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This PDF is a selection from a published volume from the National Bureau of
Economic Research
Volume Title: NBER Macroeconomics Annual 2007, Volume 22
Volume Author/Editor: Daron Acemoglu, Kenneth Rogoff and Michael
Woodford, editors
Volume Publisher: University of Chicago Press
Volume ISBN: 978-0-226-00202-6
Volume URL: http://www.nber.org/books/acem07-1
Conference Date: March 30-31, 2007
Publication Date: June 2008
Chapter Title: Comment on "Monetary Policy and Business Cycles with
Endogenous Entry and Product Variety"
Chapter Author: Julio J. Rotemberg
Chapter URL: http://www.nber.org/chapters/c4092
Chapter pages in book: (p. 367 - 375)
Comment
Harvard
Julio J. Rotemberg,
Business
School and NBER
a useful se
and Melitz
(BGM) provides
2006 paper. The earlier paper introduced
a tractable
entry was
competition model where
dynamic monopolistic
in an attractive manner. By paying an entry fee, any firm could
handled
This paper by Bilbiie, Ghironi,
quel to their already influential
become
earlier
a symmetric monopolistically
competitive
the case where
papers had considered
producer. While many
there was a fixed cost
to pay each period, Bilbiie,
firm needed
that an imperfectly
competitive
and Melitz
fixed costs and
Ghironi,
(2006) neglected
period-by-period
once.
to
costs
that
all
had
be
For
the
fixed
paid just
supposed
describing
behavior
of entrants,
this assumption
has considerable
this model
difficulty with interpreting
One
empirical
is that new
however,
try,
slowly
become
over
a priori
appeal.
as amodel of en
tend to be small firms that grow only
this is a model where
firms immediately
entrants
time. By contrast,
as large as the typical
firm after they pay their entry cost. BGM
as one where
to
thus prefer
firms are increasing
interpret this model
the number of varieties
that they sell and where
the fixed cost is the cost
of adding a variety. This interpretation
has an important
side benefit,
on
it
that
macroeconomists'
attention
focuses
the
indubitable
namely
fact that most firms sell a variety of different products.
The current paper
extends the BGM framework by letting firms have
toward
realism that Iwelcome)
and uses the result
(a
step
rigid prices
to
model
of
the
consequences
ing
study
monetary
policy. This has the
some
to
of
of how
consequences
advantage
bringing
light
unexpected
one models
in sticky price models.
entry costs and the labor market
These
lessons
pirical
model,
number
failures.
BGM
are
em
particularly well illustrated by two of the model's
The first is that, at least in the benchmark
version of the
conclude
of firms
that monetary
should
reduce the
expansions
For the case of the number
of firms,
(or products).
368 Rotemberg
(2005) show that identified monetary
Bergin and Corsetti
policy shocks
in a VAR increase the number of firms (and this result has been repli
cated by Lewis
in
is that, for output expansions
[2006]). The second
shocks, the current BGM paper features unrealis
movements
inmarkups.
tically large countercyclical
as
discussion
is
sim
follows. First, I show that amuch
My
organized
can
a
in
is
with
model
of
model
entry
explain why entry
pler
procyclical
duced
by technology
are
that is, in amodel where output fluctuations
I discuss
in the markup
of final goods. Second,
the cyclical behavior
of the number of new
concerning
no technology
shocks,
the result of variations
some
evidence
on the
is a great deal scarcer than the evidence
This evidence
products.
at
number of firms, but, as suggested
is
of
least
earlier,
probably
equal
One
for macroeconomists.
aspect of this evi
importance
interesting
is that, at least for the data I have been able to find, the number of
is not very strongly procyclical.
Third, I discuss one of the im
products
reasons
of this model
the
benchmark
version
has entry
portant
why
dence
in response
is modeled
falling
market
tomonetary
policy expansions.
in such a way that real wages
This
is that the labor
are much
are in reality. Last, I show that this weakness
cyclical than they
the
also explains
the finding that markups
labor
market
eling
to technology
in response
shocks.
sively countercyclical
1
A Simple Model
Suppose
Y\
=
of the Equilibrium
that final producers
have
Number
a production
more
pro
inmod
are exces
of Firms
function
given by
(l)
(M;)?
this firm's
Y\ represents output by firm i at twhile M\ represents
mar
use of materials
at t. In the simplest case, there is an economy-wide
so that
ket for materials
where
'
i
and q{ is the output of in
Mt equals the total available materials
earns a
are produced
with
firm ;. Materials
termediate
labor, which
is
to
labor
The
wage wt.
q{
produce
requirement
where
L{
=
q{[x + a(q{-qY]
x is a constant. While
this may seem
aU-shaped
it
has
the
benefit
of
form,
yielding
to
minimum
xwr
average cost equal
where
like an unusual
average
functional
cost function with
369
Comment
to
cost is then equal
Marginal
[x+ a(q{ qf + 2a(q[ q)q[]wt.
that the price of the intermediate
input
competition
implies
enter whenever
this price exceeds av
Firms
cost.
then
equals marginal
at effi
erage cost. This ensures that all intermediate
good firms produce
cient scale qand that the price of the intermediate
good vt is given by
Perfect
=
vt
xwr
The number
nt
=
intermediate
of firms producing
nt equals
MJq.
From both
the point
of view
the final goods producers,
are
according
goods
produced
=
and from the point of view of
to one where
final
of workers
this model
Y\
goods
is equivalent
to
(L;/*)?.
cost of the final good is zvtL\/(olY\).
In either case, marginal
is that increases
An immediate
of this model
implication
lead to increases
Since
the technologies
are held constant
goods
the result
in output
of firms producing
intermediate
inputs.
both the final and intermediate
for producing
in the number
of reductions
Thus, this model
rise if there was
in output must be
of the final goods producers.
that the number of intermediate
firms would
in this exercise,
in the markup
this increase
predicts
an expansionary
monetary
policy and final goods pro
that matching
the
ducers had sticky prices. It should be noted, however,
a
more
com
actual dynamics
of entry probably
requires
substantially
as in Lewis (2006), one probably needs further ad
plex model because,
justment costs. I return to this issue in the following discussion.
2
How
Does
It is well
of Products
Vary Cyclically?
that the number
of firms is quite procyclical.
But be
are
the
firms
for
small,
importance of this phenomenon
un
and
remains
aggregate
output,
aggregate
employment
I thus applaud this paper's emphasis on the number of products
cause most
pricing,
known.
known
the Number
new
produced
by any given firm. Unfortunately,
about the time-series
of product
properties
relatively
variety. A
little
is known
recent study by
new
in
breaks
this
area, and finds
(2007)
ground
is quite
that the number of UPC codes found in consumers'
purchases
this
includes
six
of
data
However,
(of
years
procyclical.
study
only
Broda
and Weinstein
370 Rotemberg
1999-2003
involves
consecutive
observations).
only the period
it does include one recession,
the 2001 recession may have been
to the collapse of the dot.com bubble.
itwas connected
special, because
on this issue.
sources of information
I thus consider
two additional
which
While
The
first is data assembled
(2003)
(1990) and Axarloglou
by Devinney
in the pages of the
of new products
that were announced
data cover the period
Wall
Street Journal.1 The quarterly Devinney
cover
while
the
data
the period 1984:1
1975:1-1984:4,
(2003)
Axarloglou
are
used by these two researchers
1994:2. Unfortunately,
the methods
on the number
that
identical, though their series behave
similarly over the period
as
a
as
common.
indicator
in
have
These
well
obtained
data,
cyclical
they
GDP
the
method
of
(2003), are depicted
Rotemberg
by detrending
using
in figure 5C2.1.
not
to
The plot does not reveal strong responses of product
introductions
or
a
nor
af
do they involve
either the 1990
2001 recession,
large increase
the Devinney
ter the 1974 recession. The correlation between
(1990) data
on the
is
and
introduction
GDP
of
actually -0.34,
cyclical
product
log
on
data
the
that between
while
the Axarloglou
(2003)
log of introduc
tions and cyclical GDP
0.04
The correlations
is -0.40.
the change
between
in
-1-"-p6
I'
002J
^
Devinney(1990)
\
v' *
"?'02i//v
/ Cyclical
GDP I I
,
log
-0.04-JJ
-0.06J
'0-08
-j
111 111
j 11111111111
j
76
Figure
5C2.1
Cyclical
GDP
78
\A
\
'
h
(2003)
Axarl?9lou
\l
[
[ 1111111111111111111111111111111111111111111
80
and Log of Wall
82
Street
i
|3
I j
'h\\ h
i 'I\ I // \I rl/Vl
\/
/V
V
*"
\;/
a/
\r
84
Journal New
86
Product
88
90
Announcements
111
1
[ 111111 f-
92
371
Comment
and the change in cyclical GDP is -0.57 in the
the log of introductions
it is 0.65 in the latter. This latter finding provides
early period while
some support for the idea that product
introductions
seems weak
for this proposition
the overall evidence
are procyclical,
but
from these data.2
series on the number
of available
readily available
of a certain type is available
from Ward's Automobile Reports.
products
in each calendar year by
This publication
lists new car registrations
An
even more
A nameplate
is a sub-brand,
like the Chevrolet
Impala or
a
sub-brand has two different body
Mercury
Cougar. When
particular
as
a
and
sedan
(such
types
they appear as different nameplates.
wagon),
"nameplate."
in trim, engine, or options do not
such as differences
differences,
as
in a particu
The
number
of nameplates
appear
separate nameplates.
a
measure
lar year is thus
crude
of product variety, but it has the advan
and
of
available
easy to define.
tage
being readily
Other
Data
while
on
is not available
from 1955,
foreign automobiles
consistently
on
cars
data
is. Figure 5C2.2 thus shows the logarithm
U.S. -made
as well as the measure
of U.S. nameplates
of cyclical GDP
The
correlation
series
is fairly low.
between
these
previously.
0.22 using the 1955-2005
it
whereas
sample,
equals only 0.08 if
of the number
discussed
It equals
one removes
els where
the 1959 observation.
the variety
My conclusion
of final output is procyclical
5.0-,-r
4 8
ANameplates
4.0-?
ii
I
\l
55
.06
04
1 (Cyclical
.-.04
/log GDP
V
3.8vS.o-|
exploring,
^AVV
\j
\/
\l 1/
are worth
1 Log# US
[
A
*.2-
from this is that mod
V
' --.06
i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i
p~.Uo
Figure
5C2.2
Cyclical
tions
GDP
60
65
70
and Log of the Number
75
80
85
of U.S. Automobile
90
95
Nameplates
00
in New
05
Registra
372 Rotemberg
but
that the relationship
between
appears to be fairly complex.
3
Entry and Monetary
Inow provide
so as to show
Policy
product
and business
variety
cycles
in the BGM Model
a simplified
of some aspects of the BGM model
exposition
that entry falls
that an important reason for its conclusion
to
market. To il
is
due
its
model
of
the
labor
expansions
after monetary
to enter in a model with a fixed
the incentives
lustrate this, I consider
as
the labor market
ismodeled
number of firms and I show that, when
in BGM, this incentive falls when output rises.
to enter, it
that, if a firm were
suppose
for as long as
receive a fixed fraction of the total profits available
would
in
8 of disappearing
it expects a probability
the firm stays alive. Suppose
a
amount
cost
labor.
that
consists
of
fixed
of
and
the
each period
entry
To calculate
this
incentive
if
is then attractive
Entry
(2)
?tBpd-8)]!(^y^+^^/?
where/?
is a constant while
irt and Ct represent
respectively.
With Yt = Ct and constant returns,
=
=
ir, Ct(Pt MC,)/Pt
1/?l()
C,(l
real profits
|xf as Pt/MCr
and consumption,
at t are
(3)
cost at t and
MCt is marginal
the markup
defining
where
profits
the second
At
the same
is based on
equality
time, the production
function
=
c,
mr
implies
|x,
is given
that the markup
by
=-=-.
(4)
wt
wt
Now
let variables
state. Differentiating
*=
("i^rjft
so that profits
we obtain
with
tildes denote
log deviations
around
a steady
(3) gives
+c"
rise with
output
and with
markups.
Differentiating
(4),
373
Comment
=
_
1-a
~
t??
&
which
'
ct,
implies
/ -1
\
\|UL 1/
1-a
' f
L ^-1)J
1.
'
that profits fall when
the real wage
rises, while
they rise
> 1. This condition
au.
as
is
for
necessary
output
long
profits to
in markups.
to changes
in response
be procyclical
Since BGM assume
that a = 1, this condition
is always satisfied in their paper. This condi
This
shows
as
with
tion is not sufficient, however.
Profits rise only if the resulting real wage
increases are suitably modest.
that the aver
Indeed, since they suppose
=
a
2
is
less
than
while
fall
unless
rise
|jl
1, profits
age markup
wages
less than output. The big question,
then, is what deter
considerably
mines
the real wage.
a traditional
is to suppose
that real wages
route, which
amarginal
make workers
indifferent between
increase in leisure and the
can be afforded
in
increase
that
marginal
consumption
by giving up this
leisure for work. While
this assumption
has not proved deleterious
in
BGM
follow
it proves quite problematic
here. To see
models,
Keynesian
individual
such that instantaneous
this, consider
preferences
utility is
other New
given
by
+
JJL l/<p
?1-7
-+
x
l + l/<p
1-7
With
{Q->wt
these preferences,
=
clearing
labor market
requires
that
x(Q1">.
Differentiation
=
u>,
a
near a
steady
state then yields
+
(A 7)c(.
that 7 = 1 so that the wage rises by at least 1 percent every
time output
rises by 1 percent. Lower values of the
(or consumption)
Frisch elasticity 9 accentuate
this effect. Equation
(3), on the other hand,
even
that
fall
when
if
rises,
implies
output
wages
profits
only rise by the
same percentage
as output. With wages
and
rising
profits falling, the in
more
so
is
to
be
that the incentive
to enter
violated,
(2)
equality
likely
BGM assume
falls. The conclusion
from this is that the incentive
to enter can rise only
374 Rotemberg
are only
are suitably modest.
In practice, real wages
so the case where entry becomes more attractive can
slightly procyclical,
valid one.
easily be the most empirically
if increases
inwages
the results in this paper
the contrast between
assumes
that
She
nominal
(as opposed
(2006).
wages
for goods) are rigid and finds that output rises after amon
This discussion
explains
and those of Lewis
to the prices
is to suppose that entry costs involve the
etary expansion. An alternative
of
whose
prices are sticky. This is the route pursued by
purchase
goods
and
Corsetti
(2006). As
(2005) and Elkhoury and Mancini Griffoli
Bergin
as entry costs fall relative to the future value of profits, entry rises,
long
The point of my discussion,
and BGM cover this case in an extension.
in real wages might well make entry
is that realistic changes
however,
even if all entry costs take the form of hiring additional
labor.
procyclical
rise quickly with consump
that real wages
The model's
implication,
for the finding that markups
is also responsible
tion and employment,
can be excessively
to technology
in response
countercyclical
see this, remember
that in the BGM model with a variable
firms, the total amount
=
L( Ntf
of labor hired,
Lt, is given
shocks.
To
number
of
by
+ *L,
each of
Nt is the number of firms, Lf is the number of workers
number
of
is
the
firms hires to produce
t
consumption
goods, NE
In this equa
new firms (or products),
and Zt is an index of technology.
to
needed
reduce the number of employees
tion, increases in technology
to the amount of
start a firm so as to keep the startup costs in proportion
a given level of output.
to produce
labor needed
where
these
lower la
With sticky prices and without
entry, increases in Zt usually
firms
of prices prevents
The reason is that the stickiness
bor demand.
to
so
from selling a great deal more,
produce
they need fewer workers
the quantity demanded.3
that new firms
there is a countervailing
effect, namely
Here, however,
be
hired. In the
workers
that
to
additional
this requires
wish
enter?and
of this paper, total labor demand
actually rises and, for the
With a =
this
discussed
earlier,
pushes wages up considerably.
falls a great deal. This effect
1, this is the same as saying that the markup
can be reduced by making
real wages
respond less to output. However,
costs
itwould probably also help the model perform better if adjustment
of
were
be a dampened
added so that there would
response
entry to
with
small
consistent
from
Aside
shocks.
relatively
being
technology
calibration
reasons
375
Comment
a
change would
changes in entry, such modeling
bor demand when
improves.
technology
in la
also avoid bursts
Endnotes
from a quarterly
extracted
(1990) data were
plot in his paper.
data underlying
sent me the quarterly
his analysis.
aggregate
1. The Devinney
Axarloglou
kindly
growth
(1990) and Axarloglou
introductions
product
where
the number
regressions
rates of GDP as well.
3. Gali
(1999)
con
that they find empirical
(2003) emphasize
and aggregate
but they consider more
output,
on
to depend
is allowed
of introductions
lagged
2. Both Devinney
between
nections
complex
showed
this effect
Kostas
to exist
and gave
empirically,
this explanation.
References
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29^8.
K. 2003. The
of new
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