DUPl
„
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HD28
.M414
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
CYCLICAL MARKUPS:
THEORIES AND EVIDENCE
by
Julio J. Rotemberg
Massachusetts Institute of Technology
Michael Woodford
Unive sity of Chicago
WP#3216-90-EFA
November 1990
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
THEORIES AND EVIDENCE
CYCLICAL MARKUPS:
by
Julio J Rotemberg
Massachusetts Institute of Technology
.
Michael Woodford
Unive sity of Chicago
WP#3216-90-EFA
November 1990
Cyclical
Markups:
Theories and Evidence
Julio J.
*
Rotemberg
Maissachusetts Institute of Technology
Michael Woodford
University of Chicago
current version:
November
6,
1990
Abstract
If
changes
real
in
aggregate
demand were an important
source of macroeconomic fluctuations,
wages would be countercyclical unless markups of price over marginal cost were
themselves countercyclical.
frequencies.
The
first
We
thus exaimine three theories of markup variation at cyclical
assumes only that the
elasticity of
demand
is
a function of the level
of output. In the second, firms face a tradeoff between exploiting their existing customers
and attracting new customers. Markups then depend
also
on rates of return and future
sales expectations; a high rate of return or expectations of low sales
to assign a lower value to future revenues from
and markups.
from an
In the third theory,
expectations then lead firms to be
fall.
new customers. Firms thus
markups are chosen
(implicitly) collusive understanding.
less
growth lead firms
to ensure that
raise prices
no one deviates
Increases in rates of return or pessimistic
concerned with future punishments so that markups
Aggregate post-war data from the U.S. are most consistent with the predictions of
the implicit collusion model.
*
We
wish to thank Alan Blinder, Robert King, N. Gregory Mankiw and Hal Varian and participants at the NBER
Changyong Rhee for providing us with his data on q and the NSF for research support.
Institute for suggestions,
Summer
Cyclical
Markups:
Theories and Evidence
Julio J.
Rotemberg
Michael Woodford
Real wages are not strongly countercyclical. As pointed out already by Dunlop (1938) and
Tarshis (1939), this presents difficulties for models in which technological possibilities do not vary
at business cycle frequencies. For,
is
why should
firms be willing to pay
high and hence the marginal product of labor
Keynes (1939),
is
In this paper
that the desired
we
markup
is
low?
One obvious
of price over marginal cost
consider three leading models of endogenous
explain variations in real wages at business cycle frequencies.
the elasticity of
demand
more
is
possibility,
suggested by
low when output
markup
The
when output
to workers
first
The second
is
high.
variation which might
simply postulates that
facing the representative firm varies over the business cycle.
underlying idea behind Robinson (1932) and Bils (1989).
is
This
is
the
based on the customer
market model of Phelps and Winter (1970), the macroeconomic consequences of which have been
explored by Gottfries (1989), Greenwald and Stiglitz (1988) and Phelps (1989). Finally, our third
model
is
based on the model of implicit collusion of Rotemberg and Saloner (1986) and Rotemberg
and Woodford (1989).
The
future.
first
model
is
The other two
of a tradeoS"
essentially static;
are dynamic.
The
it
does not depend on expectations firms hold about the
price charged in the
customer market model
is
the result
between exploiting the existing customer base and attracting new customers whose
profitable purchases
come
in the future. Similarly, pricing in the implicit collusion
model involves
a tradeoff between current profits from undercutting one's competitors and the future profits from
maintaining collusion
in one's industry.
While expectations about the future matter
different in the
two
cases.
In the
in
both of the latter models, their
customer market model, large purcheises
efiFect is
in the future
rather
induce
firms to try to enlarge their
market share, so that prices and markups tend to
collusion model, by contrast, high expected future
making
when
is
This
first
model
is
thus one where low
the future looks better than the present.
The
one where a rosy future leads to price increases.
is
the implication of the two models that
broader than a test of the specific models that
we need
In the implicit
increases the costliness of a price war,
The
possible for firms to raise prices and markups.
it
prices are like an investment; prices are cut
second
demand
fall.
to
measure markup variations. Like
we
we
actually test. Therefore, our test
consider.
To
we do
Bils (1987),
is
somewhat
test this implication of the models,
this
by making assumptions on the
aggregate production function and exploring the consequences of the equality between the
and the ratio of the marginal product of labor to the
assumption that the
elasticity of substitution
real
markup
wage. Unlike him, we do not impose the
between hours and other inputs equals one. Also,
our production function simultaneously allows for fixed costs (overhead labor), but does not imply
that output can be increased by adding only production workers. In our general formulation, the
marginal product of labor, as a
technology.
f'l
action of output and factor inputs, depends
Hence we use a generalization of Solow's (1957) method
technological possibilities and,
armed with
this
upon the
state of
measuring changes
for
in
measure, we obtain estimates of markup variations
that depend only on observable variables.
We show
that, for plausible parameter values, these
be quite countercyclical.
One parameter
result is the average level of the
that
measured variations
we do not measure
markup. Given that measured
return to capital seem to be small, a higher level of the average
gap between average costs and marginal
markups
cost. If this
gap
is
profits over
much
costs,
thus leading to countercyclical markups. This
in
that there
is
a wider
economies with high
change
in factor inputs
larger percentage change in the factors that are productive at the margin.
Thus high estimates of the average markup imply that marginal
markup derived by
to
and above the required
markup means
due to fixed
markup tend
and which influences our
also have high fixed costs. But, in this case, a given percentage
corresponds to a
changes
directly
in the
is
cost rises substantially in booms,
particularly true of the estimates of the average
Hall (1988a) from observations on the response of total factor productivity to
aggregate demand.
While the assumption of a high average markup produces measures of the markup that, by
necessity, rise
ship between
markups tend
when employment
does not have any direct implication for the relation-
falls, it
markups and expectations about future
to rise
when the
The paper proceeds
that our constructed
rate at which firms discount future cash fiows
discounted value of future profits
models where high prices are
We show
profitability.
high).
is
We
is
low (and when the
thus provide some direct evidence for the class of
an investment.
like
we
In Section 1
as follows.
present the framework underlying
Section 2 presents the static model of time varying elasticities of demand.
models.
all
three
Section 3
develops the customer market .nodel, while Section 4 develops the model of implicit collusion.
Section 5 gives the details of
how we
markup
construct our measures of
variations.
Section 6
explains two methods for testing the implications of the three models. Section 7 discusses our data
and section
our results in context by discussing
8 gives our empirical results. Finally, section 9 puts
the role of the various models of
markup
variation in explaining fluctuations in aggregate activity.
The Basic Setup
1.
We
one.
consider economies with
We
at time
will focus
t,
Pt-
many symmetric
firms
on symmetric equilibria, so that
For simplicity
we
will treat the
that, in units of the numeraire, Pj
is
whose
total
number
is
normalized to equal
in equilibrium all firms charge the
same
price
output of these symmetric firms as the numeraire so
one.
These symmetric firms have access to a technology of the form
x;,
where
t.
The
y{,
=
F{K\,Zii,H,-Ht))
H\ and K\ represent respectively firm
variable
Zt
I's
output, labor input and capital input at time
represents the state of technology at time
a more productive period, while Hi
for an overhead labor requirement
is
is
the
amount
(1)
t,
so that a higher z corresponds to
of labor devoted to fixed costs.
The allowance
a way of introducing decreasing average costs, of the kind
needed to reconcile an assumed markup of price over marginal cost with the apparent absence of
significant pure profits in U.S. industry.
Each firm has access
'
to competitive markets for labor
and capitad
For evidence on the existence of increasing returns, in the sense of average costs
U.S. industry, see Hall (1987).
services.
in excess of
At time
t,
firm
i
marginal cost on average, in
must pay a wage wt
for each unit of labor
F
Given the homogeneity of
number
the
of units that the firm produces
The assumption
essential for the
F
that
markup by
cost. Since
both Wf and
I's
rtk
is equail
this
are
r^
is
=
denominated
I's
At a symmetric equilibrium
all
independent of
(2)
it
constant
is
We
markups.
all
is
denote the
firms to marginal
output, marginal cost
ratio of price to marginal cost be
denoted by
= (^-ifi)„;
firms charge the
same
We
(3)
price and, given our normalization, the
denote by Xt each firm's expected present
of the stream of individual profits from period
t
+
1
onward:
X,^E^±'J±l{f^l±i^)Y,,,
Here Et takes expectations conditional on information available at
pricing kernel, so that any
discounted value in period
We now
t
random
n\,
numeraire are equal to
sales of each equal the aggregate level of sales Yt.
jisset
not
by allowing us
simplifies our analysis
in the units of the typical firm's
Letting firm
l//it.
rents.
l
the equilibrium ratio of the price charged by
n;
t
is
t
it
to
F{k,zth)
s.t.
profits gross of fixed costs in units of the
discounted value at
for each unit of capital that
firms' prices as the ratio of their respective
fit]
simply equal to
rj
homogeneous of degree one so that marginal cost
is
two
equilibrium
firm
and
models to be presented below. However,
to write the ratio of
is
must pay
it
and competitive factor markets, marginal cost at
minwth +
in (2)
and
(4)
t,
and qt^j/qi
yield Zj+y (in units of period
t -\-
is
the stochastic
j goods) has a present
of Et{qt+}Zi+j/qt)-
distinguish between three
models that
difi"er
in
both the specification of demand and
of market structure.
2.
The
Static Monopolistic
In this
Competition Model
model each firm behaves
like
a monopolistic competitor in that
prices of all other firms, the level of marginal cost
and the
"symmetric" monopolistic competition model of Dixit and
4
level of
Stiglitz
it
takes as given the
aggregate demand.
(1977),
As
in the
we assume that
the
demand
for firm
i
Equivalently, firm
by
all
depends on the ratio of
t
demand
's
at
t
its
price to the average price charged by
depends on the ratio of
we
other firms in the symmetric equilibrium
its
own markup
will consider, Ht.
n\ to the
all
other firms.
markup charged
Thus we write firm
t's
demand
as
v;
=
i>(^,y',)
(5)
where the firm's demand depends on aggregate demand through the
To preserve symmetry we require that the demand
same
the
price.
Thus we
D{1,Y)
require that
homothetic preferences so that demand
demand
prices,
is
D
In this special case both
Vj.
Di, are proportional to
Since the firm's problem
is
only
if
all
static
and the
same,
falls.
are not homothetic.
/ij.
if
which we
they
all
charge
will return heis
D
with respect to relative
its
decision rule by substituting (5) into (3)
This yields the familiar formula
firms charge the
is little
Z)i
=
(6)
same markup,
the elasticity of
Thus the markup can
There
pEirtial derivative of
we can obtain
—Di{l,Y)/D{l,Y) = —Di/Y,
prices are the
special case to
Y
Yt.
the product of a function of relative prices and aggregate
D+^
symmetric equilibrium
A
Y.
be equal to
aggregate sales
Y
and maximizing with respect to
In a
=
for each firm
level of
rise
so that the
demand
markup can
rise if
and
evaluated at the point where
with a change
in Yf
if
and only
if
all
preferences
a priori reason to expect either direction of deviation from
homotheticity, so that markups seem as likely to rise with increased sales as to
fall.
The Customer Market Model
3.
The customer market model continues
its
markup taking
pattern.
A
expands
its
t
markup
firm that lowers
given price.
at time
the
its
to have each firm meiximizing profits with respect to
in all other firms as given. It differs in that
current price not only sells
customer base. Having a larger customer
One simple
more
demand has a dynamic
to its existing customers, but also
bcise leads future sales to
formulation that captures this idea involves writing the
be higher at any
demand
for firm
t
as
function (5) we have avoided considering the effect of changes of the composition of demand on its
and hence on markups. We have done this because we are interested in the effects of changes in aggregate
demand and no particular compositional shift seems plausibly associated with a large fraction of changes in aggregate demand.
^In writing the
demand
overall price elasticity
yi
The
variable
m{
r„<0,
r,(-,Yt)m\
the fraction of total
is
as all other firms.
=
demand
The market share m' depends on past
g'
so that a temporary reduction in price raises firm
Klemperer (1987), and
new customers who are then reluctant
One obvious
costs.
if it
charges the same price
pricing iaehavior according to the rule
g{l)
0,
=
1
(8)
market share permanently. Equations
demand.
demand
(6)
and
is
A
reduction in price attracts
to change firms for fear of having to pay these switching
permanent
is
that the long run elasticity of demand,
increcise in price, is larger
In our case, a firm that charges a higher price
customers, though this
The
to a
and Shapiro (1988).^
Farrell
implication of (6) and (7)
response of eventual
its
I's
<
t
(7)
capture the idea that customers have switching costs, in a manner analogous to the models of
Gottfries (1986),
of
=Y
Vi that goes to firm
rr^Ux-9(-\rrx\
(7)
r,{l,Y)
than
its
than the short run
the
i.e.,
elasticity
competitors eventually loses
all
not essential for our analysis.
firm's expected present discounted value of profits
from period
t
onward
is
thus
J-1
n
,
Firm
t
chooses
/i}
to
maximize
(9),
.
taking as given the stochastic processes {/Xj} and {Vi}.
Therefore
"d.-^-l^.^-Ol
^nx
<^^^
/
'
^
A-M +
fit
,.(!i)£.f;?i±i[!^kzi],(!!i±i.K,^,)'n^(^) =0.
where subscripts denote partial derivatives. At a symmetric equilibrium where
same
(10)
price,
is
each has an m, equal to one and g equals one in
equal to the
common
all
all
(.0)
firms charge the
periods. So the expectation term in
present discounted value of profits given by (4). Therefore, (10) gives
^This idea haa been applied to the analysis of international pricing iuues by Gottfries (1988) and Froot and Klemperer
(1989).
the
markup
as:
/i(
nt
=
=
^i{Xt,Yt)
—-—
+
yt
The second order condition
maximum
for a
Therefore, the derivative of
negative.
/i
11
r]i{l,Yt)+g'{\)Xt
of profits implies that the denominator of (11)
X
with respect to
is
negative.
that profits from future customers are high so that each firm lowers
market share. The
case where
r/i is
proportional to
to
X.
A
Y
markup with
the elasticity of the
high value of
Y
markup
current sales Yt on the
effect of
(11) implies that the
,
Y
respect to
is
level of sales. Differentiating (11)
y
means
more ambiguous.
its
In the homothetic
the ratio Xt/Yt\
equal to the negative of the elasticity with respect
is
elasticity of
are relatively profitable so that, in the
demand
is
relatively attractive.
This
facing an individual firm depends on the
and ignoring time subscripts, the derivative of
/i
with respect to
is
-/i
y+
which
is
prices
and
positive in the homothetic case
Y
,
is
derivative
is
elastic as
negative only
if
+
(l
-
r,i(l,y)
where
n)r}u
+ s'(l)X
T712,
the second particil of
can be negative
zero. This derivative
becomes much more
is
X
order to increase
markup depends only on
means that current customers
must be modified when the
increase in
its price in
homothetic case, raising prices and exploiting existing customers
intuition
An
is
output
rises.
if 7712 is
1712 is
with respect to relative
sufficiently negative so that
However, because this term
the magnitude of
r]
is
multiplied by (1
substantial, particularly
if
demand
— /i),
the
markup
the typical
small.
Put broadly, equation (11) says that lower
market share. Such an investment
is
attractive
prices are a
when the
form of investment, an investment
in
present discounted value of the future
returns from investment (X) are high relative to the payoff from current consumption, which in the
homothetic case
is
represented by
they are closely related.
rates does not
make
the
An
Y
.
increase in
While the story
distinct
from the
static
model,
X through, for instance, a ial\ in interest rates and discount
demand curve more
that go to customers with relatively
is logiccilly
eleistic
elastic.
However,
it
raises the
importance of the sales
demand, thus promoting reductions
in price.
4.
The
The model
We
Model
Implicit Collusion
a simplified presentation of Rotemberg and
in this section is
many
consider an economy with
each industry collude implicitly
industries, each of
the sense that there
in
the other hand, the firms in each industry, even
prices, the level of aggregate
demand, and the
is
somewhat, we can view industries
when
level of
(1989).
which consists of n firms. The n firms
in
no enforceable cartel contract, but only
an implicit agreement that firms that deviate from the collusive understanding
On
Woodford
be punished.
will
acting in concert, take other industries'
marginal cost as given. Abusing the language
as monopolistic competitors in the usual sense, while the firms
within each industry collude implicitly.
Keeping
mind, we write the demand
this distinction in
yO
=
(^^
V
z)'
.
,
.
.
lit
^^t
The function D*
J
=
1,.
.
for firm
.
t
symmetric
is
,n) are
in industry
other industries
all
same
the
ail
j when
of
all
I'th,
markup
nl
,
profits,
it
would maximize
^^(/ij,
Fj.
If
equilibria of this type
The
(13) with respect to its
If
£is
own markup
resulting Bertrand equilibrium in the industry
more
thcin /i^(/i{, Fj),
Higher prices, with their
a subgame perfect equilibrium
if
deviators are
firms interact repeatedly and have an infinite horizon, there are
and these
differ in
the price that
is
charged
their implicit
many
in equilibrium.
Eissume that firms succeed in implementing that symmetric equilibrium that
is,
while firms in
(13)
the firms in an industry charged
can only be sustained
punished after a deviation.
them. That
(for
(3), profits
'-^....AyX
individual firms would benefit from undercutting the industry's price.
for
and the functions D*
permutation of the arguments. Using
^
^^Liio-p
-D'i —
other firms as given.
would have a markup equal to
We
(12)
charge nt, equal
markups
attendant higher
j as
=Y
other firms in industry j charge the
each firm lived for only one period,
treating the
in industry
D\\,...,l,Y)
n arguments except the
after appropriate
all
t
I
fit
in its first
TV nv
=
If
y^
^,
ut
for firm
is
jointly best
agreement maximizes the present discounted value of expected
equilibrium profits for each firm in industry j, taking as given the stochastic processes for {/i{} and
{Yi}.
As shown by Abreu
(1982), the punishment for any deviation
8
is eis
severe as possible in the
optimal symmetric equilibrium. Therefore, a deviating firm sets price to meiximize current period
The
profit n'/.
result
is
that the single period profits of a deviating firm equal:
= max
n^j
£>(—,...,
— ,...,—
,Yt]
After any deviation, the firms in the industry punish the deviator to the
Because of the possibility of
precludes
it
(14)
mziximum
voluntary participation of the firm that
exit, the
earning an expected present value lower than zero after a deviation.
Let
being punished
is
We
that ensure that a deviator indeed earns a present discounted value of zero in
Woodford
possible extent.
give conditions
Rotemberg and
(1989).''
Xl
denote, by analogy to (3), the expected present discounted value of the profits that
firms in industry j can expect to earn in subsequent periods
if
there are no deviations. Then,
if
the
expected present value of profits after a deviation equed zero, firms in industry j will not deviate
as long as
ni<ii{ + x/
where
We
X\\
is
the value of
Fl'/
when
charges the same price as the other firms in
i
consider the case where the incentive compatibility constraint (15)
At a symmetric equilibrium,
xl
firm
(15)
equals
Xu
all
industries have the
Using D{p,Y) to denote
max
P
-
1
l,y),
industry.
always binding.^
same markup so that eaxh firm
I»'(l,. ..,/),...,
1
is
its
we then have from
and
sells Vj
(13)-(15)
1
D{p,Yt)=\l--Yt +
Xt
(16)
p
where p represents the
Ht yielding once again
Bertrand
relative price chosen
/ij
=
fi{Xt,Yt).
level, so that deviators
The
by the deviating
firm.
relevsmt solution of (16)
Equation (16) can be solved
is
for
the one where ^t exceeds the
undercut the equilibrium price and p
is less
than
1.
Differentiation of (16) yields
of
*The main condition requires that there exist a ji smaller than one such that when all Arms in industry } charge a markup
A while the fimu in other industries charge a markup greater than or equal to one, a deviating firm cannot sell positive
quantities by chsirging a price in excess of marginal cost. This aasumption requires that the goods produced by firms in the
industry be relatively good substitutes. It ensures that the deviating firm cannot make positive profits in the periods following
a deviation by deviating from the behavior it is expected to follow after the deviation.
^In Rotemberg and Woodford (1989) we give conditions under which a deterministic steady state exists in which (15) is
always binding. We also show that, for small enough stochastic shocks, there continues to exist a perturbed equilibrium in
which (15) always binds.
9
= Dip,Y)-Y
D{p,Y) > D{1,Y) = Y and nx is positive. An
^''^
'^^
Since p
less
is
than one,
increase in
markup
the cost of deviating, raises the equilibrium markup. Such an increase in the
can also bound the response of the markup to changes
X={p-
is
raises
necessary
between the costs and the benefits of deviating.
to maintain the equality
We
X, which
-
l/ti)D{p,Y)
(1
- l/n)Y <
-
(1
in
X
from above. In
l/n)[D{p,Y)
-Y] =
particuleir
^li^iUll
(ig)
MX
where the
(17). Therefore, the elasticity of
The
effects of
changes
Y
in
for all prices, (16) implies that
benefits to deviating
in
Y
raise the left
from p <
follows from (16), the inequality
first equeility
now and
hand
with respect to X, while positive,
/x
are
/i
the
1,
more ambiguous.
In the
depends only on the ratio
markup
side of (16)
falls.
More
more than they
is
and the
last equality
smaller than ^
1.
Dy = D/Y
homothetic case, where
X/Y. Thus an
—
from
Y
increase in
raises the
generally, fiy is negative as long as increases
the right hand sid
reiise
.
This occurs as long
as
n^i(i,Y)D2ip,Y) ^ n(/i,y)
^
D{p,Y)
While
this
Y D2/D
of
is
demand
must hold
in the
sufficiently less
homothetic case where
than one
faced by a deviating firm,
for p
<
1.
much
larger than
Since
IT.
smaller than one, so that /iy
5.
is
equals
—pDi{p,Y)/D{p,Y),
1, it
Series for
We assume
from
(1).^
'Our
markup
(as in the theoretical
The markup
Markup
it
could
fail
more generally
increasing in p only
if
if
the elasticity
a decreasing function of y. For goods
seems
likely that
YD2/D
is
not
FIj
much
Variations
first
that
we
over the postwar period for the U.S.
construct a time series for
Our method
is
quite simple.
models discussed above) an aggregate production function of the
of price over marginal cost
results are little a&ected
,
implausible in this model.
Empirical estimation of a markup equation requires
cyclical variations in the
is
is
l/Y
only slightly less than one, even though
is
Y D2{l,Y)/D{l,Y) =
>
Time
Construction of a
D2/D
This queintity
that are close substitutes, the optimal deviating p
is
Y
is
then
by the choice of the functional form
(1) over a
Y,=F(K,,x,H,)-*,.
10
form such as
=
t^t
We
FH{K,,z,{H,-Ht))
(19)
can thus construct a markup series from aggregate time
series for output, factor inputs,
real wages, given a quantitative specification of the production function
Ht), and given a time series for the productivity shocks {zt}-
an obvious
Woodford
difficulty, since
(1989)),
they
(including a value for
The productivity shocks
present
not directly observed. In our previous paper (Rotemberg and
eire
we measured the
markup by choosing
F
and
effects of a particular
type of aggregate
demand shock on
the
a shock (innovations in real military purchases) that could be argued to be
uncorrelated with variations in {zt}. This will not, however, suffice
series for cyclical variations in the
to reconstruct a series for {zi}
markup
from
(l),
if
we wish
over the entire postwar period. Here
using what
is
essentially the familiar
to construct a time
we propose
instead
Solow (1957) method,
corrected for the presence of imperfect competition and increasing returns to scale.
We
consider a log-linear approximation to (1) around a stezwiy-state growth path along which
Ht grows at the same rate as Hf, while Kt and Yt grow at the same rate as ZtHf^ This approxi-
mation yields
where hatted lower case variables
refer to log deviations
from trend values, and where the other
expressions represent constant coefficients evaluated at the steady-state growth path.
We
assume that,
for
both factors, the marginal product equals
steady-state growth path, where
are respectively equal to
/i*
h'sk and
share of output's value. Because
F
is
times the factor price in the
the steady-state markup. Therefore,
fi'sfj,
is
/i*
where
sjc
FiK/Y and zF^H/Y
and s^ are payments to capital and labor as a
homogeneous of degree
1,
Euler's equation implies that
contrast, the aisumed aite of the fixed costs in relation to total costs (or more generally, of average cost in relation to
marginal cost), represented here by the average site of Ri/Ht, is important to our conclusions.
^Bils (1987) avoids the need to construct series for {zi} altogether by assuming a Cobb-Douglas production function with
no overhead requirement (at least for production hours) so that Fh in (19) can be replaced by aYi/Hi. We show that this
restrictive functional form is not necessary and are able to consider the consequences of alternative assumptions regarding factor
By
substitutability
and the
size of flxed costs.
'The assumption
that the overhead labor requirement grows at a constant rate allows us to obtain a stationary equilibrium
with growth (in which, among other things, the ratio of flxed costs to total costs fluctuates around a constant value). Presumably
this should be due to growth in the variety of goods produced as the economy grows, although we do not model that explicitly
We could have assumed instead that the overhead labor requirement is constant in per ca^ta terms. Because, per capita
hours appear stationary, this too would have allowed us to apply our techniques.
here.
11
.
H SK
+ fi SH
H --—
H
—
=
U
1
(21)
Using (21), (20) can be written as
^t
=
This allows us to construct a time series for
is
set to
1
zj
detrended output and
in
for the single free
parameter
.
This
have the same trend growth rates, the analogous log-linear approxi-
=
Zt
- Wf^
[kt- Zt^
e
e represents the elasticity of substitution
—
1
—
fi
ht
Sfc
I
^
between the two factors
in
F, evaluated at the
factor ratio associated with the steady-state growth path. Substituting (22) for
=
Ht
Hence we need
—
e-(^'sK
e
—
en
.
(1
+
,
yt
e
sji
-e)fi'sK
—
;
markup
somewhat problematic. Our
series.
-
j
kt
'
1
efi Sf(
to specify only the parameters e
shares to construct our
and
/i*
fi'sH
—
I
-—ht
/i
is
this
becomes
.
wt
(23)
s/f
in addition to the
Assigning numerical values to e and
basic strategy
zt
observable factor
/i*
is
admittedly
to determine ranges of plausible values, and then to
check the degree to which our results are sensitive to the exact values chosen for e and
those ranges.
The parameter
of observed long run trends.
e
is
elasticity of substitution near
The absence
1.
within
of a significant trend in factor shares, in the face of a
But
is
sometimes taken to indicate an
this is not a particularly persueisive justification. First, this
might simply indicate that most technical progress
a long run elasticity of
/x*
often "calibrated" in real business cycle studies on the basis
significant trend in relative factor prices over the last century,
fact
fx'
fac-
(19) yields
Ht
where
from the variations
Solow's original method.^
in
Assuming that wt and
mation of
Zt
and given values
tor inputs, given average factor shares,
parameter
22
:
is
labor-augmenting, as in
(1), rather
than
1.
Second, there need not be much relationship between the long run
elasticity (relevant for our purposes).
On
the one hand,
if
eleisticity
and the short run
one assumes a "putty-clay" technology.
* Technically, Solow's calculation also differs from (22) in allowing the factor shares to be time-varying. This amounts to
preserving some higher-order terms in the Taylor series expansion of (1), but there is then little reason to drop other second-order
terms. We thus stick here to a simple log-linear approximation.
12
much
the short run elasticity of substitution might be
less
than that indicated by long run trends.
But, on the other hand, cyclical variations in capital utilization might
elasticity
is
even greater thcin the long run
elasticity.
make
the relevant short run
Suppose that the current production function
not (1) but
Yt
where
zt{Ht
= F{utKt,Zt{Ht-Ht))
U( represents the degree of utilization of the capital stock.
—
Then
Uf varies positively
if
at cyclical frequencies, the relevant elasticity c in the above calculations
Ht)/Kt
is
with
the one
associated with the reduced-form production function
y,
But,
if
= HKuZtiHt -
Ht))
= F{u[
the long run utilization of capital
prices, the elasticity
one would
infer
is
)Kt,zt{Ht
is
Ht))
from growth observations would be that
u}
In this case, the
would be smaller than the relevant short run
the relevant elcisticity
-
constant and thus independent of trends in factor
true production function evaluated at constant
of substitution
''^"'~"'^
We
not easily measured.
eissociated
with the
measured long run
elasticity
elasticity.
We must
thus admit that
take as our baseline case the value e
=
1
(Cobb-Douglas), the value must often used in real business cycle studies, but we also consider the
possibilities e
We
=
0.5
and
e
—
2.
are similarly unable to directly observe
fi'
.
Hall (1988a) proposes to measure
it
on the
basis that the zt series given by (22) should be orthogonal to changes in variables such as real
military purchcises or the party of the President. Hall uses value aidded as his measure of output
and
finds values
above
1.8 for all
seven of his 1-digit industries. Domowitz, Hubbard, and Petersen
(1988) use gross output instead and obtain smaller estimates of
around
1.6
is
typical of their findings. However, since
we study
/i*
for
most
industries; a value of
the behavior of value added, their
estimate would have to be adjusted upward to be appropriate for our analysis. Nonetheless,
take 1.6 as our baseline case, but also consider the value 2.
the existence of
markups even
as high as
As some readers may be
60%, we present some
results for a
markup
we
skeptical about
variation series
in response to cyclical as opposed to secular changes might be due to adjustment costs, so that changes in
would be used more in the case of transitory fluctuations. Properly taking into account such adjustment
costs would, of course, require a more complicated specification of production possibilities.
'°The difference
capital utilisation
13
constructed under the assumption
/x*
—
1.1,
although we regard this as an extremely conservative
choice.
markup growth
Figures 1,2, and 3 illustrate the constructed series for
period, under different assumptions regarding
departures of capital from trend,
A;,
and
level of
the
markup
level.
Figure
in order to construct the series,
make
Figure 2 shows the consequences of assuming instead e
=
=
2, e
I.
In each ceise, the
it
growth rate of hours
is
=
effects of
parameter variation are
/i'
=
1.6, e
=
1.
0.5, while Figure 3 presents the case
shown
as well;
it is
clear that for each of
markup
these sets of parameters the constructed series displays strongly countercyclical
The
we do not
clear that
represents our baseline case,
1
Because
in section 8 below.
present here only our constructed series for meirkup changes, to
pretend to have directly measured the
fi'
These are constructed by ignoring the
e.
and using the data described
we make an assumption about the average
we
fi'
rates over the postwar
easily understood.
Assuming a lower
variations.
elcisticity e
implies
a sharper decline in the marginal product of hours in booms, and so increases the amplitude of
the countercyclical variation in the series constructed for
higher steady state
Ht
—
Hf
in the
for
H/H
any given observed increase
countercyclical variation in
results
implies a
/i'
because of (21), and hence a larger estimate of the percentage increase
in Ht-
For any given
marginal product of hours in booms, so that a higher
Our
Assuming a higher
/i<.
e,
this then implies a sharper decline
fi'
results in a greater amplitude of
(Note the different scales for the markup series
fit.
on the countercyclical pattern
in the
in
markup confirm
in
Figures 1-3.)
the conclusion of Bils (1987),
although we obtain this result for a different reason. Focusing on the beiseline case of c
=
1,
(23)
becomes
Ht
where
sm
= yt-
;
ht
-wt = -snt -
denotes log deviations of the share of hours.
(so that there are
cyclical.
But
added to
/}{.
if
then also no fixed costs),
we assume
Bils
\i
>
\
/it is
If /x'
[-
is
(24)
equals one, and given that s/f + *if
simply the negative Qisjjt, which
is
=
final
term
1
not very strongly
(and hence increasing returns), then a countercyclicad term
assumes instead constant returns (and ignores the
out that the relevant wage wt
Ijht
;
in (24)),
is
but points
the marginal wage (the wage paid for marginal hours) rather than
the average wage. These two can differ
if
the utilization of overtime labor
14
is
cyclical
amd
if
overtime
hours must be paid more than straight-time hours. With this correction, he obtains
= -SHt -
Ai
where
U( represents the log deviation of the ratio of the
the Appendix
ut
we show how
to
compute
this correction
marginal wage to the average wage. In
with our data.
depends crucially upon regarding the overtime premium as
(1988b). Because
is
ut
justified,
Our
many
that
we
we present most of our
of its shortcomings deserve
of the
method
for estimating
allocative. For a criticism, see Hall
are uncertain of the extent to which Bils' treatment of the overtime
premium
results without this correction.
specification of production possibilities
many
Bils'
more
is
obviously overly simple in
careful attention in the future.
We
many
respects,
and
should, however, note
most obvious corrections to our simple measure would tend to imply even stronger
evidence for countercyclical
markup
variation.
One might wish
to consider adjustment costs for
hours. In this Ccise (19) becomes
^^
where
Aj represents the
^
FH{Kt,zt{Ht-Ht))
Wt
T~s
+
At
shadow cost of increasing hours
suming a convex adjustment cost function,
period
in
A{ will be positive
t
in addition to the wage.
when hours
As-
are increasing (due to
current adjustment costs) or higher than they are expected to be in the future (due to expected
future adjustment costs), and similarly negative
when hours
are decreasing, or lower than they are
expected to be in the future. Hence A{ should be a procyclical correction, and imply an even more
countercyclical markup.
As another example, one might wish
of different workers' hours.
As many
to consider composition biases due to the heterogeneity
studies have
shown
(see, e.g.,
Kydland and Prescott
Barsky and Solon (1989)), the most important such bias has to do with the greater
ability of
low wage (and presumably low-productivity) hours. The precise
conclusions depends upon
seems
likely that it
many
efifect
(1988),
cyclical vari-
of such bias on our
aspects of the assumed true model of heterogeneous hours, but
reduces the extent to which measured
markup
it
variations are countercyclical.
Suppose that low-wage and high-wage hours are two distinct factors of production, and assume
a Cobb-Douglas production function.
We
can measure the markup as the ratio of the marginal
15
product of low-wage hours to the low wage.
- -SHLt -
Mj
where
Then, correspxjnding to
[-
;
IJ/iLt
\1-H'sk
'
represents the log deviation of low-wage hours from trend,
hi,i
one obtains
(24),
sj/x,
represents the trend
value of the share of payments to low-wage hours in output, and so on. Both sm,i and
be more procyclical than the corresponding sjn and
tend to
make
\it
Method
Our
we adopt
all
yield relationships of the
not certain.
form
=
^^{Xi,Yx). For purposes of estimation,
+m
(25)
/i(
=
fxi<
-
eyyt
where, again, hatted variables represent logarithmic deviations from trend values, while
sents a possible stochastic disturbance.
in antitrust
Examples of stochastic disturbances of
the implicit collusion model has
the preferences are homothetic,
is
zero.
< e^ <
The customer market model
(/^*
~
!)
h^
for dealing
with this
market value to the value of
-\-
Ki
The
static
<
while
implies that e^
the
is
equal to tx- Even without imposing
same sign
eis
(.x
unless the elasticity of
extremely dependent on the level of demand.
is
The problem with estimating
Xx
repre-
one imposes the additional requirement that
models imply that ey
all
homotheticity, the dynamic models imply that ty
methods
If
tjj
this type include
enforcement and changes in the degree of foreign competition.
theory of section 2 implies that tx
demand
is
the log-linear approximation
At
changes
aju,
competing theories
for evaluating the
three theories
is
should
These considerations would both
more countercyclical when hours are disaggregated. On the other hand,
smaller than s^, so the direction of the overall bias
6.
hi in (24).
}\i_x
—
^i
\-
(25)
issue.
is
The
that
first
we
lack direct observations
uses measurements of Tobin's
their capital in place.
The
total
on
q,
market value of
i^.
We
have two
the ratio of firms'
cill
firms
is
equal to
Nt where Kf equals the current returns to capital plus the present value of the
depreciated capital stock at the beginning of next period $<
is
the present value of fixed costs and
Nf captures any additional influences on market values such as the the present discounted value of
'
'
One can
equivalently consider the marginal product of high
wage hours but adjustment
results in this case.
16
costs are
more
likely to distort the
random misvaluations
taxes levied from firms as well as
of the stock market.
Then the logarithmic
deviation of Tobin's q should equal
X
^- X - N
.
where the ratios with {X
where
$
.
X+K-^+N
X+K-^+N
^
+ K — ^ + N)
1
.
X+K-^+N
X+K-^+N^
in the
denominator represent steady state values, and
from the steady state value
ht represents a deviation (rather than a logarithmic deviation)
N.
Tobin's q
is
one on average^' so that {X
+
JV
—
$) equals
the last two terms in the previous equation, and using (25)
0.
Letting
i/t
represent
—n^
times
we have
jr
= —^xqt -
At
eryt
+
i^t
+
Equation (26) can be estimated by ordinary least squares
residual
if Ut
+
i>t
is
r]t
variables.
+
Vt is
uncorrelated with
qt
might well have a direct
effect
that positive realizations of
On
be biased upwards.
yt
we can
,
recover
rjj
one
rft
is
Y
on
i>t
its coefficients
is
raise
Xt and
qt
as well.
As a
likely to
result,
these variations affect only
unimportant and
be recovered by regressing
qt
Ut is
with this reverse regression
insofar these raise
/i«>
important variations
is
our estimate of
r/t
v^x
i>t
uncorrelated with
would bias the
will
/tj
and
y^,
/»<
'*This
ia
starts
i/j
17
{X =
with
this
i/t
so that,
difficulty is that
in the reverse regression
from the observation that
conaistent with the absence of equilibrium pure profit*
to
One immediate
that the estimated ex would be too large.
Our second procedure
is likely
then the coefficients in
be biased downwards. Another
coefficient of
would
qt.
that increases in real discount rates lower $< and
(it
rjt
would tend to
on the other variables. Examples of shocks to
the coefficient of
in
on the other
be serially correlated so
the other hand, the existence of important variation in
if
qt
such as changes in antitrust enforcement
rjt
Moreover, such shocks are
.
by regressing
property might include those that affect Nt and some of those that affect $<.
difficulty
assume that the
willing to
would have to be unimportant and
However shocks to
/ij.
bias this coefficient toward zero
(26) can
and
For the residual to have this property,
instead,
if
uncorrelated with any two of the three variables in the equation. In particular,
have to be correlated only with
If,
(26)
rit
) and with an average N of lero.
toward zero so
= Et{^-^[nt+i +
Xt
where
In the steady state
equals the trend value of
and
capital, output
ITt
divided by
(r*
— g)
profits
where
Xt+i]}
(27)
grow at the rate
r* is
g,
the trend value of Xt
the trend value of the real rate at which
profits are discounted. Therefore, the log-linearization of (27) gives
it
where
ft is
=
{r'
g)ex^t+i
+ (1 +
l + r*
9)xt+i
-
n+i
J
the deviation from trend of the real rate of return between
implies that
irt
is
tit
equal to
+
cyyt
yt
+
—
i^t/ifJ-'
!)•
+
—
t
jl,^'+i
is
the estimate of ex
the
markup
is
Moreover, (3)
t.
j yt+i
:^-^,
- Y77''+i 1 +
r)
(28)
''»
terms one obtains an
supposed to be uncorrelated with information available at
the suggestion of Hansen (1982)
The presence of the
and
-m+ij
one eliminates the expected value operator from (28) and ignores the
equation whose residual
I
Hence (25) and (27) together imply that
——
= ^/t^l
[(Y
If
-
Et{
eta's
we
if
Following
estimate this equation by instrumental variables.
might
biased only
t.
affect the results
from
this procedure.
In this case, however,
such shocks have effects on both the expected rate of change
(since ftt+i enters with a coefficient almost equeil to one)
return on financial assets. While this
is
certainly a possibility
it
in
and on the expected rate of
seems
less likely
than that such
shocks affect the levels of q and the markup simultaneously.
7.
Data
Our time
series for Tobin's q
comes from Blanchard, Rhee and Summers
of the output (value added) of the private sector
GNP
goods
is
obtained from the
and the value added by the Federal, State and
is
local
the ratio of nominal to real private value added.
Our measure
as the difference between
governments. Our index of the prices of
Our measure
from the establishment survey as the difference between total hours
hours employed by the government.
NIPA
(1989).
of private hours
is
obtained
in nonagricultural payrolls
and
These hours do not have exactly the same coverage as our
18
output
series.
Thus, for our meeisures to be
strictly accurate, the
percentage changes in agricultural
hours must equal the percentage changes in the hours of private nonagricultural establishments.
We employ
two measures of wages. The
principeil
one
is
This measure equals private employee compensation from the
a measure of hourly compensation.
NIPA
government compensation) over our measure of private hours.
One advantage
hourly earnings in manufacturing.
coverage both
in
(i.e.
compensation minus
total
The second measure
of the compensation series
is
that
it
is
average
has a larger
terms of the sectors whose payments are recorded and in terms of the forms of
compensation that are included.*
8.
Empirical Determinants of
We
Markup
Variation
present results both from estimating equation (26) via ordinary least squares and from
estimating (28) with instrumental variables.
markup on
i/(
the
left
and
q
on the right hand
can be neglected while those of
rjj
We
side.
affect only
start with estimates of equation (26) with the
This specification makes sense
markup
q,
y and the constructed
variation series
is
markup
also allow the residual
to have
rjt
as well
eis
first
we
include the loga-
a constant and a linear trend.
constructed assuming an average
ticity of substitution of capital for labor e
the variations in
/i(.
Since the variables are supposed to be logarithmic deviations from trend
rithms of
if
markup n' equal
to 1.6
Our
baseline
and an
equal to 1.0, and ignoring the overtime premium.
order serial correlation, so that
it
equals prjt-i plus an
elas-
We
i.i.d.
disturbance. Under this specification, estimation of (26) for the period 1947. Ill to 1988.IV yields
/it=-0.72
(0.6)
-
0.002
t -
0.42
yj
(0.0007) (0.09)
Period: 1952:11-1988:4;
Both
coefficients are positive as is predicted
+
0.035
?,
(0.014)
/j=0.934
R2=0.997;
D.W.=1.54
by the implicit collusion model and thus of the opposite
'^A Becond advantage is that there is resison to believe the compensation series has smaller measurement error, at least in
way we use it. We use the real wage only to construct our series on markups. Ignoring fluctuations in capital, equation
(23) gives the detrended markup as a function of the detroided levels of output, yi, hours, hi and the real wage, W|. A
simple transformation allows one to write the detrended markup as a function of the detrended labor share {shi = ^t + ht —yi,
detrended output and detrended hours. The use of the two different wage series is thus equivalent to the use of the corresponding
two series for fluctuations in the labor share. To see which series has more classical measurement error we use US data from
the
1947JII to I989.I to run regressions of the logarithm of one share on the other including a trend and a correction for first order
When the share using hourly earnings is on the right hand side its coefficient equal 0.73 and is statistically
different from one. When that using compensation is on the right hand side, its coefficient is 0.93 and is not statistically
different from one. We thus cannot reject the hypothesis that the earnings share equals the compensation share plus noise.
serial correlation.
19
sign than the coefficients predicted by the customer market model. Moreover, since both coefficients
are significantly different from zero at conventional significance levels, the customer market model
The
statistically rejected.
is
fact that
tx
is statisticeilly
different
from zero also leads us to
models of the markup where the only determinant of the markup
static
is
reject
the current level of
output.
According to
of
(.X
(26), the coefficient
we thus must obtain a measure
equals
SOY/ K
for
on
for
t/j
is
ey while that on
^. According to our model,
our base case. The coefficient on
an estimate of €x- Since
Y/K
is
qt
We show
Table
in
variability of the
As a
on
1
how
markup.
falls
as
coefficient
on
yt
rises.
/i*
these coefficients vary as
For a given average markup, increases
(23) giving our
markup
qt
.
The
we
—
ex
is
and
/i*
is
e.
jit
markup by more. This
approximately
Increases in
explains
anomalous
^l
on
result
yt
produces
less
(and hence
if
/i*
raise the
why
/«*
the coefficient
also raise the
„_q ) changes
markup.
markup.
in e affect
In particular
These increases
/i^.
turn to estimation of the seime equation but with
biased coefficients
This
can be seen from the formula
increases in e raise the weight of changes in output on the meeisured
We now
0.1.
while having no effect on
variations only by affecting the influence of private output on the
on
to obtain
for a given increase in ht-
that increases in
in e raise the coefficient
measure of markup variations. For given
j/j
which
rises as well.
reeison for this apparently
therefore raise the estimated effect of
i~._\f(
1.
vary
somewhat more unexpected
is
q so that the implied value of
the coefficient on
^
In particular, they amplify the reduction in
What
this equals
roughly 10,** the implied value for ex
result, a given increase in yt reduces the
obtain an estimate
must thus be multiplied by ZOY/K
consistent with the restriction that ex be smaller than
is
-^- To
qx is
there are important variations in
qt
i/f
on the
left
hand
side.
This
and unimportant movements
in rjf
We
series
on markup variations, the estimation of such an equation including both a constant and a
again, let the residual in the equation have
trend yields:
'*See Rotemberg and Woodford (1989).
20
first
order serial correlation. For our baseline
qt=-4m
0.006
-
t
(0.006)
(3.5)
+
1.29
coefficient
+
(0.52)
Period: 1952:11-1988:4;
where the
yt
1.20 nt
(0.48)
p=0.969
'
on the markup equals
j^
D.W.=1.81
R*=0.952;
and that on private value added equals
estimates of both cy and ex are positive. In addition, the ratio of the coefficient on
on
(it
gives £y
which
is
Y/K,
models.
we must, again, obtain a measure
for this result
same time so that they
the coefficient on
rj
of ex
the resulting estimate of ex
One reason
over that
thus estimated to be near one.
To obtain an estimate
of
y^
^^- The
is
may
very large, too
leirge
for
30Y/K. For
plausible values
to be consistent with any of our three
be that increases in expected returns lower Xt and $t at the
also raise Vf. Insofar as this increase in expected returns reduces
markups
will
be too small and our estimate of ex
that are correlated only with nt have the
same
efiFect
will
be too
markups,
large. Variations in
since they bias the coefficient
on nt toward
zero.
In Table 2
the average
we show how
the coefficients on
markup (and hence
falls.
effect
on the estimate of j^^. The reason
we vary
/i*
and
e.
As we
increase
markup and
we
e
^^
while having
once again, that increases
in e raise the
lower the estimated value of
for this
is,
Increases in e therefore reduce the regressions estimate of the independent
output on stock
We now
vary as
average markup.
influnece of y^ on fif
effect of
yj
In contrast, the latter coefficient estimate rises as
For a given average markup, increases in
no
and
increase its variability) the correlation between the
stock prices falls so that the former
increeise the
fit
prices.
turn to the estimation of (28) via instrumental variables. There are several advantages
to this procedure. First, the estimates are
somewhat
less subject to
endogeneity
method does not require observations on the present discounted value
of profits
bizis.
X.
It
Second, the
does however
require information on discount rates (or marginal rates of substitution). Given the inadequeicies
of various rates of return as discount rates
we experiment with
the return on the stock market, the
return on Treasury Bills and the return on prime commercicil paper. Third,
quantitative estimates for both ey and ex
We
more
it
allows us to recover
easily.
include a constant and a trend as well as the logarithms of the markup, output, hours,
21
wage and the
the real
level of real returns in our estimation.
wage as
The
series
use a constant, a
and one lagged value of the logarithms of output, the labor input and the
linear trend, the current
real
As instruments we
well as the ex post real return between
t
—
and
I
t.
results of estimating (28) for the period 1947.III to 1988.IV using our baseline
and the return on the stock market
statistics for
both the
ceise
where ey
=
presented in Table
aire
(x
=
*nd
f>
1.
for the case
markup
We show estimates and summary
where €y and €x are allowed to
differ.
The summary
statistics reported in table 1 concerning the
The Durbin- Watson
couraging.
fit
of the two equations are en-
statistic reveals that little seri2il correlation
remains in the errors.
Because we use more instruments than there are coefiRcients, the two equations are overidentified.
The
test statistic
the row
proposed by Hansen (1982) to
marked J and
distributed
is
that the restrictions are valid.
The
x with
5
test these overidentifying restrictions is reported in
and 6 degrees of freedom under the null hypothesis
actual values of this statistic are very small, which probably
indicates that the instruments are quite coUineftr.
Turning to the estimates, consider
equal.
A 1%
increase in
point.
A 1%
increeise in
X
Y
is
first
the case where ey and ex are not constrained to be
then estimated to raise the markup by about a
of a percentage
fifth
by contrast lowers the markup by about 1%. Both these
coefficients are
again and significant.
of ey and ex are inconsistent with the homothetic versions of both
The estimates
models because they are
is
statististically significantly difiFerent
from each other. Once homotheticity
dropped, ey can be larger than ex as long as the elasticity of
Then, increases
in
Y
given change in his
coefficients.
number
Y
increases.
difficulties
To gain some
They thus
higher
when
Y
is
large.
of customers that a deviator gets for a
require relatively large reductions in the markup.
intuition into the source of this discrepancy suppose
growth of private value added
expected change in the logarithm of the markup between
in
is
provide an alternative explaination for the difiFerence between the two
real discount rate r' equals the average
change
demand
markup. This disproportiante increase implies that deviations become much
more attractive when
Measurement
raise disproportionately the
dynamic
t
and t+1 a
g.
first
that the average
Then, (28) makes the
linear function of the expected
logarithm of private value added (with coefficient ey) and of the expected real return
22
rate between
t
and
+
t
(with coefficient ex).
1
Given that the difference between
that €y exceeds ex
with the change
r
and g
is
in fact quite
An
in the
error in
markup than the expected discount
equals 0.0126), the finding
f^
added
is
more correlated
This could well be due to the
rate.
from the expected return on stocks, so that the
biases the estimate of ex downwards.
additional prediction of the implicit collusion model
This restriction
(it
a finding that the expected chemge in private value
is
fact that the relevant discount rate for firms differs
measurement
small
is satisfied
whether (y and ex are allowed to
is
that ex should be less than ^
differ as in
the
first
—
1.
column or whether
they are constrained to be equal as in the second column. In the latter column, the estimate the
elasticity of the
markup with
respect to
X/Y
,
e,
of 0.22 which
is
well below
.6
while remaining
significantly positive.
The
difference
between the J
statistics reported in the
the restriction that the two elasticities are the same
ratio test proposed by Gallant
are at variance with those
in this case, the
two
Wald
statistics is 1.35
tests
it
This
is
two
test
whether
the analogue of the likelihood
sometimes pro'^uces inferences which
based on the standard errors of the
test rejects the equality of the
is
valid.
and Jorgenson (1979) and
from Wald
which
is
two columns can be used to
coefficients
coefficients. Indeed,
but the difference between the
well below the critical value for the x^ distribution with one degree
of freedom.
In Tables 2, 3
and 4 we report variations on the model which are designed to gauge the
Tables 2 and 3 are devoted to obtaining estimates for different values
robustness of our results.
of the average
markup and
for different values of the elasticity of substitution.
particular elzisticities of substitution equal to 0.5,
much
smaller than what
is
1
and 2 and average markups of
found by the methods of
devoted to estimates when the two
elasticities are
We
Hjill), 1.6
(our base case) and
consider in
(which
is
Table 2
is
1.1
2.
equal while the estimates of Table 3 are obtsdned
without imposing this restriction.
The two parameters
and reductions
in e
/i'
and
e affect the results.
As explained
in Section 5, increases in
both increase the tendency of the markup to be countercyclical.
surprising that our estimates of e in Table 2 and those of ey in Table 3 rise with
e.
What
is,
once again, more surprising
is
/i'
fi*
It is
thus not
and
fall
with
that the estimates of ex in Table 3 which correspond
23
to estimates of the effect of expected rates of return on the
falls
with
One
e.
notable feature of Table 2
;i*
—
1
as required by our theory.
also increases with
and
/i*
that, with the exception of the estimates for an
and an average markup of
elasticity of substitution of 0.5
corresponding
is
markup
1.1,
the estimates of
The estimates
e
are lower than the
of ex in Table 3 are below
/i'
—
1
as well.
Table 4 presents other variations while holding the average markup and elasticity of substitution fixed at our beise levels of 1.6
and
The
1.
first
variation replaces one useful instrument of real
returns on stocks, the lagged return, by another, namely the lagged dividend price ratio. ^^ This
has no material effect on our results.
The next two
lines present the
estimates
when we
use either the Treasury Bill rate plus a
constant or the commercial paper rate plus a constant as a discount rate.
to
add constants to these rates
is
Somewhat
premium must be added
We
assumed
the second and third row of Table 4
is
when we
from
different
show
significant.
The
last
it is
premium have no
We
Bills, this
two rows show that the
effect
on our conclusions.
is
is
not statistically significantly
probably a more 2K;curate representation
results are not sensitive to our use of hourly
we
com-
use stock returns or return on
measure of wages produces essentially the same results as hourly compensation.
our results to the addition of the Bils correction for the
between the average and marginal wage.
spelled out in the Appendix.
*See
is
comforting that the results using this latter return are somewhat more
finally consider the sensitivity of
difference
the
does affect the standard errors. In partic-
it
pensation instead of hourly earnings in manufacturing. Whether
Treasury
make
that the use of alternative instruments does
is
Because the commercial paper rate
of firm's discount rates
to these rates to
premia which are equal to the
use the return on Treasury Bills, the estimate of ex
zero.
lower than
estimated only from the variation in ex ante
risk
not affect the magnitudes of the coefficients although
ular,
risk
is
we have
and the average return on the instrument that
did this to ensure that the ex
returns. However, small differences in this
What
we choose
arbitrarily
difference between the economy's growth rate
being considered.
reeison
that the average real return on these instruments
the economy's growth rate. Therefore a risk
firm's prob.'*'m well defined.
The
Keim and Stambaugh
The
We
obtain this correction using the method
resulting correction reasonably substantial.
(1986).
24
We
estimate that
the increased use of overtime implies that,
of
1%, while the marginal wage
when hours
rise
by
1%
the average
wage
by 0.417 of 1%. Using the resulting markup
rises
rises
by 0.056
series estimation
of (26) for our base case yields
/i,=-0.56
0.002
-
t -
0.66
+
y,
(0.0009) (0.10)
(0.7)
reverse equation with q on the
0.006
-
gt=-4.92
t
p=0.944
1.49
(0.006)
(3.5)
hand side
left
+
y,
both cases, the estimate of ey
correction
makes marginal
affected
by the correction.
markup
series,
cost
and 1.443 respectively, and
more
When we
both estimates
rise.
(0.41)
rises
with the correction. This
imate (28) via instrumental
is
/^
—
1.
is
not surprising since the
However, the estimates of ex are not very much
their standard errors &ie 0.07
models
D.W.=1.82
R*=0.952;
The parameters ex and cy
ex remains much smaller than
9.
/i,
p=0.969
e:
D.W.=1.54
R'=0.998;
yields instead
1.06
procyclical.
higher,
even stronger
+
(0.55)
Period: 1952:11-1988:4;
In
qt
(0.017)
Period: 1952:11-1988:4;
The
0.043
and
veiriables using the corrected
are then estimated to equal 0.281
0.24.
While both
elasticities are
now
Note also that the rejection of the two alternative
in this Ccise.
Conclusion
Our
results provide further evidence that the
countercyclically over the business cycle.
We
markup
of prices over marginal cost
moves
have also found that the type of markup variations
that occur are reasonably consistent with the predictions of the model of endogenous
markup
determination that we have previously discussed (Rotemberg and Woodford (1989)). Our results are
quite inconsistent with the other leading "dynamic"
model of markup determination, that proposed
by Phelps and Winter (1970), and we are also able to reject a simple
to
which the
eleisticity of
demand
varies with the level of aggregate
"static" specification, according
demand. These conclusions are
consistent with our previous analysis of the effects of military purchases on economic eictivity; in
Rotemberg and Woodford (1989) we
collusion
model that are harder
also found empirical regularities consistent with the implicit
to reconcile with either of the alternatives.
25
These conclusions suggest that markup variations may well be an important mechanism by
which changes
in the
demand
goods translate into changes in output. In the case of competitive
for
demand
product markets, firms'
for
hours Hf
a decreasing function of the current real wage Wf,
is
given by the relation:
FH{Kt,ztHt)
An
stock
is
demand
increase in the
predetermined
technology
for
government purchzises, a change
in the
wt
demand
in export or
demand curve
curve, because the capital
whether as a
demand
investment
in response to lower real wages.
demand
for goods should not ciffect the state of
for goods,
hours) only insofar as the short run labor supply curve
the labor
labor
shift this
and the demand
(in the short run)
Hence an increase
Z(.
goods cannot
=
is
etc.
result of
an increase
in
can increase output (and
shifted outward,
Such labor supply
and firms move down
shifts
can result from
intertemporal substitution and, in the case of government purchases, be the consequence of wealth
effects.
But,
real
if
wages
the
way demand shocks
affect the
economy, they cannot be very important since
this
is
fail
to be countercyclical (and are furthermore procycliccil
when composition
associated with aggregation of high-wage and low-wage hours are taken account of).
biases
Therefore,
only shifts in the aggregate production function can be very important in explaining business cycles
if
one maintains perfect competition.
For shocks to the
hire additional
demand
for
goods to be important, they must
workers at a given real wage. As Kalecki (1938) and Keynes (1939) recognized, this
requires that the
markup
fall in
the modified
demand
F„{Kt,ZtHt)
We
it
termination.
in
aggregate
sign.
=
for labor function:
ntWt
have presented evidence that, as required, the markup
thermore
increeise firm's willingness to
moves
in a
way
that
That theory, the
demand
for
is
(29)
is
indeed countercycliczd, and fur-
consistent with a coherent theory of endogenous
oligopolistic collusion
produced goods can
The customer market model, by
would be much
26
de-
model, explains how transitory movements
result in fluctuations in labor
contr<ist,
markup
less
demand
of the
same
promising as a basis for such
a theory, for most of the sources of variation in aggregate
-
example, temporary increases
for
in
to future consumption, or investment
opportunities
-
would
interested in
export demand, shifts of tastes toward present as opposed
booms due
to discovery of especially productive investment
tend to raise current output relative to future profits, and to raise real
all
interest rates. Therefore,
demand that one might be
markups would tend
to increeise shifting the labor
so that an even greater labor supply shift and real
wage decline
is
demand curve inward
needed to increase output than
in the competitive model.'
A
simple "static" ipecification,
fit
=
(^{Yt),
FH{Kt, ztHt)
This
still
=
establishes a relation between Wt
would mean
repljicing (29) by:
fi{F{Kt, ztHt))wt
(30)
and Ht that cannot be
by anything other than a technology shock. Thus,
in
shifted, in the short run,
such a theory, aggregate
can affect output and hours only by shifting the short run labor supply curve.
negii>-ive,
real
If
If
fi!
is
variations
sufficiently
such variations along the fixed schedule (30) might involve an acyclical or even procyclic^i
wage. But
aggregate
demand
it
would seem to us undesirable
demand
variations
upon
their effects
to place the entire responsibility for the efficacy of
upon household labor supply.
one assumes a representative consumer with preferences that are additively separable be-
tween periods, as
is
optimal labor supply
common
in the real business cycle literature, the first order condition for
is:
MRS{Ct,Ht) = wt
where Ct denotes aggregate consumption.
tion between consumption
and
leisure
is
It is
usual to suppose that this marginal rate of substitu-
increaising in
consumption and decreasing
of leisure. Hence an outward shift in the labor supply curve
sumption; but consumption
would make
it
'^In
movements
fact, increases in
must coincide with a decrease
procyclical rather than countercyclicad.'
hard to understand the procyclical variation
of the Beveridge curve)
cyclical
is
and quit rates
(see, for instance.
in firm's willingness to hire
government purchases
'^In Rotemberg and Woodford (1989)
may
in
in con-
Moreover, such a model
vacancy rates (the relative constancy
Parsons (1973)) which both suggest pro-
workers at a given real wage. Furthermore, such a
well reduce output
we show that
in the quantity
and employment
in
increases in military spending lead
decline.
27
such a model. See Phelpa (1989).
rise rather than to
consumption to
model would
rely critically
both upon labor-supplying households being able to quickly understand
and respond to the future consequences of current aggregate shocks, and upon those households'
effective integration into the capital markets, either of
that, as in
many popular
efficiency
which might be doubted. Finally suppose
wage models, households
are rationed in the
amount
they can supply. Then, variations in desired household labor supply due to wealth
tertemporal substitution
may have
little efifect
upon which
of labor
efiFects
or in-
of the points consistent with (30)
is
realized in equilibrium.
Hence a "dynamic" model of markup determination, such as the
offers the greatest
oligopolistic collusion model,
promise as a basis for understanding the role of aggregate demand variations
in
the generation of business cycles, quite apart from the evidence provided here in support of such
a specification. Further quantitative investigations of the extent to which this
for the character of
model can account
observed aggregate fluctuations, under various hypotheses about the ultimate
driving shocks, would seem to be warranted.
28
Appendix
The
In this
Appendix we consider the computation of
wage to the average wage
total
Bils Correction
in the presence of
wage payments can be written
U(,
the variations in the ratio of the marginal
varying use of overtime workers. Bils assumes that
cis:
wt{Ht+pV{Ht)]
where wt
V{H)
is
the straight-time wage, p
indicates
how many
is
the overtime
premium which
Wt[l
wage
Msumed
to equal
50%, and
overtime hours firms employ as a function of total hours. Therefore, the
marginal wage (the increased expenditure when hours
while the average
is
+
rise
by one unit)
is:
pV'{Ht)]
is
1+p
Wt
Ht
Therefore the percent change in the marginal wage for a
1%
increase in
employment
is
pV"H^
H + pV'H
while the corresponding percent change in the average
wage
is
_ pjV'H - V)
H + pV
^'^~
The logarithmic deviation
To obtain estimates
of the ratio of marginal to average wage, U(
of 7a/ and
7^ we use the
cover only the manufacturing sector.
We assume
by V{Ht) times a stationary residual.
of overtime hours,
on
ht
and
hj.
We
is
then equal to {'jm
available data on overtime which, unfortunately,
that the eictual value of overtime hours V^
thus rim a regression of
Allowing for an error with both
correlation yields
29
— 7A)^t-
Vf,
first
is
given
the detrended logarithm
and second order
serial
t)t= 7.01 ht
+
(0.59)
2.69 h^t
(8.11)
AR(1)=1.17
Period: 1956:111-1989:1;
Assuming that the residual
is
equals
V'H/V
while the second equals one half of
As
the latter. Bils's estimates are both
V/H
in Bils' analysis, the
somewhat
—y
(-
-y
i^^)^- Using
equals 0.0187, gives a value for f\f of
former
is
about eight times larger than
larger because his index of total hours covers only
production hours in manufacturing, so that his average
10.
D.W.=2.05
second order logarithmic expansion of V[H). Thus, the
these facts, together with knowledge that in our data
0.417 and one for "ja of 0.056.
R^=0.97;
uncorrelated with the right hand side variables, the coefficients
in this regression are the coefficients in a
first coefficient
AR(2)=0.24
V/H
is
higher.
References
Abreu, Dilip: "Extremal Equilibria of Oligopolistic Supergames," Journal of EcoDonuK. Theory,
39, 1986, 191-225.
Barsky, Robert and Gary Solon: "Real Wages over the Business Cycle,",
2888, March 1989.
Bils,
:
Working Paper
Mark: "The Cyclical Behavior of Marginal Cost and Price," American Economic Review,
77,
—
NBER
December 1987, 838-57.
"Pricing in a
Customer Market," Quarter// Journal of Economics, November 1989.
Blanchard, Olivier, Changyong Rhee and Lawrence Summers: "The Stick Market, Profit and
Investment," National Bureau of Economic Research Working Paper 3370, May 1990.
Dixit,
Avinash and Joseph Stiglitz: "Monopolistic Competition and Optimum Product DiverAmerican Economic fieview,297-308, 1977.
sity,"
Domowitz,
Ian, R. Glenn Hubbard, and Bruce C. Petersen, "Market Structure and Cyclical
Fluctuations in U.S. Manufacturing," Review of Economic Statistics, February 1988.
Dunlop, John T.:''The Movement
in
Real and
Money Wage Rates" Economic
Journal, 18,
1938, 413-34.
Joseph and Carl Shapiro: "Dynamic Competition with Switching Costs,"
of Economics, 19, Spring 1988, 123-37.
Farrell,
30
Rand Journal
Froot, Kenneth A. and Paul D. Klemperer: "Exchange Rate Pass-Through
Matters," American Economic Review, 79, September 1989, 637-54.
when Market Share
Gallant, Ronald A. and Dale W. Jorgenson: "Statistical Inference for a System of Simultaneous, Non-Linear, Implicit Equations in the Context of Instrumental variables Estimation,"
Journai of Econometrics, 11, October/December 1979, 275-302.
"Price Dynamics of Exporting and Import-Competing Firms," Scandinavian
Journal of Economics, 88, 417-436.
Gottfries, Nils:
:
:
"Market Shares and Pricing Behavior in the Treideables Industry: An Exannination of
Swedish Manufacturing", Institute for International Economic Studies Paper No. 412.
"Customer Markets, Credit Market Imperfections and Real Price Rigidity" Economica,
forthcoming, 1989 mimeo.
Greenwald, Bruce and Joseph
cles,"
Hall,
Stiglitz: "Financial
NBEfi Working Paper
Market Imperfections and Business Cy-
2494, 1988.
Robert E.:"The Relation Between Price and Marginal Cost
Economy, 96, October 1988, 921-48.
in U.S. Industry,"
Journal of
Political
— "Investment
under Uncertainty: Theory and Test with Industry Data,"
Paper 2264, May 1987.
"Substitution over
Time
in
Work and Consumption," National Bureau
December 1988b.
NBER
of
Working
Economic Re-
search Working Paper 2789,
Hansen, Lars Peter: "Large Sample Properties of Method of Moments Estimators," Econometrica, 50,
July 1982, 1029-54.
Kalecki, Michael: "The Determinants of the Distribution of National Income," Econometrica, 6,
97-112, 1938.
Keim, D., and Robert Stambaugh: "Predicting Returns
Journal of Financial Economics, 17, 1986, 357-90.
in the
Bond and Stock Markets,"
Keynes, John Maynard:"Relative Movements of Real Wages and Output," Economic Journal,
49, 34-51, 1939.
Klemperer, Paul D.:"Markets with Consumer Switching Costs," Quarteriy Journal of Economics, 102, May 1987, 375-94.
Kydland, Finn E. and Edward C. Prescott: "Cyclical Movements of the Labor Input and its
Real Wage," Federal Reserve bank of Minneapolis Working Paper 413, November 1988.
31
Parsons, Donald 0.:"Quit Rates over Time, A Search and Information Approach," American
Economic Review, 63, June 1973, 390-401.
Edmund S.: "Aggregate Demand in a Non-Monetary Model of Labor-Market and
Product-Market Equilibrium," mimeo, Columbia University, June 1989.
Phelps,
Edmund
and Sidney G. Winter: "Optimal Price Policy under Atomistic CompetiMicroecoDomic Foundations o{ Employment and InBation Theory,
W.W.Norton and Co, New York, 1970.
Phelps,
S.
tion" in E. Phelps ed.
Robinson, Joan: "The Economics of Imperfect Competition," Macmillan, London, 1932.
Rotemberg, Julio J. and Garth Saloner:"A Supergame-Theoretic Model of Price Wars during
Booms," American Economic Review, 76, June 1986, 390-407.
Rotemberg, Julio J. and Michael Woodford, "Oligopolistic Pricing and the Effects of Aggregate
Demand on Economic Activity," National Bureau of Economic Research, Working Paper
No. 3206, Cambridge, Massachusetts, December 1989.
Solow, Robert M.: "Technical Change and the Aggregate Production Function," Review of
Economics and Statistics, 39, August 1957, 312-20.
Tarshis, L.:"Changes in Real
and Money Wage Rates," Economic Journai,
32
19, 1939, 150-4.
TO
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TABLE
1
Estimation of equation (26) for different specifications
AVERAGE MARKUP
1.1
1.6
TABLE
2
The levels equation with q as the dependent variable
AVERAGE MARKUP
1.1
1.6
TABLE
3
The basic instrumental variables specifications
US data 1947:III-1988-IV
Separate Coeffs.
Constrained Coeffs,
Parameter
Constant
Coeff. on trend
0.223
0.19 5
(0.06)
(0.05)
0.66e-4
-0.85e-5
(0.4e-4)
(0.3e-4)
1.062
(0.20)
•X
0.184
(0.06)
0.195
e
(0.05)
r2
0.995
0.980
D.W.
2.36
2.00
J
1.09
1.46
Table
4
Instrumental Variables Method
Elasticity of the markup with respect to X/Y
AVERAGE MARKUP
1.1
E
L
A
0.5
S
B
T
S
C
I
I
U
T
IT
Y
O
F
0.118
0.224
0.366
(0.04)
(0.07)
(0.12)
U
S
T
1.6
1
0.099
0.204
0.335
(0.03)
(0.06)
(0.10)
I
O
N
2
0.092
0.195
0.322
(0.03)
(0.05)
(0.09)
TABLE
5
Instrumental Variables Method
Separate Elasticities with respect to Y and X
AVERAGE MARKUP
1.1
gy
E
L
S
A
U
S
B
T
S
I
T
T
U
T
Y
I
O
O
N
0.515
1.726
3.124
(0.11)
(0.20)
(0.32)
0.099
0.185
0.396
(0.06)
(0.11)
0.5
€x
CI
I
1.6
€y
(0.035)
0.139
1.062
2.127
(0.11)
(0.20)
(0.32)
1
ex
0.097
0.184
0.293
(0.03)
(0.06)
(0.09)
F
-0.049
0.729
1.628
(0.11)
(0.20)
(0.32)
0.096
0.183
0.292
(0.03)
(0.06)
(0.09)
TABLE
6
Instrumental Variables Method
Variations with average markup equal to 1.6 and
elasticity of substitution equal to 1.
Use of lagged dividend/price
ratio instead of lagged
return as an instrument
Use of return on Treasury
Bills instead of stock return
Use of return on commercial
paper instead of stock return
Use of hourly earnings in
manufacturing instead of
hourly private compensation
Use of hourly earnings and
return on Treasury Bills
Use of hourly earnings and
return on commercial paper
1.184
0.165
(0.22)
(0.05)
0.933
0.365
(0.17)
(0.25)
0.916
0.455
(0.19)
(0.24)
1.274
0.255
(0.24)
(0.07)
1.055
0.655
(0.19)
(0.29)
0.878
0.953
(0.19)
(0.28)
296fe
06U
I
i
i,
Date Due
MAY
2S
1993
Lib-26-67
MIT
LIBRARIES
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