iffw, iffx, and a.
former
is
preserve comparability with earlier studies we calibrate a and chw-
The
the inverse of the intertemporal elasticity of consumption growth holding hours worked constant
while the latter
The
two independent parameters among
is
the intertemporal elasticity of labor supply.
log-linearized equilibrium conditions can then be written as
y,
=
fiSKKt
+ ttSHHt -
nsKl't
^^{kt-Yt-Hi) =
Ht
sc[ecww,
+
-ayt
"The method
is
the
same as
ecx'Xt]
-f-
+
s/[Tf
£,{a,+ i -
= CHwW, +
-
1)A
(2.15)
w,
(2.16)
(2.17)
(^)(^< " t/)] + sgG,
(f±-^) -^(^,+i
/^,+i
+
Y.+:)}
=
=
V,
(2.18)
(2.19)
and Rebelo. This can be made rigorous, and justified £is an application of
shown in Woodford (1986). It should be understood that when we refer to small
values, we have in mind stationary random variables with a sufficiently small bounded
in King, Plosser
a generalized implicit function theorem, as
fluctuations around the steady state
(/^
(HX>^t
+ (J-^)k.+i -
A, -^
-
support.
18
This system
may
functions of
A',
be further simplified as follows.
and
A(.
We
can solve (2.15), (2.16) and (2.17)
for H,, Yt
and
iut
as
Substitution of these solutions into (2.18) and (2.19) gives a system of two difference
equations of the form
We
assume that the exogenous variables {y{ ,Gt,
shown
for
matrix
A
It) are subject to stationary fluctuations.
example by Blanchard and Kahn (1980), (2.20) has a unique stationary solution
is
non-singular, and the matrix
A~^B
has one eigenvalue with modulus
modulus greater than one. Woodford (1986) shows that
this
also the case in
is
equilibrium conditions have a locally unique stationary solution. Moreover,
shocks whose support
is
state. For the calibrated
we
find that there
In section 6,
is
indeed exactly one stable eigenvalue.
where there
is
The
We
thus focus
We
is
the
willi
when perturbed by exogenous
next section, and for
only one stable eigenvalue, there
with which we are concerned.
log-linear
in the
if
than one and one
sufficiently small, this solution involves only small fluctuations
parameter values discussed
and only
which the original nonlinear
all
much
we discuss alternative parameter values that lead both eigenvalues
In the case
less
if
Thus, as
around the steady
sufficiently
nearby values,
of our analysis on this case.
to be smaller than one.
a unique equilibrium response to the shocks
can approximate this unique response by calculating the solution to
llie
system (2.20) using the formulae of Blanchard and Kahn (1980) or Hansen and Sargent (1980).
resulting solution
is
a linear function of the exogenous variables. This means that we can decompose
fluctuations in the state variables into the contributions from each of the shocks that affect our exogenous
vciriables. It also
means that the
cuialysis of the effect of Jiny
one shock would not be affected by the inclusion
of additional exogenous shocks.
The
coefficients in the log-linear equation
presented
in
Table
1.
Column
system (2.15)-(2.19) have been written
2 of the table gives the formulas which,
values of the detrended state variables, allow us to
in
when evaluated
terms of parameters
at the steady state
compute the value of these parameters.
Witii the
exception of population growth and the parameters related to the lack of perfect competition, the values we
have assigned follow those presented
is
King, Plosser and Rebelo (1988a). Note that,
in
the case wjiere
equal to one the model we have presented reduces to the standard real business cycle model.
some of
in
in
the evidence relating to values for the average inefficiency
the next section.
The same evidence
is
wedge
fi
(for
now taken
survey
to be a conslniit)
equally relevant for calibration of the steady state
19
We
//
markup
in
the
case of the variable-markup models discussed later.
Evidence on the Size of Markups and Increasing Returns
3
Evidence on the
size of
markups and increasing returns comes from
literature that attempts to
with returns to scale
in
this literature,
regulated industries.
which
The
summarized
is
Panzar (1989) has concerned
in
Those found
1.4.
specification. Christensen
for electric
power generation seem to be somewhat sensitive
substantial returns to scale
when taking
cost.
By
contrast, Chappell
i.e.,,
analysis.
many
electric utilities.
These studies seek to measure the degree
is
perfectly consistent with large gaps between short
run average costs and short run marginal costs. This would happen in particular
minimizes costs. Firms would rationally make such capacity choices
an additional location or introducing an additional
vjiriety raises
Chamberlinian model of monopolistic competition. This
fixed cost per plant so that lowest average cost
all
at a scale
the rate at which average costs decline as one goes from a small plant to
a larger one. However, constant returns in this sense
there are several plants,
to the exact
and Wilder (1986) found much more
into account the multiplicity of outputs of
These findings are of only limited relevance to our
of long run returns to scale,
itself
in (1.10)
rj
and Greene (1976) found that only half the 1970 plants were operating
where marginal cost was below average
size that
a
returns to scale found in the telecommunications industry
tend to be substantial, with most studies finding returns to scale, which correspond to a value of
of the order of
is
measure the degree of increasing returns from engineering studies of the average
Most of
costs of different plants.
several distinct sources. First, there
of which have the
is
if,
if
plant size exceeds the
for instance,
producing at
a firm's sales for any given price, as in the
in essence
what occurs
in
our model.
We
have a
would be obtained by having a single plant. In equilibrium
same average
cost and, nonetheless, marginal cost
is
below
average cost.
Second, there
is
a literature which attempts to measure the elasticity of demand facing individual prod-
ucts produced by particular firms. This literature
it is
never profit maximizing to set the
demand
for the
product. There are
marketing literature.
ticity is just
under
2.
is
relevant because, as
is
markup 7 lower than one over one
many
estimates of the elasticity of
Tellis (1988) surveys this literature,
clear
from the derivation of (17),
plus the inverse of the elasticity of
demand
for particular
and reports that the median measured
This suggests that the markup 7 of these individual firms would equal 2
20
products
if
in
price
the
ela.s-
they behaved
monopolistic competitors.
like
the marketing literature
elcisticities
in
of
demand
demand probably
for
demand
tiieir
elasticity of
is
our symmetric model where correct, the
would correspond to the
the marketing literature
the
If
is
differ across
elasticity of
products and the
probably atypically low. This
probably
demand
is
less price sensitive.
that exceeds
is
elasticity of
markup and
One
these two parameters that
demand. The aim of
Her estimates of 7 and of
notable feature of these estimates
we imposed through our zero
Hall (1988, 1990) proposes a variant of this
using instrumental variables.
The share
rather than estimated, so that only
tiiis
is
fi
large estimates of
/i
for
many
price
in
some
approach
to
is
that he
is
and
itself.
Thus the
relation
,
which, essentially, equation (2.15)
known (from measured
and endogenous
U.S. manufacturing sectors;
it is
between
appears to be validated.
is
factor
need be estimated; instruments are used that are believed
-ff
16
1.4 for
that her industry estimates of the ratio
markup
coefficients are treated as
that one reason that Hall's estimates of the
is
1.2
variation in
/< is
estimated
payments)
a
prion
to
ignored. Hall obtains
over 2 for six out of seven one-digit sectors.
and related estimates at the end of the next section. Here we wish simply to note
discuss this approach
as Morrison
in
range between
77
profit condition
approach
be orthogonal to exogenous technological progress
estimating
Before closing this section,
are zero, so that
/i
it
is
/i
"markup
ratio"
cire
larger than those obtained by authors such
rather thcin 7.
worth discussing the basis on which we state that
must equal
times that years private value added.
'^
economy probably has a
of the degree of increjising returns. Morrison
of average to marginal cost closely resemble her estimates of the
18%
the
in
tliat
an example of this approach. She estimates a flexible functional form cost function, using data on
out of her 18 industries.
economy
of those products studied
a literature which tries to obtain econometric estimates of marginal cost and,
gross industry output and materials inputs.
We
demand
2.
combine them with econometric estimates of the
1990)
in
because the marketing literature focuses on
Thus, the typical product
obtain simultaneous, independent estimates of the
(
estimated
faced by the typical firm. In practice,
elasticity of
is
elasticity
branded consumer products which are more differentiated than unbranded products so
Finally, there
cases,
demand
demand
tj.
'-
Total tangible assets minus durables
in
US.
profits in the
1987 were equal to 2.25
Since private investment (again excluding durables) equaled about
of private value added and the yearly growth rate
For a more complete discussion along similar
lines,
is
about 3%,
it
follows that the yearly depreciation
with independent estimation of the degree of increaising reiums, see
(1990).
21
Hfill
of this capital stock
must be about
5%
one must subtract the growth rate from the ratio of
(to obtain this
investment to capital which equals 8%).
The
share of payments going to capital has been
25% on
average.
These payments can be decomposed into the product of the capital output ratio and the sum of the rate of
depreciation and an implied rate of return on capital. Thus, this
6%
about
per
annum.
It is
the fact that this rate of return
securities that leads us to say that there are
some pure
profits, the
payments
no
impUed
rate of return to capital has been
close to the rate of return
is
economy.
profits in the
If
on stock market
owners of capital
also received
would exceed the product of the stock market rate of return
to capitalists
and the actual capital stock. Yet another way of making the same point
is
to note that, on average Tobin's
one (Summers (1981)). This again says that the present value of payments to the owners of capital
q is
discounted at the required rate of return on equity shares equals the cost of replacing the capital stock.
In the ne.xt
effects of
two sections we study the
effects of
having a constant markup different from one
for tiie
shocks to government purchases and of technological shocks.
Responses to Government Purchases
4
The
first
exercise
we consider
is
a change
postulate a stochastic process for Gt-
model depends also on
in
government purchcises Gt- To perform
The reason we must do so
their expectation of future
is
this exercise
we must
that the behavior of the agents
government purchases of goods.
We
in tiie
assume that Gt
is
given by
Gt
we assume constant growth
In the present section
assume that the number of firms
1
and
For this case
4> is
we
/,
/(
equal to one.
the profits of the existing firms.
rate as ZtNt (so that
/(
of
z<
and Nt] hence
(4.1)
(4.1) specifies
an exogenous
is
i^f
,
we
does not respond to the shock. In the perfectly competitive case where
equal to zero this involves no
just set
\P^\<1
For the purposes of analyzing the response of the economy to the shock
stochastic process for Gt-
equals
= p^G,.i+uf
We
loss of
generahty since the number of firms
In the case of imperfect competition, changes in
nonetheless Eissume that
constant).
is
/(
//
indeterminate.
Gt do change
continues to grow exogenously at the same
Abstracting from variations
in
the rate of entry
is
reasonable as an
approximation because entry decisions involve relatively long lead times.
In
a model with constant markups, a change
in
G increases output
22
only through an increase
in
the suppl>
of hours at a given real wage. This
wedge
n, a relationship
is
apparent from (1.14b). This equation
firms to hire labor at a given real
Barro (1981) why labor supply
raise the
wealthy.
less
marginal
employment
We
and capital are
is
fixed, the willingness of
emphasized by
resisons
that they tend to increase real interest rates. Both of these
wealth A( and thus raise Ht for any given Wt-
Thus
the real wage
p"^
because changes
This
is
'^
We
in
uf
for the case
where
p*^
assume that the share of materials
a conservative choice since value added in manufacturing
crucial in the imperfectly competitive case.
(which, using (1.8) with
sm
We
report results for both
.
We
1
and 2 report the percent response
in hours,
was suggested by the
earlier discussion, real
effects, for given values of the
and
equal to
is
equals
Sf,i
only about half of the value
equal to one and for
fi
model but
equal to
markup
to 1.17). This
is
is
1.4.
fairly
values are listed in
output and the wage to a one percent change
11.7% of GNP the multiplier
imperfect competition.
equals 1.4 than
when
it
On
=
/x
for
it
1.4.
increases by
We
0.05% when
government purchases
is
less
ft
and the wage
Output and hours
wages decline. But, there
model's other parameters.
case of perfect competition while
bi
is
output,
in total
The other parameter
see in the figures that the qualitative response of hours, output
equals one as in our imperfectly competitive case where
The
falls
they are taken from King, Plosser and Rebelo (1988a).
Figures
uf
fi
markup 7 equal
equal to 0.5 corresponds to a
low relative to those that have been estimated in the literature.
1;
efi"ects
government purchases are persistent but also have large
of gross output in manufacturing. This parameter plays no role in our perfectly competitive
Table
depends on
latter
that the increase in government purchases makes
first is
simulations of the model's response to changes in
chose this value of
half.
The
change.
will
The second
utility of
capital. Since technology
wage does not change. However, there axe two
components which are mean reverting.
one
a given constant inefficiency
rises.
We compute
.9.
for
between the wage and the marginal product of labor where the
employment, the state of technology and
households
is,
is
a change
is
the
rise in
in the
same
1.4.
//
both cases and, as
magnitude of these
see that output rises by about
=
wiien the
in
0.04%
in
the
Because government purchases equal
than one half in both cases but
the other hand, the percent response in hours and real wages
is
it is
larger with
smaller
when
/i
equals one.
difference in the responsiveness of hours
and output does cast some doubt on the accuracy of the
our analysis of military purchases we found these to follow & very persistent but stationary AR(2) process. For simplicity
literature we consider a persistent AR(1) here.
and comparability with previous
23
common
view according to which the presence of imperfect competition, in
effect of
government purchases on economic
demand
spillovers"
on consumption demand
government purchases
in
activity. ^^
idea
is
argued to
is
It is
activity through a "multiplier" process of the
magnifies the short run
reflect the
presence of "aggregate
that the increase in output induced by the rise
raises the profits of the imperfectly competitive firms
income makes consumers purchase more.
for
The
.
This
itself
argued that these
Kahn-Keynes
effects
type. It
is
and the resulting increase
in
amplify the response of economic
true that, in our model, a larger
given values of the other parameters, magnifies the response of output. But this
is
solely
due to the
^/.
fact
that imperfectly competitive firms set the wage below the marginal product of labor so that a one percent
increase in hours raises output by
fis}{
percent rather than by
sh
percent.
'^
On
the other hand, a larger
H reduces the response of hours.
The reason
for this
is
easily seen.
Hours become
less
responsive
when
fi is
increased because the (negative)
wealth effect of an increase in government purchcises become smaller. For given prices (wages and interest
supply depends upon the present value of after tax income net of wages.
rales), labor
increase in
the
G
amount
increases the present discounted value of taxes (and hence reduces after-tax income) by e.xactly
of the increase in G.
value of income.
If
zero
But, potentially, chzinges
G
in
they lead equilibrium hours and output to
amount by which the
is
In either case, an
have an additional
of hours exceeds the real wage
of hours equals the real
(i.e., if
on the present
income net of wages increases by the
rise,
wage
increase in output exceeds the increase in the
when the marginal product
effect
wage but
it is
bill.
To
positive
first
if
order, this
amount
the marginal product
firms have market power). Thus, in the case of perfect competition,
a one dollar increase in
G
lowers the present value of income by one dollar, while in the case of imperfect
competition
by
less
it
lowers
In a sense the
it
"demand
than one dollar.
spillover" literature
is
correct in arguing that the increased profits in the case
of imperfect competition give an additional boost to household income.
supposing that the stimulative
effect of
effects of
government purchases
government purchases on household income.
Where
this
argument
errs
is
in
result
from a positive, rather than a negative
It also errs in
supposing that the direct determinant
Mankiw
(1988), StarU (1989) and Silvestre (1993).
understand from (2.15) the basis of Startz's (1989) argiunent that this is just a short run effecl. A pennanent
increase in G would permanently increase profits, requiring an eventual increase in the number of firms /. In a coniparison ol
steady state equilibria (in whidi / is assumed to adjust so as to keep profits equal to zero), the percentage increase in oulpul
'*See, e.g.
'^One
Ccin also
equals only 5/y limes the percentage increase in the labor input.
24
of equilibrium
employment
is
the effect of household income on consumption
demand, rather than the
efTect
of income on labor supply.
Another implication of Figure
1
worthy of note concerns the
labor productivity. Since output increases
it
is
obvious that measured productivity
behavior of the Solow residual, which
business cycle literature,
is
is
effect of
more and hours increase
more
rises
(falls less) in
government purchases on measured
less, in
the case of
/i
greater than one.
used as a mezisure of exogenous productivity growth
especially noteworthy. Recall that the
Solow residual
the real
in
given by
is
Ay, - shAH, - SKAKt
where AY] represents the change
in the
difFerentiation of (1.13) using (1.14)
and keeping
,
7,
The numerator
is
of (4.3) thus
logarithm of
/
^'(
(4.2)
and analogously
for
By
A//, and AA',.
contrast.
constant establishes that
AV, - fisnAHt - hskAK,
_
—
must be invariant
The
the case of imperfect competition.
\^oj
But
(to first order) to changes in Gt-
this implies that
greater than one and Ht rises for any reason other than a technological shift (so that
7,*
is
if /;
unchanged)
the expression in (4.2) will rise. In other words, an increase in hours induced by an increase in government
purchases or any other non-technology shock raises the standard Solow residud.
The
reason
that, with
is
imperfect competition, an increase in the labor input must necessarily raise the value of output by more than
it
raises labor costs (since firms
make
profits
on the marginal
units).
This results
in
an increase
in
measured
productivity.
This shows that ignoring imperfect competition when
it
is
incorrect measures of total factor productivity. If one wants to
formula (4.3) which depends on
The
fact that the
fi
in addition to
Solow residual
(4.2)
some observed anomalies concerning Solow
in
is
actually present
is
dangerous.
measure true changes
in 2,
leads to
It
one must use the
depending on observable magnitudes.
not a correct measure of true technical progress
residuals. For
may
explain
example, a number of authors have observed that,
postwar U.S. data, Solow residuals are correlated with various measures of government purchases (Hall
(1988), Baxter
and King (1991), Burnside, Eichenbaum and Rebelo (1993)).
One might argue
that this
simply indicates that government purchases are not exogenous with respect to technology shocks.
might be true of some components of government purchases, especially spending by
25
local
This
governments thai
But
are forced to have balanced budgets.
it is
of national defense-related goods, that have
hard to defend the "reverse causation" thesis
moved
posed by communist regimes. Yet this component
is
positively correlated with Solow residuals as Hall (1988)
this observation insofar
it
predicts that hours
response to an exogenous increase in government purchases and, as a result, the Solow
in
residual should increase as well
if /i
>
'®
1.
Imperfect competition might similarly explain the observations of Hall (1988) that changes
prices (that, again, should be
Solow residuals,
^'^
ability of
is
world
oil
exogenous with respect to the state of U.S. productivity) are correlated with
^^
imperfect competition to explain these anomalies provides not only an argument that
imperfect competition
Indeed, this
in
and the findings of Evans (1990) that various measures of monetary policy shocks forecast
future Solow residuals.
The
case
changed perception of the threat
mziinly in response to
and Baxter and King (1991) show. Our model can explain
should increase
in the
is
important but
may
also be the basis for a quantitative estimate of
the basis for Hall's (1988) estimates of
observes a variable
Vt,
/i.
The parameter
ft
is
known
to be orthogonal to the
importance.
can be estimated using
such as military purchases or changes in the world
with output and hours changes and
its
oil price,
change
in
that
is
(4.3)
if
one
both correlated
technology 7/
.
Then
v,
should be orthogonal to the right hand side of (4.3). In particular
Cov(i;,,
Hall's proposal
moment
is
to estimate
condition (4.4)
actually zero
if /i is
/i
Ay, - fiSnAH, - (iskAK,) =
(4.4)
so as to minimize (under an appropriate metric) the extent to which the
fails to hold.
In the case
where
Vt
is
a single variable, the expression
in (4.4)
is
replaced by the instrumental variable estimate
L,vtAY,
Hall's estimates indicate estimates of the
wedge
of over 1.8 for
fi
all
seven 1-digit industries he considers.
Subsequent work by Domowitz, Hubbard and Petersen (1988), uses gross industry output so that
it
estimates
'^Alternative possible explanations of the anomaly that do not depend on imperfect competition are proposed by Baxter and
King (1991) and Bumside, Eichenbaum and Rebelo (1993).
"For a complete dynamic equilibrium model of the effects of oil prices which is constructed along the lines of this paper, see
Rotemberg and Woodford (1993).
'^Explicit development of this last idea would require, of course, a model where monetary policy shocks affect economic
activity, a topic we do not take up here. Imperfect competition in product markets does not in itself imply any real effect of
monetary policy. On the other hand, as we mentioned in footnote 2, imperfect competition is often a crucial element of models
In which monetary non-neutrality results from price rigidity.
26
the
markup
Their estimates of 7 range between
7.
sets of estimates
and
1.4
1.7 for 17
do not contradict each other because, as long as the materials share s^
smaller than 7 as can be seen from (1.66). For example,
and a materials share of
.5
(which
Ls
those estimated by both Domowitz,
is
positive,
fi
is
equal to 2.3 (a typical value for Hall's industries)
/i
also typical for those industries) imply
=
7
Hubbard and Petersen (1988) and Morrison
1.4
which
is
in the
range of
(1990).
Responses to Technology Shocks
5
In this section,
economy
we show that the
level of the
to changes in technology.
average mcirkup matters when
compute the
how much
productivity.
firms, as
size of the
we do not wish
productivity
is
a
As we showed
steady state.
We
On
comes
to the response of the
The
(4.3).
number of
reason
is
consume depend upon
firms.
It is
not enough to simply
that, once again, household's decisions
their expectations of the future state of
are also unable, in this case, to ignore the issue of variation in the rate of entry of
In fact, in this section,
shock.
technology shocks using
labor to supply and output to
We
it
Before we can compute the economy's response, we must postulate a
stochastic process for the level of technology itself and for the
of
out of their 19 industries. These two
to
we
assume that technology shocks have a purely transient
follow King, Plosser
random walk,
in (1.12),
the
so that
7,^
number
the other hand,
on productivity.
effect
and Rebelo (1988b) and Plosser (1989)
in
an independently distributed random variable.
is
new
assuming that
'^
of firms must grow with z for profits to remain equal to zero in the
we do not
believe the
number of firms adjusts very rapidly
to a technology
thus wish to concentrate on short run effects of technology shocks by assuming that entry plays
only a small role in these short term dynamics.
To do
this,
we
let /(
follow
cin
error-correction process of the
form
log/,
where
itself
/
=
Klog(/2, AT,)
and k are positive constants with k
stationary as
we assumed
in
Section
2.
<
I.
By
entry in response to a technology shock, even
+ (!-«) log /,_i
(5.1)
This process implies that with a stationary {7/}, {/(}
letting
when
k be small we ensure that there
it is
permanent.
We
is little
is
immediate
conjecture that our results hinge
'^\Ve made this assumption because the results we obtained for the case where Zi is stationeiry were unsatisfactory. We showbelow that there are exist two different methods of computing the variance of output implied by the model as a response lo
technology shocks. While the methods are difTerent, they ought to give the same answer for the volatilities of output and hoiii-s.
The two methods do so when we assume that 2 is a random walk but we lead to very different theoretical variances for output
and hours when we eissumed that 2 is stationary. For more on the sensitivity of theoretical variemces of output as one varies
the stochastic process for the technology shocks, see Eichenbaum (1991).
27
mainly on the fact that the response of entry with a small k
(5.1). In particulcir,
is
slow and not on the precise specification of
a small k preserves comparability between our results and those obtained by Hornstein
(1993) for a model without permanent technology shocks in which the effects of technology shocks on entry
are ignored
Differencing (5.1),
we obtain
A/,
=
+
/c(-r/+T'^)
(l-'c)A/,_i
which implies that
oo
= J]K(l-/c)^7f_;
A/,
;
(5.2)
=
where A/( denotes A/, minus the unconditional mean of that stationary variable while,
-fi
minus
its
mean.
now
,
This implies that the change
Ay, - ^iSHAH^ - fiSKAK,
—
=
in the
number
the case of imperfect competition. This
in
productivity
assumption such as
and substituting
(5.1)
(5.2),
is
if
is
fl for the U.S.
is
The
-
l)AIt
5.3)
because entry of firms increases fixed costs and thus requires
is
is
to be produced with the
necessary in order to measure technology shocks.
=
in the lag
fi(I)
same
inputs.
Thus an
Removing means from
AY, - tisnAHt - fiSKAKt
(5.3)
(5.4)
operator whose coefficients depend on p and k. This polynomial has
circle; in particular, it
equals
1
when
economy using quarterly data from 1947:1
hours while assuming that the change
series
(fx
we obtain
a polynomizd
no roots inside the unit
+
of firms enters the corrected Solow residual (analogous to (4.3)),
a given quantity of output
7/
where Q{L)
denotes
yields
ft
an increase
-/,'
^°
Differentiation of (113)
in
as before,
fi is
one. Using (5.4),
until 1989:4
in capital is constcint.
^^
The
we construct a
series for
on private output and private sector
construction of our output and hours
discussed in Rotemberg and Woodford (1992).
first
part of Table 2 presents the measured vfiriance of 7f for various values of p.
measured variance of technology
falls
as
we increase the markup. The reason
is
It
shows that the
that typical U.S. business
^°Note thai with this notation, if a variable A' is stationary, then AA' is the first difference of A'.
^'This is not strictly correct but, because investment is such a small fraction of capital, it does not induce a laige bias into
our calculation.
28
cycles involve procyclical
movements
in
output, hours and the standard Solow residual.
than one, one expects the Solow residual to move procyclically even
explained in the previous section. Thus a model with
/i
in the
If
^
is
greater
absence of technology shocks as
some
greater than one can explain
fraction of the
variation in the Solow residual leaving smaller unexplained variations in total factor productivity.
We computed
the model's responses to shocks in f' using the King, Plosser and Rebelo (1988a) param-
eters listed in Table
that K
is
equal to 0.02 so as to
The model's
We
a share of materials of one half and, again, values p equal to
1,
make
reason
is
and
1.4,
We
assumed
sure that immediate entry hcid a relatively trivial effect on the results.
prediction for the effect on output and hours of a
see that, for a given increase in
1
r,
shock to
7,*
is
presented
Figure
in
3.
higher under imperfect competition.
The
an increase in the effective units of labor that firms
hire.
the response of output
that, an increase in z represents, in effect,
1%
is
Because firms with market power set the marginal product of labor higher than the wage, an increase
in
the effective labor input raises output more under imperfect competition. This can be seen directly from
equation (2.15) which shows that the change in output for given hours and capital input
times 7^. This
By
a higher
/i,
change
worked
is
smaller
hours are nearly insensitive to changes
in technologiccd
opportunities
is
when
the
markup
work
and
for future leisure.
ambiguous
this reduces labor supply.
wealth effect
section,
is
larger.
The
On
is
is
well
and the wage and
net effect depends
who
Hornstein (1993)
technology shocks.
There are two
to
changes
in z.
We
discusses
in
this leads
workers to
If
/i
is
made
still
effect, as in the
slightly larger
previous
than
1.4, a
increases.
fluctuations are smaller with imperfect competition,
it
fixed in the short
on whether the intertemporal substitution or the
Imperfect competition increases the size of the wealth
employment
is
the other hand, an increase in z also makes people wealthier
and so reduces the extent to which labor supply increases.
result, that
That the response of hours
known. Because capital
positive technology shock actually reduces equilibrium hours, though output
This
higher. Indeed, for our chosen
in technological possibilities.
run, an increase in z raises temporarily the marginal product of labor
substitute current
equal to ^isn
raises the response of output.
/i
contrast, the response of hours
value of
to a
why
is
is
is
also obtained by
terms of the variances of output and hours that can be explained by
next turn to the consequences of imperfect competition for this type of exercise.
diflferent
They both
ways of computing the variance of output and hours that can be attributable
rely
on the impulse response functions which axe plotted
29
in
Figure
3.
Let the
impulse response functions be written as
^yt = T.^Yrt-i
1
(5.5)
=
A^, =^^fTf..,
(5.6)
i=0
Then one estimate
of the implied variance of the change in output
is
f;(e)'Var(7/)
(5.7)
«=o
where Var(7,')
is
the variance of the technology shock reported in Table
2.
The
variance of the change
in
hours can be computed analogously.
An
alternative computation of the variances of output and hours relies on the historical time series
the technology shock that can be
for
computed using
(5.4).
As
in
we can compute the
Plosser (1989),
values of output and hours that these time series for technology shocks predict. If 7f gives the (de-meaned)
historical series for technology shocks, the predicted series for (de-meeined)
changes
in
output and
iiours are.
respectively
00
^Yt
«
We
oo
= T^^'it-i
=
(5.8)
i=0
can then compute the sample variance of the series {Ay,} and {A.^i}.
Column
2 of the second
and
third part Table 2 give the empirical variances of output
while column 3 gives their theoretical variances
report the variances
/i
^Ht = 5^^."7f_.
computed using
(5.7)
computed using the sample variances of
because they are nearly identical.
equal to one, the predicted variance of output
is
predicted variance of hours
is
is
^^
more substantial
eflFect
(5.8).
We
do not
For the standard case where
somewhat smaller than the actucJ variance while the
quite a bit smeiller than the actual variance. Increases in
variances though they have a
and hours growth
on the variance of hours
/i
lower both predicted
for the reasons that
we gave
above.
We
also present in Table 2 a statistic that provides a further test of the empirical plausibility of the
model's predictions regarding the effects of technology shocks.
As we said
This
statistic relates to the orthogonality
footnote 19 above, this is not true when technology shocks are assumed to induce only transitory changes
that zi followed an autoregressive process we obtained much smaller theoretical variances
for output changes when using the method of Kydland and Prcscott (1982) than when we asked about the vaiiabjiity of
output generated by the model in response to the entire time series of Solow residuals. This was true even when we made the
autoregressive coefficient equal .o .99.
in technology.
in
When we assumed
30
of the predicted
We
movements
output and hours on the one hcind, and the prediction errors on
in
other.
have mentioned above that a correct measure of technical progress should be independent of the other
shocks that affect the economy.
In the previous section
we showed that
if
some
of the other shocks can
an orthogonality condition that can be used to
test the validity of
method of measuring technology shocks. But even when the other shocks cannot be
directly measured,
be directly measured, this gives
the
tlie
rise to
the independence principle can be used as the basis for a specification test of a
technology shocks. For
coefficients ^^
if
model of the
effects of
the technology shocks are correctly measured and the theoretical impulse response
and ^^ are
correct, then the prediction errors
AV — AV"
AH — AH
and
should be expressible
as distributed lags of the other exogenous shocks. ^^ It follows that
Cov{Ay',,(Ay, - Ay,)}
=
o
(5.9)
Cov{AH„iAHt-AH,)}=0
Testing the validity of these
moment
(5.10)
conditions provides a specification test which does not require
knowledge of the other types of shocks. To provide a convenient measure of the extent to which the moment
conditions (5.9) and (5.10) are violated
Var(Ay,)
we decompose the variance of
actueil
changes
in
output
eis
follows
= Var(Ay,) + Var(Ay - AY,) + 2Cov{Ay,, (Ay, - Ay,)}
so that
^ Var(Ay,)
.
Var(Ay,
Var(Ay,)
- Ay,)
y
Var(Ay,)
where
Y
'^
Thus w^ measures the extent
to which the
technology shocks and the variance
The
size of the
departure of
such as Var(Ay,)/Var(Ay,
)
it
w^ from
as a
_ 2Cov{Ay«,(Ay, -Ay,)}
~
Var(Ay,)
sum
of the variance of output that the model attributes to
attributes to other sources
zero thus gives one
fails
to equal the total variance of output.
some idea how
seriously one can take a statistic
measure of the degree to which observed variations
be explained by technology shocks.
Here we rely on the validity of
tlie
log-linear
approximation introduced
31
in section 2.
in
output growth caa
The
of
fifth
column
of Table 2 gives values of
w^ and
of the analogously defined u)^ for difTerent values
For the model to be correct, both w's ought to be zero
fi.
restrictions that can be used to estimate
fi.
Such an estimate
is
moment
Hence, these provide additional
then based entirely upon the way
in
which
one parameter value as opposed to another improves the model's ability to produce empirically plausible
predictions regarding the part of aggregate fluctuations that are due to aggregate technology shocks.
As we can
see, raising
Thus, the results of
1.6.
competition.
What
is
/i
from
to 1.4 lowers
1
this estimation
both w's which reach a minimum
for
between
fi
1.4
and
procedure also yield relatively important departures from perfect
perhaps even more interesting
is
that the resulting estimate of ^ implies that technology
shocks lead to practically no fluctuations in hours worked. Thus, essentially, the entire movement
in
hours
worked must be due to some other type of shock.
Fluctuations
6
The
Due
to Self-Fulfilling Expectations
introduction of imperfect competition and increasing returns also makes possible an entirely new source
of equilibrium fluctuations in economic activity.
activity fluctuates in response to
In particular, equilibria
random events that do not
it
is
(1992)).
be possible
They
in
many
in
response to the event in question.
is
in
else's
now
Guesnerie and Woodford
For there,
must maximize the expected utihty of the representative household,
sections 1-2.
^*The indetermjnacy
"'^
as above, the first welfare
theorem no longer holds, and as
such a simple way that equilibrium must be unique. Indeed,
Benhabib and Farmer (1992) show
first
e.g.,
such
a unique allocation with this property.
one cannot show
liere in
everyone
are not, however, possible in the case of the standard neoclassical growth model.
Once we introduce imperfect competition,
result
if
in
Equilibria of this kind are
kinds of intertemporal equilibrium models (see,
the equilibrium allocation of resources
and there
people's expectations of the future path
correct to expect a different future path for the economy,
expectations and actions change
to
in
This need not be because individual agents' expectations are incorrect - instead,
a "sunspot equilibrium"
known
which economic
exist in
involve any change in underlying fundamentals
("sunspots"). These fluctuations are caused simply by changes
of the economy.
may
in
the case of a
Recall that in section 2
model with monopohstic competition
we observe
of rational expectations equilibrium,
discussed in the c:>ntext of a model of this kind by
and the
Hammour
32
that, for our calibrated
possibility of
it
a
need not be, as
like tiiat
described
parameter values, the
endogenous equilibrium Huctuations, were
(1988). For other examples of stationary sunspot equiUbiia
matrix
A~^B
A
(where
cind
B
are the matrices in (2.20)) has one real eigenvalue with absolute value less
than one, and another with absolute value greater than one; this allows us to compute a locally unique
stationary solution to (2.20). This need not be true, however, for
Farmer show that
one (which
for
if /i
and
are sufficiently large,
rj
some parameter
values
Eire
A~^B
all
parameter values, and Benhabib and
instead has two eigenvalues with modulus less than
a complex pair).
In this case, there exists a large multiplicity
of stationary rational expectations equilibria, including equilibria in which output fluctuates in response to
"sunspot" events.
Consider, for simplicity, the case
in whicli
there are no stochastic variations in any of
exogenous
liie
"fundamentals" {tt ,Gt,It}- Then (2.20) becomes simply
A
stationary solution
is
given by the bivariate stochastic process
-U.-sfi; ).("-)
where {u(}
only at date
{ut}).
is
<
a mean-zero white noise "sunspot" variable, and the realization of Uj+i becomes known
+
Thus the
1.
^^
In fact,
all
stationary solutions
multiplicity of equilibria does not
must be of
mean
this
form
(for
some sunspot
variable
that theory lacks testable implications about the
character of aggregate fluctuations. In the absence of exogenous shocks and to the extent that the log-linear
approximation
is
accurate,
Thus the model does not
all
of the stationary equilibria are simply scedar multiples of a single equilibrium.
predict the amplitude of the fluctuations, but one
is
able to obtain definite numerical
predictions about the relative variability of output, hours, investment, real wages and so on, as well as definite
predictions about the serial correlation and cross correlation of
are added, the set of stationary equilibria
is
a set of
finite
all
these series. ^^ Even
when other shocks
dimension (linear combinations of a small number
of possible types of fluctuations), so that relatively strong restrictions are plsiced on the data.
Farmer and Guo (1993) show that
in
the case of a
model of
standard fashion, except for the large values assumed for
in
/i
this kind that
and
t],
is
"calibrated"
in
in
aggregate
Hammour
(1991), and
the predicted fluctuations
models with imperfectly competitive product markets and increasing returns, see Woodford (1991),
a relatively
Gali (1991).
^^This solution to the log-linearized equilibrium conditions (2.20) approximates a solution to the exact equilibriiun conditions,
See Woodford (1986) for details.
in the case that the amplitude of "sunspot" fluctuations eire sufficiently small.
^^ Early illustrations of this were given in Woodford (1988, 1991).
33
quantities, in tlie absence of
any exogenous shocks, exhibit relative
variabilities
and co-movements similar
de-trended U.S. data. They argue that in this respect the model's predictions are not
to those observed in
clearly less consistent with the facts
RBC
model, with perfect competition,
The standard model,
of course, also seeks to explain the
than are those of a standard
constant returns, and exogenous technology shocks.
amplitude of aggregate fluctuations, given that measured Solcw residuals can be taken to indicate the
of the exogenous technology shocks, while the
Guo
model.
ampUtude of fluctuations remains unexplained
The Farmer-Guo model, however, can
residuals with other aggregate variables; for the
in principle
is
of market
model predicts variation
in
measured Solow residuals
power and increasing returns assumed by Farmer
cind
Guo
in
(/i
4.
However,
it
=
1.72,
the stationary sunspot equilibria exist only
must be outside the unit
if
it
=
1.61)
sections
:j
circle in the case of perfect
be a point at which
/i
and
ij
still
the case of other consequences of imperfect competition
The
reason
is
that, as
generate somt procyclical productivity even
variations in productivity.
On
altogether. -* For
circle.
Since one of tliem
competition (because of the
/i
and
r?
first
welfare theorem),
toward one, there must
exceed one but one eigenvalue has a modulus greater than one.
quantitative reasonableness of their assumptions about
of productivity variations.
it
eliminates
both eigenvalues are inside the unit
and since the eigenvalues vary continuously as one varies the parameters
/i
and
and
if
r}
is
therefore a criticcJ issue,
more so than
Hall,
/i
and
in
any depzirtures from perfect competition
the departures are not big enough to explain
the other hand. Farmer and
The
increjising returns, such as Hall's interpretation
shown by
Indeed, in the case of Farmer and Guo's calibration,
that they assume.
in
r?
should be noted that in their model, assuming somewhat lower values does not simply
reduce the magnitude of the equilibrium response to the sunspot events;
will
in
section 4. -^
not completely outside the range of values suggested by the empirical evidence discussed
and
the Farmer-
explain the co-movement of measured Soiow
response to "sunspot" events that cause variations in output, for the reasons discussed
The degree
in
size
Guo
r)
all
tiie
require that the departures be significant.
c2innot be
made much
smaller than the values
Further research on the magnitude of these parameters thus seems crucial to establish
observed co-movement of measured Solow residuals with output could be consistent witli a model
due to self-fulfilling expectations was first illustrated in Woodford (1991).
The notion that the possible ampUtude of the sunspot equilibria is unaffected by the parameter values is to some extern
an artifact of the log-linear approximation used here. In the case of the log-line&r equilibrium conditions (2.20), if any sunspoi
solution exists, solutions exist with fluctuations of arbitrary eunplitude. in the case of the exact equilibrium conditions instead,
it is possible that the set of possible stationary sunspot equilibria includes only fluctuations over a certain range of amplitudes,
the bounds on which collapse to zero eis the critical parameter values are approached at which local sunspot equilibria cease to
be possible. However, the general point derived from analysis of the log-linear system, that stationary sunspot equilibria cease
to be possibb while some amount of n\arket power and increasing returns still exist, remains valid.
^'The
in
which
possibility that the
all
fluctuations are
34
the empirical validity of their model.
Models with Exogenously Varying Markups
7
Up
is
to this point
constant.
One
we have considered a model
benefit of considering models with imperfect competition
contains models where
markups vary over
those with constant markups.
In the ne.xt section,
is
markup
To show
we take up models
may
variations
this,
we
first
that this class of models also
in
play an important role
consider the
markup
of endogenous
Suppose that there are exogenous variations
each firm's
eflTect
t,
elcisticity
=
[i
+
of exogenous changes in
of
demand
D'{\), resulting from
Giving
in
(7.1)
well.
This variation
in
the
markup
implies
the ratio of the marginal product of labor to the wage. In particular, (1.14b) becomes
z,F2(;^,, .-,//,)
Thus varying markups imply labor demand
a given real wage. In this respect changes
=
/i,u;,
shifts, i.e. .changes in
in
In terms of the detrended variables this
(7.2)
the
amount of
markups axe similar to changes
labor that firms will hire at
in the productivity
variability of
markups
also cheinges equation (2.13)
l=/3(Tn-^g.{(^)[
t \
^1 /
which becomes
fit
These are the only equilibrium conditions affected by the
a,
+ r-±i)
-^^(//,+i
35
+(1-^)11
J J
variability of the
^^iI<,-yf~H,) =
,
(2.10')
^''^^'"'^'^^'^"^'^'^
L
-ajt + eJx, + -
parameter
becomes
F,r^,H,]=fitW,
The
this elasticity a
i/£>;(i)]-'
Equation (1.8) then implies that the value added markup varies as
2(.
generating
equation (1.7) becomes
7i
a variation
in
variation.
variations in the degree of substitutability of the various differentiated goods.
subscript
markup
time. This leads to specifications that are considerably richer than
In particular,
fluctuations in equilibrium employment.
markups.
which, as in the perfectly competitive model, the
in
-
markup. Their
(2.13')
linearization yields
w,+fit
A',+1
+ 7,%i) - (f^)/*.} -
(2.16')
(219')
where
To
/j).
/j,
solve the current model,
difference equations which
To compute how
particular,
markup from
the logarithmic deviation of the
is
now
we substitute
(2.15), (2.16')
also involve the stationary
the system responds to
markup
steady state value (which we shall denote by
and (2.17) into (2.18) and
random
shocks,
fit.
we postulate a
stochastic process for
(7.3)
mean
of
/j
is
1.4.
We
^^
For the markup, we assume as before
experiment with a variety of values of p"
output, hours, consumption and investment to a unit shock to u^
same responses when p^ equals
0.9.
when
p**
Figure 4 reports the response of
.
equals
while Figure b reports the
Figure 6 reports the response of real wages for both values of
instantaneous responses of all three variables do not depend to any significant extent on
the higher value of
p''
makes the responses of output, hours and wages more
Figure 6 shows that real wages decline
markups lower labor demand. What
shocks, real wages
One
In
/i(.
=/>"/},_! +1/,"
use the same parameter values as in previous simulations.
that the
variable
two
(2.19') to obtain
we assume that
/i,
We
its
move
is
when markups
rise.
important about this
is
This
that
is
it
p''
.
p''
.
The
Not surprisingly,
persistent.
to be expected since increases in
shows
that, in response to
markup
procyclically.
notable feature of figures 4 and 5
is
that, in the
immediate aftermath of the shock, consumption moves
less
than output while investment moves more. Thus, our model with markup shocks makes consumption
less
variable than output whereas investment
is
is
more
variable. This higher relative variability of investment
a robust feature of business cycles which the model reproduces.
dimension
is
The
due to the relative unwillingness of consumers with concave
success of the model along this
utility functions to substitute their
consumption intertemporally coupled with the small sensitivity of the marginal product of capital
run changes
in
to short
investment. These also account for the relative variability of consumption and investment
in
standard real business cycle models.
We
equals
in
also observe that the short run
0,
a unit increase in
i/''
impact on hours of a markup shock exceeds that on output.
lowers hours by 1.38 while output
falls
When
p''
only by 1.13. This rather large change
hours must be contrasted with the negligible effect of a unit technology shock that we displayed above.
^^Hence, as earlier, the matrix A~^ B has exactly one eigenvalue with a modulus less than one, and so the equilibrium
response to the markup variations is determinate, just as in the case of the responses to variations in government purchases
and to technology shocks.
36
The reason
that hours
fall
so dramatically
that, in the latter case, wealth
The
reason
is
effect of increases in
importance of wealth
fiSH
<
1-
We
effects
As a
work
opposite directions. In peirticular, an increase
is
n have only very small wealth
by the variance of the changes
is
due to the value of /xs//
.
if
in
However,
fi
is
in
hours and
in
output
/i
for
a variety of values of
The reason
markup shocks
is
that, as
Icirger
we saw
in
We
normalize
raise p^.
earlier, the variance of
predicted variance of
We
variability
booms than
H
possibly be the
hours
is in
can be reconciled with
is
why hours
1.33%. This number
is
fact
tiie
fluctuations are
larger than the vciriability of hours.
in recessions
veiry,
and thus of how much
markup
of
Important markup variations, with markups
were found by Bils (1987) and Rotemberg and Woodford
Using a somewhat different specification of technology, Rotemberg and Woodford (1991) find
the assumption of an average
see
coexist with technology shocks. Since the latter affect mainly the variance
the observed variation in hours can be attributed to them.
lower
we
fi.
markup shocks cannot
This discussion raises the question of whether average markups actually
much
in
//
the variance of hours changes exceeds the variance
of output, a combination of the two types of shocks can potentially explain both
(1991).
smaller than the ciiange
greater than one, the variance of output actually exceeds
for smaller values of
smaller than the variance of output. However, a
being
is
so that the variances do not grow spuriously as
only shocks impinging on the economy.
and why output
small
fisn were bigger than one.
of output changes. If parameter values of this type axe entertained,
significant
The
For our choice of parameters
holding z constant, the change in output
that for large values of p, which imply that fiSn
as
effects.
exactly offset by the losses to consumers.
Table 3 we display these variances as ratios of the vctfiance of the log changes
model as long
is
fi.
result, (2.15) implies that,
the variance of hours.
z rises
probably accounts also for the similarity of the responses to temporary and
This conclusion would be reversed
In
in
to lead households to substitute leisure for consumption.
fi is
have also computed the variance of the log changes
p*'.
even though they hardly change when
contrast, increases in
difference in the response of output cuid hours
in hours.
and
effects
persistent changes in
The
By
rises,
fi
that, to first order, the increase in firm's profits
Thus, the main
more
and substitution
wealth which discourages work.
in z raises
when
of 1.6 implies that the variance of quarterly changes in
tlial
markups equals
not directly comparable to the variance in markups in our theoretical model because
of differences in specification and because the actual stochastic process for
37
markups
is
not (7.3). Nonetheless,
worth noting that the numbers of Table 3 suggest that such a large variability
it is
in
markups implies
that
output and hours should vary even more than they actually do.
Models of Endogenous Markups
8
In the last section
hours worked.
we showed
markup
that
The problem with
variations of a plausible
the analysis of that section
is
magnitude can explain the fluctuation
that exogenous changes in
markups do not
appear to be particularly plausible. Models of imperfect competition would be more attractive
changes could, themselves, be explained by changes
are changes in aggregate
present.
^°
Changes
in
demand,
aggregate
i.e. .changes
demand
in
other variables.
many
particular interest
and changes
in
fit
tliis
regard
in
the expected future
in the productivity of the existing capita! stock),
"consumer sentiment".
In this section
to
opposed to changes
markup
of the variables traditionally held responsible for
business fluctuations, including changes in current government purchases, changes
profitability of current investment (as
in
if
away from the future and towards the
in desired purcheises
include
Of
in
we
briefly describe three
models of endogenous markup determination and
These models can be separated
business cycle facts.
only on the size of aggregate
demand
in
two types.
at different points in time but
The
first
their ability
has markups depend
makes the markup independent of the
composition of demand. In this category are the models of markup determination discussed by Rotemberg
and Woodford (1991). The second type of model makes markups depend on the composition of demand but
not on the level of aggregate
demand
itself.
In the latter category
fall
the models of Bils (1989) and Gali
(1991).
We
first
consider two models of the
and Winter (1970) which
is
Rotemberg and Woodford
(1992).
first
type.
The
first is
a customer market model based on Phelps
similar to Phelps (1992), the second
is
an implicit collusion model based on
"'From a macroeconomic perspective another potentially important determinant of average markups, and hence of aggregate
is the level of inflation.
Benabou (1992) shows both that many search models imply a connection between inflation
and markups, and that markups in the retail sector constructed zilong the lines of Rotemberg and Woodford (1991) aie in faci
activity,
negatively correlated with the rate of inflation.
38
The Customer Market Model
8.1
The customer market model we consider
profits with respect to their
from the
sells
earlier
more
to
model
based on Phelps and Winter (1970). As before, firms maximize
is
own markup taking
in that
demand has a dynamic
existing customers, but also expands
its
markup charged by
the
future sales for any given future price.
It
pattern.
its
A
other firms as given.
all
firm that lowers
its
It differs
current price not only
customer base. Having a larger customer base
raises
would be attractive to obtain such a specification of demand from
underlying aggregator functions for consumers such as (1.1) which would depend on previous purchases.
Unfortunately,
from firm
;'
we
are unable to do so and capture the basic idea by simply writing the quantity
at time
q\ Uls
t,
<}\
The
all
variable
m\
other firms.
cost
is
is
= T-'^i-)"i\,
the fraction of average
The
demanded
ratio of
markups
^'<0,
demand Qt/It
in (8.1)
»/'(l)
(S.l)
l.
that goes to firm
i
if it
charges the same price
represents the relative price of firm
independent of the scale of operation and the same for
straightforward generalization of (1.2).
=
all
t's
good, since marginal
firms (as in section
The market share m' depends on
a-s
1).
Thus
(8.1)
is
a
past pricing behavior according to
the rule
m\+i=9(^)m\
g'<0,
so that a temporary reduction in relative price raises firm
(8.2) are
t's
g(l)
=
(8.2)
I
market share permanently. Equations
intended to capture the idea that customers have switching costs,
in
(8.1)
and
a manner analogous to the
models of Gottfries (1986), Klemperer (1987), Farrell and Shapiro (1988) and Beggs and Klemperer (1992).
A
reduction in price attracts
these switching costs.
i.e., the
of
One
are then reluctant to change firms for fear of having to pay
obvious implication of (8.1) and (8.2)
response of eventual
demand.
new customers who
demand
to a
permanent increase
In our case, a firm that charges a higher price
customers, though this
is
not essential for our analysis.
Ignoring fixed costs, firm
t's
profits at
t
are given by
7r
/,
39
V/i, /
is
that the long run elasticity of
in price,
than
is
its
demand,
larger than the short run elasticity
competitors eventually loses
all
its
Using
(1.8)
and an analogous condition
for individual
markups
Y
as well as the fact that
equals
(1
—
s;\/)Q,
these profits also equal
^f^(^)mi
(8.3)
Thus, the firm's expected present discounted value of profits from period
where our
earlier analysis implies that P^
ofT in period
+
t
The quantity
j.
assigned a market share
in
1
— q
-^
is
represents the probability that a firm
is
independent of
the firm might cease to exist with this probability. Firm
all
periods.
all
firms charge the
in A',
its
market share.
Equation
past pricing behavior.
price,
is
profits
An
in (8.5)
is
increase in Yt
equations of section
7,
means that
/x,
profits
unimportant. The result
(8.7) replaces the
For example
equal to Xt/It where
t^t+j
(8.6)
> It+j
expected
in
the future by
is
all
the e.xisting firms.
is
X/Y
from future customers are high so that each firm lowers
relatively
reasons, be
each has a an equal share m' equal to
and g'{l) are both negative, the derivative of /i with respect to
means that
market share
same
profits
equation (8.5) can be transformed so that
ip'
random
chooses n] to maximize (8.4), taking as given the
^
It
Note that Xt can be interpreted as the aggregate
Because
its
will, for
= ItEtTc^^-^(f^^±^^)^
fr{
(8.6),
i
So the expectation term
Xt
Using
is
and {Yt/It}- Therefore
At a symmetric equilibrium where
one, and g equals one in
onward
the pricing kernel for valuing contingent securities that pay
the next period that
stochastic processes {fit}, {^t}
t
its
is
negative.
An
increase
price in order to increase
stem mostly from current
sales so that increasing
that firms raise their price.
exogenous stochastic process
however, continue to hold.
40
(7.3) that
we employed
in section 7.
The
otiiei
The
8.2
The model
Model
Implicit Collusion
in this section is
a simplified presentation of Rotemberg and Woodford (1992) which
is
itself
based on Rotemberg and Saloner (1986). In this model, there are two levels of aggregation needed to go
from individual products to aggregate output.
total
First, there
is
an aggregator function
like (1.1) that gives
output as a function of the output of a measure of industries. The output of each industry
is
itself
given
by a homogeneous of degree one aggregator function which depends on the output of n constituent firms.
The goods produced by each
of the n firms that constitute a particular industry are very good substitutes
and, to prevent what would seem the inevitable
in
each industry collude implicitly.
Collusion
fall in
price until price
is
close to marginal cost, the firms
implicit in the sense that there
is
is
no enforceable
cartel
contract, there exists only an implicit agreement that firms that deviate from the collusive understanding
will
be punished.
The
firms in each industry, even
demand, and the
level of
when acting
in concert, take
We
marginal cost as given.
other industries' prices, the level of aggregate
symmetric equilibria and the
will consider
of deviating from this equilibrium by either a single firm or by an industry as a whole.
the
demand
firms in
its
for firm
t
in
industry j at
t
when
its
price corresponds to
industry charge a price which corresponds to
which corresponds to
^(.
and
/i^
all
cin
inefficiency
We
wedge of
profitability
thus consider
n'/
,
all
other
firms in other industries charge a price
Given the homogeneity of demand, we can write the demand faced by firm
i
in
industry j as
qY
=
D'(^d\9L
Using the same substitution that led to
D'il,l)
(8.3), profits for this firm
=
l/n.
(8.8)
equcJ
^ = t!tLlir(^,i^^.
If
each firm existed for only one period,
the
markups
and low
benefit
of
profits.
all
other firms as given.
If
it
The
would maximize
with respect to
resulting Bertrand equilibrium
the firms in an industry charge
from undercutting the industry's
(8.9)
price.
be sustained as a subgame perfect equilibrium
(8.9)
its
own markup
would have
more than the Bertrand
relatively low prices
price, individual firms
Higher prices, with their attendant higher
if
deviators are punished after a deviation.
repeatedly and have an infinite horizon, there are
many
41
treating
equilibria of this type
and these
profits,
If
would
can only
firms interact
differ in the price
that
is
charged in equilibrium.
We assume
That
is,
that firms succeed in implementing that symmetric equilibrium that
their implicit
each firm
in
industry
Abreu (1986),
is
jointly best for them.
agreement maximizes the present discounted value of expected equilibrium
j,
taking as given the stochastic processes for
this requires that the
punishment
for
{/ii},
possibility of exit, the voluntary participation of the firm that is being
As shown by
{A(} cind {Vi//,}.
any deviation be as severe as
possible.
profits for
Because of the
punished precludes
earning an
it
expected present value lower than zero after a deviation. This leads us to assume that a deviator earns
a
present discounted value of zero after his deviation. Sufficient conditions for this punishment to be feasible
and subgame perfect are given
Because the punishment
to
maximize
is
in
Rotemberg and Woodford (1992).
independent of the
size of the deviation,
expected present value of profits after a deviation equals zero, firms
max
tt^
is
the value of
ttJ-'
when firm
i
5r|-'
<
Trf
+
q can be given a
avoid punishment can reenter.
is
Assuming
there are no deviations. Then,
in industry j will
in the present
is
the
not deviate as long as
its
industry.
We
consider
always binding. Thus, firms are indifferent
and the future
different interpretation.
if
The
loss of
quantity
now mean
(1
—
A. Since
A'
is
what firms
a) remains the probability
that (1
—
q)
is
the probability
renegotiated and a firm that has deviated in the past and has exited to
^*
At a symmetric equilibrium,
equals Xt/nlt.
/
(8.10)
that sales will be independent of the history of prices. This can
that the collusive arrangement
if
charges the Scime price as the other firms in
between the additional profits from deviating
deviate give up,
price at
A"/
the case where the incentive compatibility constraint (8.10)
who
its
by analogy to (8.5), the expected present discounted value of the profits
(8.9). Let A'/ denote,
that each firm in industry j can expect to earn in subsequent periods
where
a deviating firm sets
all
industries have the
same markup, so that each
firm sells Qt/nl, and
A/
(8.10) holds with equality, (8.9) implies that
4+4
nit
nit
(8-in
where p represents the relative price chosen by the deviating firm. Equation (8.11) can be solved
for p,,
yielding once again
=M^,/y,)
/i,
In this case,
in
A'/V
however, the derivative of n with respect to
raises the size of the
punishment (the foregone
current sales (as represented by Yt).
It
markup with
equal to ^
—
respect to
X/Y We
.
is
The
positive.
profits represented
model
theoretical
show
reason
by
is
that an increase
A'() relative to the size of
also implies
an upper bound on the
Rotemberg and Woodford (1992) that
in
elsisticity of
upper bound
this
is
1.
The two models we have presented both make
effect of
X/Y
(1991).
Here we are interested
effect of
aggregate demand.
8.3
XjY
thus allows the firms in each oligopolistic industry to charge higher
markups without fearing deviations. The
the
(8.12)
differs,
markup depend on Xt/Yt. Because
the
they are empirically distinguishable and this
The Response
in seeing
of the
what
Model
this
is
pursued
in
Rotemberg and Woodford
dependence of the markup on
Exogenous Changes
to
the sign of the
in
X/Y
implies about the
Government Pur-
chases
To compute
the responses of the model to exogenous changes in aggregate
and (8.12) around
fl
fit
their steady states.
For this purpose we assume that Xt
give the steady state level of expected profitability
represent the logarithmic deviations of Xt and
these values, and assuming a constant
Xt
=
Et{Xt^,
-
A,
number of
linearized
model now
/i(
as functions of A(,A',,
to solve for A'j,
and
/j(.
given by
and of the markup respectively.
from
firms
/<,
is
We
while
then
their respective steady state values.
let
In
X
and
Xt and
terms of
equations (8.6) and (8.12) become approximately
(813)
(8.14)
consists of (2.15), (2.16'), (2.17), (2.18), (2.19'), (8.13)
/(
j^
= i^iXt-Yt)
are interested in the effect of temporary changes in
of firms stays constant so that
is
to linearize (8.6)
+ {LZA) (^/i.+i + y.+i) + (l77)^^.+i}
fit
The
demand we have
government spending, we
zero in these equations.
We
shall
and
(8.14).
Since we
assume that the number
can solve (2.16') and (2.17)
for
H, and
I'v,
Substitution into (2.15) gives y,, and substitution into (8.14) then allows ns
both again as functions of the same three state variables.
43
We
can then eliminate these four
state variables
from the remaining three equilibrium conditions, obtaining a system of difference equations
of the form (2.20) except that
has three endogenous variables {A,A',/i} instead of only {A, A'}.
it
Assuming once again that the stochastic process
p'^
with
to 0.9 because this
is
with the average inefficiency wedge
1
In the second,
-1.
0.39 because
it is
The response
.39
We
and
it
case,
first
it
of output and hours
intermediate answer.
bound
of 0.4 which applies for our average
in
the case where
The reason
military purchases also raises
which by
is
it
and hours
equals
model the
fall in
have set q equal
Finally,
,
demand
much
X/Y
cis
unambiguously
An
We
chose
falls.
in the ccise
case of Figure
This lowers
rise.
Thus
in the
wage.
where the mcirkup
markups which
in the case of e^
1
equal
yields an
increase in military purchases requires thai
for labor at Jiny given real
lowers
we have
markup.
most pronounced
is
The constant markup
-1.
easy to understand.
Y X/Y
(7.2) lowers the
labor input do not rise as
collusion
We
displayed in Figure 7 while Figure 8 displays the response of real
is
individuals postpone their consumption so that interest rates
rise,
set equal to 1.4.
computed
has the sign implied by the implicit collusion model and equals 0.39.
just below the upper
pronounced
are
.
in (4.1)
has the sign suggested by the customer market model and
see in figure 7 that the response of output
least
^
u^ These responses
consistent with (8.10) holding as an equality with about ten firms.
looked at two values of i^. In the
wages.
government purchases takes the form given
equal to 0.9, we can compute the economy's response to the shock
using the parameters of Table
equals
for
The
demand
raises the
in
customer market model markups
constant.
is
Since the increase
A'.
result
By
is
that output and the
contrast, in the implicit
for labor.
This accentuates the
increase in output.
The
8
difference
between the models' implications
where we plot the responses of the
real
wage wt
accentuates the reduction in real wages that
reason
is
that, as
we saw, the reduction
contrast, in the implicit collusion
This occurs because the
the
markup
fall in
in
for the
to changes in i/^
we displayed
X/Y
is
in
lowers the
model with (^ equal to
X/Y
demeuid for labor
The conclusion from
rises in real
this exercise
demand
in
Figure
that the customer market model
for labor at
wage actually
so pronounced that the increased
demand
any given
real
rises, albeit
for labor
wage.
The
By
only slightly.
from the
fall in
Rotemberg and Woodford (1992) we obtained
that the implicit collusion
44
even more apparent
Figure 2 for the constemt markup case.
wages by assuming a smaller
is
We see
.39 the real
actually exceeds the increase in labor supply. In
much more pronounced
.
is
elasticity of labor
supply
model can generate
chw
procyclical
movemeius
in
real
wages
response to changes
in
generating these responses
government purchases of goods.
in
Because the key ingredient
the increase in interest rates that leads to a
is
X/Y
fall in
would be observed to other shocks that increase aggregate demand such as increases
,
in
similar responses
in firms desire to invest
because of changing perceptions of future profitability.
In
Rotemberg and Woodford (1992) we considered the actual response of real wages
purchases.
We
showed
in military purchases.
wages have tended to
that, indeed, real
That paper
its
defense purchases of produced goods.
It
In
military personnel at the
shows that, even
of the sort implied by the implicit collusion
model
We
type of model.
follow actual
oil
showed that
price increases
this
same time
after this
as
it
increases
its
national
taken into account, reductions
is
in
are needed to explain the reaction of real wages.
Rotemberg and Woodford (1993) we demonstrated that increases
this
United States following increases
rise in the
also considers alternative explanations for the finding such as the fact
that the government raises the size of
markups
to changes in military
tend to raise markups
in oil prices
in
consistent both with the large size of output reductions that
is
and with the
failure of the value
added deflated
real
wage
to rise
on these
occasions.
A Model
8.4
In this subsection
with Composition Effects
we describe an example of a model (that of Gali (1991))
the composition of aggregate
in
which markups are affected by
demand. In Gadi's model both households and firms purchase the
of differentiated goods, but (unlike our assumption in section 1) their aggregator functions
In particular, the elasticity of substitution
prices for
all
goods,
is
different for the
between
/(
entire range
are different.
different goods, again evaluated at the case of
two types of purchasers. In
all
other respects, the model
uniform
is
one of
static monopolistic competition like that described in sections 1-2.
Profit
demand
maximization by price-setting firms now implies a markup that depends on the share
that consists of
demand by
6t
of aggregate
firms so that
-In
7,
where
D',
and
£)(,
= 7(^.)=
\\
+
[e,D'j{\)
+
{\-e,)D'^{\))
indicate the elasticities of demeuid of firms and households respectively. This reduces to
(1.7) in the case that
Dj =
D),
= D.
D'A\) < D'h[\) < — 1, one finds that 7
In the case
is
argued by Gali to be of greatest
a monotonically decreasing function of
45
0,
.
interest, that
Because the
iii
which
inefficiency
wedge
remains the same function of
fit
function of
i/i is
=
—+ M,
I,
= SM + {l-
-p:
the share of investment spending in value added,
t*t
where
fi{sj)
is
fit
is
also a monotonicaliy decreasing
=
SMJsit
we obtain
(8.15)
fi{sit)
a monotonicaliy decrecising function. Gali's model
with (8.15) added
In this
(1.8)),
Finally, identifying
6.
Of
where
by
7( as before (given
in
is
then essentially the model of section
place of the exogenous marivup process.
model, shocks that
affect the
composition of aggregate demand affect equilibrium markups. Tiiis
demand may
introduces a channel through which some kinds of increases in aggregate
expansionary effects
(for
example an increase
not a model where increases in aggregate
in
investment due to a change
demand
same aggregator
will increase
constant
The
demand
predictions of such a model depend critically
upon the
similar to that of
is
For example,
if
the government
less
expansionary than
in the
can occur in equilibrium
in
for the levels of
demand
of different purchasers.
aggregate output and hours. (Thus the association
is
that, for
some
demand.
The
reason
is
is
countercyclical).
choices of the parameters, aggregate fluctuations
the absence of exogenous shocks.
increase current investment
for
elasticities of
Rotemberg and Woodford (1991)) shows a strong negative association with the
Another consequence of Gali's model
He shows
that low expected future markups
that the low expected
markups
raise the
expected
labor and thereby increases the expected marginal product of capital for any given capital stock.
In addition, the
its
it
show that the average markup (measured using
not simply a reflection of the fact that the average mzu'kup
and
But,
markup model.
method
demand
increase.
markups. This would imply that government purchases are even
investment share, even when one controls
is
tax incentives).
as households (an issue not discussed in Gali) an increcise in government purchase.?
Gali provides no direct evidence on this although he does
a
in
iiave additional
as such have an expansionary effect through a change in
desired markups. It depends entirely on the category of
uses the
7
reduction
user cost.
in
expected markups lowers the wedge between the marginal product of capital
This means that low expected future markups raise current investment which,
reduces current markups. For some parameter values this effect
46
is
so strong as to
make
in
turn,
the expectation of
low markups
self-fulfilling.
Gali demonstrates this possibility, and analyzes the cheiracter of the fluctuations
that can exist due to self-fulfilling expectations, using techniques like those discussed in section
Conclusions
9
In this paper
we have shown that imperfect competition matters;
responds to a great variety of shocks.
if
6.
It is
it eifTects
the way
in
which the economy
thus not possible to ignore departures from perfect competition
one wants quantitatively accurate assessments of the importance of various disturbances.
imperfect competition matters so
of labor and the real wage.
Because so
many
It
much
that
it
affects the relationship
between the marginal product
thus affects the relationship between output, the labor input and the wage.
of the puzzles in macroeconomics, including Okun's law and the Dunlop-Tarshis observation
relate to these three variables, imperfect
We
is
competition
is
central to the concerns of business cycle analysis.
have also shown that incorporation of imperfectly competitive product markets into standard dynamic
models of aggregate fluctuations
is
relatively simple.
The models
that
we have presented can
numerically using standard techniques. At most, a small increase in the state space
also
The reason
is
still
be analyzed
required.
We
shown that imperfect competition need introduce only a small number of additional parameters
models can improve the
ability of
The degree
to
which
plausible
this direction of generalization of
standard
such models to explain observed aggregate fluctuations
continuing research.
47
to be
bound the
calibrated and that both empirical evidence and theoretical considerations cam be used to
range of variation in the new parameters.
have
is
the subject of
10
References
Abreu,
Dilip:
"Extremal Equilibria of Oligopolistic Supergames," Journal of Economic Theory, 39, 1986,
191-225.
Barro, Robert
J.:
"Output Effects of Government Purchases
Basu, Susanto: "Intermediate Goods,
Menu
"
Journal of Political Economy, 89, 1981.
Costs, and Business Cycles,"
mimeo, 1992.
Baxter, Marianne and Robert King :"Productive Externalities and CycliccJ Volatility," mimeo, 1990.
Beggs, Alan and Paul Klemperer: "Multi-Period Competition with Switching Costs," Econometrica, 60,
May 1992, 651-66.
Benabou, Roland; "Inflation and Markups: Theories and Evidence from the Retail Trade Sector", European Economic Review, 1992.
Benassy,
J.
Benhabib,
Bils,
in W. Hildenbrand and H. Sonnenschein
Amsterdam: North Holland, 1991.
P.:"Monopolistic Competition,"
Mathematical Economics
J.
vol.
4,
and R. E. A. Farmer: "Indeterminacy and
Mark: "Pricing
in
Incre2tsing Returns,"
eds.
Handbook
of
mimeo, 1992.
a Customer Market," Quarterly Journal of Economics, November 1989.
Blanchard, Olivier Jean and Charles M. Kahn: "The Solution of Linear Difference Models under Rational
Expectations," Econometrica, 48, 1305-13, July 1980.
Bils,
Mark:"The Cyclical Behavior of Marginal Cost
auid Price,"
American Economic Review,
77,
Decem-
ber 1987, 838-57.
Burnside, Craig, Martin Eichenbaum and Sergio Rebelo:"Labor Hoarding and the Business Cycle," Journal of Political Economy, 101, 1993, 245-273. 1990.
Chamberlin, E.:The Theory of Monopolistic Competition, Cambridge, Mass., Harvard University Press,
1933.
Chappell,
Jr.
H.W. and R.P. Wilder: "Multiproduct Monopoly, Regulation and Firm
Costs:
Comment,"
Southern Economic Journal, 52, 1168-74, 1986.
Christensen, L. and
W.
Greene:
"Economies of Scale
Economy, 655-76, 1976.
48
in U.S.
Power Generation," Journal of
Political
Avinash and Joseph
Dixit,
ican
Domowitz,
Stiglitz:
Economic Review,
Ian, R.
"Monopolistic Competition and
Optimum Product
Diversity,"
Amer-
67, 297-308, 1977.
Glenn Hubbard, and Bruce C. Petersen, "Market Structure and Cyclical Fluctuations
Manufacturing," Review of Economic Statistics, February 1988.
in U.S.
Eichenbaum, Martin: "Real Business Cycle Theory: Wisdom or Whimsy," Journal of Economic Dynamics
and Control, 15, 1991, 607-26.
Evans, Charles: "Productivity Shocks and Real Business Cycles," mimeo, 1990
Farmer, R. E. A. and J.T. Guo:"Reai Business Cycles and the Animal Spirits Hypothesis, "mimeo, 1993.
Parrel!,
Joseph and Carl
Siiapiro:
"Dynamic Competition with Switching Costs," Rand Journal of Eco-
nomics, 19, Spring 1988, 123-37.
Gaii, Jordi: "Monopolistic Competition, Business Cycles,
and the Composition of Aggregate Demand,"
mimeo, 1992.
"Price Dynamics of Exporting and Import-Competing Firms," Scandinavian Journal of
Economics, 88, 417-436, 1986.
Gottfries, Nils:
Guesnerie, Roger and Micheiel Woodford: "Endogenous Fluctuations," in Jean Jacques LafTont, ed. Ad-
vances in Economic Theory: Proceedings of the 6th World Congress of the Econometric Society
Vol
2,
Cambridge University
Press,
Cambridge, 1992.
Hairault, Jean-Olivier and Franck Portier: "Money, New-Keynesian Mcicroeconomics and the Business
Cycle," mimeo, 1992, European
Economic Review, forthcoming
Robert E.:"The Relation Between Price and Marginal Cost
Economy, 96, October 1988, 921-48.
Hall,
in U.S. Industry,"
Journal of Political
Diamond ed.Growth, Producand Unemployment, Essays to Celebrate Bob Solow's Birthday, Cambridge: MIT Press,
:"Invariance Properties of Solow's Productivity ResiducJ," in Peter A.
tivity
1990.
Hammour, Mohamad.
L. :"Increasing
Returns and Endogenous Business Cycles," ch
1
of Ph. D. Disser-
tation at Massachusetts Institute of Technology, 1988
:
"Overhead Costs and Economic Fluctuations," Discussion Paper 547, Columbia University Working
paper, 1991.
Hansen, Lars Peter and Thomas Sargent: "Formulating and Estimating Dynamic Linear Rational Expectations Models," Journal of Economic Dynimiics and Control, 2, 7-46, February 1980.
49
Hornstein, Andreas: "Monopolistic Competition, Increasing Returns to Scale eind the Importance of Productivity Changes," Journal of
Monetary Economics,
31, 1993, 299-316.
King, Robert G., Charles I.Plosser and Sergio Rebelo: "Production,
Growth and Business
Cycles:
I.
The
Basic Neoclassical Model," Journal of Monetary Economics, 21, March 1988, 195-232.
"Production, Growth and Business Cycles:
21,
March
II.
New
Directions." Journal of
Monetary Economics.
1988, 309-342.
Klemperer, Paul D.:"Markets with Consumer Switching Costs," QuarteWy Journal of Economics, 102,
May
1987, 375-94.
Kydland, Finn E. and Edward C. Prescott:"Time to Build and Aggregate Fluctuations," Econometrica,
50,
(November 1982): 1345-70.
Mankiw, N. Gregory: "Imperfect Competition and the Keynesian Cross," Economic
Letters, 26, 1988,
7-13.
Morrison, Catherine J.:"Market Power, Economic Profitability and Productivity Growth Measurement:
An
Integrated Structural Approach,"
NBER
Working Paper 3355, May 1990.
C: "Technological Determinants of Firm and Industry Structure," in R. Schmalensee and
R.D. Willig, eds.. Handbook of Industrie Organization, North-Holland, Amsterdam, 1989.
Panzar, John
Phelps,
Edmund S.: "Consumer Demand and Equilibrium Unemployment in a Working Model of the
Customer-Market Incentive-Wage Economy," Quarterly Journal of Economics, 107, August 1992,
1003-32
Edmund
Phelps,
Phelps
New
Co.,
Plosser, Charles
and Sidney G. Winter: "Optimal Price Policy under Atomistic Competition," in E.
Microeconomic Foundations of Employment and Inflation Theory, W. W. Norton and
S.
ed.,
York, 1970.
I.;
"Understanding Real Business Cycles," Journal of Economic Perspectives,
3,
Summer
1989, 51-78.
J. and Garth Saloner:"A Supergame-Theoretic Model of Price Wars during Booms,"
Americaji Economic Review, 76, June 1986, 390-407.
Rotemberg, Julio
Rotemberg, Julio
J.
and Michael Woodford: "Markups and the Business Cycle," Macroeconomics Annual,
1991, 63-128.
——
and
:
"Oligopolistic Pricing and the Effects of Aggregate
of Political Economy, 100, December 1992, 1153-1207.
50
Demand on Economic
Activity," Journal
—
"Imperfect Competition and the Effects of Energy Price Increases on Economic Activity,"
and mimeo, 1993
Silvestre,
:
Joaquim:"The Market- Power Foundations of Macroeconomic
March 1993, 105-141.
Policy,"
Journal of Economic
Literature, 31,
Richard: "Monopolistic Competition as a Foundation for Keynesian Macroeconomic Models,"
Quarterly Journal of Economics, 104, November 1989, 737-52.
Startz,
Summers, Lawrence: "Taxation and Corporate Investment: A
Economic Activity, January 1981, 67-127.
Gerald J.:"The Price
Teilis,
Sales," Journal of
Elcisticity of Selective
Marketing Research,
25,
DemcUid:
g
Theory Approach," Brookings Papers on
A
Meta-Analysis of Econometric Models of
November
1988, 331-41.
Woodford, Michael: "Stationary Sunspot Equilibria: The Case of Small Fluctuations around a Deterministic Steady State," unpublished, University of Chicago, 1986.
:
"Expectations, Finance and Aggregate Instability," in
M. Kohn and
S.-C. Tsiang eds.. Finance
Constraints, Expectations and Macroeconomics, Oxford: Oxford University Press, 1988
(1991),"Self-Fulfilling Expectations
D.
Romer
and Fluctuations
in
Aggregate Demand,"
eds.,JVew Keynesian Economics, Cambridge:
MIT
in N.
G.
Mankiw and
Press.
Yun, Tack:"Nominal Price Rigidity, Endogenous Money and Business Cycles," University of Chicago,
mimeo, 1993.
51
Table
The
Parameter
Defined by
Vcilues
1
Cfilibrated Parameters
Description
7;
1.004
steady state quarterly growth rate of technology
7jv
1.004
steady state quarterly growth rate of population
sc
§r
0.587
share of private consumption expenditure in value added
sa
^
0.117
share of government purchases of goods in value added
Si
(9
0.296
share of private investment expenditure in value added
+ ^)^
0.025
6
't
si{
iJLS^.fi
r
0.58
0.016
rate of depreciation of capitcil stock (per quarter)
share of labor costs in total costs
steady state real rate of return (per quarter)
or 7f /?-'-l
1/(7
1
Intertemporal elasticity of substitution of consumption
€[{^
4
Intertemporal
eiiif
^
elasticity of substitution
holding hours worked constant
f'^^f
fi
1,1.4
K
0.02
-^
(ft
a
,G
p''
Except
-1,.39
of labor supply
between capital and hours
steady state value-eidded markup (efficiency wedge)
rate at which entry adjusts to changes in technology
elasticity of the
markup (endogenous markup model)
depend on price history
government purchases
correlation of /i (exogenous markup model)
0.9
probability that future sales
0.9
serial correlation of
0,0.9
for
elcisticity
serial
population growth, parameters displayed above
(1988a).
52
/i
take the values in King, Plosser and Rebelo
TABLE
2
THE EFFECT OF TECHNOLOGY SHOCKS
PREDICTED VERSUS ACTUAL SECOND MOMENTS
TABLE
3
VARIANCE OF THE LOG DIFFERENCE OF OUTPUT, HOURS AND WAGE
VARIANCE OF OUTPUT CHANGES DIVIDED BY VARIANCE OF MARKUP CHANGES
M
1.2000
1.4000
1.6000
1.8000
2.0000
rho/^=0
rho'^=,3
rho'^=.6
rho'^=.9
0.9269
1.2285
1.5626
1.9262
2.3166
0.9363
1.2295
1.5494
1.8926
2.2559
0.9580
1.2317
1.5210
1.8216
2.1303
1.0577
1.2430
1.4145
1.5726
1.7180
VARIANCE OF HOURS CHANGES DIVIDED BY VARIANCE OF MARKUP CHANGES
M
1.2000
rho^=0
rho^=.3
rho^=.6
rho^=.9
Percent Change in Output and Hours
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Percent Change in the Wage
1
Percent Change in Output and Hours
Percent Change in Output, Hours, Consumption and Investment
1
o\
I
I
P
b
CO
I
CO
re
P
a\
o
c
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ro
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05
-
Percent Change in Output, Hours, Consumption and Investment
Percent Change in the Wage
1
Percent Change in Output and Hours
Percent Change in the Wage
1
MIT LIBRARIES
3
TD6Q QOaSbblb
5
2267 030
Date Due
•JAN.
O
-1995