Download This PDF is a selection from a published volume from the... Economic Research Volume Title: NBER Macroeconomics Annual 2007, Volume 22

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: Monetary Policy and Business Cycles with Endogenous Entry and
Product Variety
Chapter Author: Florin O. Bilbiie, Fabio Ghironi, Marc J. Melitz
Chapter URL: http://www.nber.org/chapters/c4090
Chapter pages in book: (p. 299 - 353)
5_
Monetary
Policy and Business Cycles with
Entry and Product Variety
Endogenous
Florin O. Bilbiie,
Fabio Ghironi,
Marc
1
HEC Paris Business
School
Boston College, EABCN, and NBER
Princeton University, CEPR, and NBER
J.Melitz,
Introduction
1980s, a large body of literature
inmicrofounded,
monetary
policy is analyzed
eral equilibrium
of the business
(DSGE) models
Since
the mid
competition
sian literature
and nominal
The
in which
has developed
stochastic
gen
dynamic
cycle with monopolistic
of this New Keyne
importance
rigidity.
for instance, by Woodford
(summarized,
use of such models
is evidenced
current
the
by
making
banks or international
2003) for policy
by many central
as input for
institutions
policy decisions.1 Most of
this literature, however,
as a
relies on monopolistic
competition merely
to introduce price- (or wage-)
vehicle
assume
and
then
setting power
that price (orwage)
setting
ity and a role for monetary
els abstract
is not frictionless,
resulting in nominal
rigid
of
mod
policy. The overwhelming
majority
from producer-entry
a constant
and assumes
mechanisms
number
of producers.
The joint assumptions
of monopolistic
competi
tion and no entry raise both theoretical
and empirical questions.
First,
or increas
absent either properly designed
subsidies
markup-offsetting
in these
ing returns of appropriate
degree, monopolistic
competition
models
results in permanent
(i.e., steady-state)
positive profits, casting
doubts on the theoretical appeal of the zero-entry
Further
assumption.2
recent
for the United States has substantiated
more,
empirical evidence
the endogenous
in the number of producers
fluctuations
and the range
of available
goods that take place over the typical length of a business
A
literature documented
the strong procyclical
behavior
previous
cycle.
of net producer
as
firms or as pro
entry (measured either
incorporated
duction
and Schott
Bernard, Redding,
establishments).3
(2006) docu
ment how existing U.S.
a sub
establishments
devote
manufacturing
stantial portion of their production
to goods that they did not
previously
300 Bilbiie, Ghironi, and Melitz
the value of new goods pro
produce. For U.S. aggregate manufacturing,
duced represents
under
10
out
annual
of
just
percent
manufacturing
(2003) and Broda and Weinstein
(2007) directly mea
put.4 Axarloglou
sure
the
document
introduction
of new
varieties
a strong correlation with
consumer purchases,
U.S.
of
sample
ment that a 1 percent
in the U.S.
and
economy
a wide
Across
cycle.
and Weinstein
(2007) docu
the business
Broda
in aggregate
sales is associated with a 0.35
in that quar
increase
in
the
sales
of
introduced
percent
newly
products
ter.5 These theoretical and empirical observations
that there is
suggest
increase
in models
creation
entry and product
and imperfect price adjustment,
and
for
of endogenous
business
product variety
scope for introducing
producer
with monopolistic
competition
the consequences
and policy in these models.
cycle propagation
the
This paper takes an initial step in this direction by reintroducing
and
link
creation
between
(firm entry)
monopolis
product
endogenous
in a DSGE model with
tic competition
imperfect price adjustment. We
studying
and normative
the positive
of endogenous
consequences
pro
explore
ducer entry and product variety over the business
cycle by introducing
nominal
by Bilbiie, Ghi
rigidity into the flexible price model developed
nominal
and
We
Melitz
roni,
BGM).
(2005?henceforth,
incorporate
a
in
recent
in
lit
the
New Keynesian
standard form often used
rigidity
as in Rotemberg
cost of price adjustment,
erature?a
(1982).6
quadratic
creation
of
The endogenous
response
subject
producer
entry?product
a
to sunk entry costs?over
the business
key new trans
cycle provides
in
in our model.
This producer
mechanism
entry,
general equi
via the purchase
of
librium, is tied to the household
saving decisions
In
in the portfolio of firms that operate in the economy.7
share holdings
mission
simi
under flexible prices, performs
BGM, we show that such amodel,
the
model
to
business
real
the
standard
concerning
cycle (RBC)
larly
are
that
of key U.S. macroeconomic
aggregates
traditionally
cyclicality
ex
can additionally
this model
the subject of RBC studies. However,
over
the
business
other
cycle,
important empirical patterns
plain many
noncon
of firm entry and profits, and?with
such as the procyclicality
stant elasticity of substitution
(CES) preferences?the
countercyclicality
are induced
these
of markups.
markups
countercyclical
Significantly,
of profits (due to the response of
the procyclicality
while
still preserving
for the benchmark New Key
well-known
challenge
entry)?a
producer
nesian model
The
model
with
introduction
of the business
sticky prices.8
of endogenous
cycle allows
variety
product
us to address issues
in a sticky-price
that are absent in
Policy with Endogenous
Monetary
Entry & Product Variety
301
as well as to qualify some of the results of
existing fixed-variety models,
in the presence
of this new margin. To start with,
those models
the con
sumer price index coincides with the price of each individual product
in
In a
the symmetric
of one-sector,
models.
equilibrium
fixed-variety
a
with endogenous
distinction
the
between
variety,
meaningful
consumer price index and the average product price arises because
the
model
consumer
price index varies with the number of vari
to satisfy a given level of demand with more varieties)
for given product price level. Otherwise
put, the price of each good rel
to
the consumption
basket
increases with
ative
the number
of vari
welfare-relevant
eties
(it is cheaper
benefit from consuming
the bundle
is thus higher
marginal
to the marginal
benefit of any unit of an individual
good, mak
more
desirable.
of
the
basket
We
that
show
when
ing consumption
price
concerns
for individual
price setting
rigidity
goods,
optimal
policy
eties?the
relative
should
stabilize product prices (the average
to as producer price in the following)
consumer price index.9
consistent
ferred
Our
a new motive
for price stability as a
suggests
as
in
Since,
(1982), price ad
policy prescription.
Rotemberg
costs are deducted
from firm profits, and these costs are pro
to (squared) producer
the latter acts as a
inflation,
price
framework
desirable
justment
portional
price of output, often re
rather than the welfare
also
tax on firm profits in our model. This tax distorts the allo
distortionary
to product
cation of resources
creation
of existing
(versus production
a
and
amount
induces
of
in each
varieties)
suboptimal
product variety
an
is
This
intuitive
for
period.
explanation
why the central bank should
and an extra argument
for
pursue producer price stability in our model,
stability absent from fixed-variety models.
that qualify results from fixed-variety
mod
Turning to implications
area
in
but
now
con
the
of
it
is
els,
remaining
policy prescriptions,
by
ventional
wisdom
from the benchmark
model without
fixed-variety
that
the
central
bank
should
follow
has become
what
physical
capital
known as the Taylor Principle. This policy prescription
requires that the
central bank be active, in the sense of increasing the nominal
interest rate
more
than one-to-one
in response
to increases
in inflation.10 Perhaps
the
introduction
of
however,
surprisingly,
physical
capital in the fixed
model
this
as shown by
variety
changes
prescription
dramatically,
a
in
continuous-time
model
and
further developed
(2001)
Dupor
by
price
Carlstrom
and Fuerst
time and in the presence
of
(2005) in discrete
shows that passive
interest rate setting (a less
to inflation)
is necessary
and sufficient
for
response
costs. Dupor
adjustment
than proportional
302
Bilbiie, Ghironi, and Melitz
local determinacy
and stability, while Carlstrom
and Fuerst conclude
that it is essentially
to
achieve
with
forward
impossible
determinacy
rate
interest
In
contrast
to
these
the
results,
looking
setting.
Taylor Prin
our
in
in
holds
which
accumulation
takes
the form
economy
ciple
capital
of creating
new
of whether
the monetary
lines, regardless
production
or
to
current
inflation.11
authority
responds
expected
product price
The Taylor Principle
is restored with our form of capital accumulation
features an endogenous
precisely because our framework
price of capi
a
tal that plays
crucial role inmonetary
Indeed, we
policy transmission.
show that free entry implies that the price of equity shares (the value of
the firm) appears in the New Keynesian
the
Phillips curve that governs
a
of
inflation.
condition
links
the
real
Moreover,
dynamics
no-arbitrage
return on bonds
(which the central bank affects by setting the nominal
ratio of next period's div
rate) to the real return on equity?the
and share price to the current price of equity. This identifies a
novel channel of monetary
transmission
that links interest rate
policy
to
and
the Phillips
free
curve,
and,
entry
equity prices
setting
through
a temporary
interest rate cut reduces the real re
inflation. In a nutshell,
turn on bonds,
return on equity to fall and the
the expected
inducing
interest
idends
in the expected
return
to consume more today. The decrease
in product creation is brought about by an increase in to
from investing
The
day's price of equity (the value of the firm) relative to tomorrow's.
to
cost
is
of
value
of
the
related
firm)
(the ra
price
equity (the
marginal
in
to labor productivity)
tio of the real wage
the
condition
by
free-entry
household
cost rises, inducing a fall in the markup
and, by the
Marginal
an increase in inflation. This transmission
of
curve,
monetary
Phillips
fixed-variety
through the price of equity is absent in standard,
policy
even when
do feature an endogenous
those models
models,
price of cap
costs (see Carlstrom
and Fuerst 2005).
ital due to adjustment
our model.
cre
of explicitly modeling
endogenous
product
implications
in
to
As
the
standard
and
inflation
markup
dynamics.
pertain
a New Keynesian
Phillips curve relating producer
fixed-variety model,
Further
ation
our
price inflation to its expected value and the current markup holds in
conse
creation
has
model.
However,
important
product
endogenous
that estimate Phillips curves. First, in the
quences for empirical exercises
presence of endogenous
variety, the markup
the labor share of income, as in Sbordone
is not simply the inverse of
(2002) or Gali and Gertler
as the inverse of a la
can be expressed
the markup
(1999). In our model,
labor used to set up
for
bor share in consumption
output, controlling
new production
from an aggregate
lines (labor that is overhead
per
Monetary
Policy with Endogenous
A
spective).
close
proxy
and Woodford
Rotemberg
should be used
to estimate
Entry & Product Variety
for this
labor
share has
303
been
estimated
by
that
(1999), and it is the relevant variable
the Phillips curve in the presence of endoge
an alternative proxy for the
on
markup based
nous variety.12 We propose
is 'model-free,'
which
the inverse of the share of profits in consumption,
in the sense that it could be used regardless
of one's stand on product
we identify an endogeneity
creation. Furthermore,
bias in the identifi
cation of what
the literature
labels cost-push shocks (see, e.g.,
commonly
in
the
of endogenous
1999):
presence
variety,
on the number of
features an extra term that depends
and Gertler
Clarida, Gali,
the Phillips curve
varieties.
available
a researcher
when
one
using
estimating
of the main
This term would
a
markup
the Phillips
drawbacks
to cost-push
shocks by
account
for variety
it has been pointed out that
be attributed
that does
proxy
curve.
not
Finally,
of the forward-looking
New Keynesian
to
inflation
generate endogenous
Phillips
persistence
1995). We show that our version of the Phillips
(e.g., Fuhrer and Moore
curve can potentially
alleviate
this problem, because
the number of va
curve
rieties
is its failure
in the Phillips curve
in inflation.
featured
extra persistence
Numerical
examples
duces
is a state variable,
and hence
it in
to aggregate productiv
that the responses
shocks under simple, but plausible
of
specifications
show
ity and deregulation
interest rate setting are close to the flexible-price
responses.
Exogenous
to expand but reduce entry, be
interest rate cuts induce the economy
cause the associated
increase in real wages
increases the cost of firm cre
ation and the expected return from investing
in new products
falls. With
productivity
shocks
as the source
rule
plausible,
for interest
of fluctuations
rate setting
and an empirically
interest rate
involving
simple
to expected
and a response
the
price inflation,
producer
are
of endogenous
variables
cyclical properties
very close to those of the
in
to
those
of the benchmark
RBC
turn,
and,
counterpart
flexible-price
as documented
In
contrast
to
BGM.
the
model
model,
by
flexible-price
with translog preferences
studied in BGM, sticky prices with CES pref
erences yield too much
and a counterfactual
markup
countercyclicality
time profile of this cyclicality. This happens
because
the markup
is no
smoothing
(as in BGM) with translog pref
longer tied to the number of producers
erences. On the
(con
bright side, aggregate
profits remain procyclical
sistent with stylized facts) even in the presence of a very
countercyclical
and the model
remains able to explain
the procyclicality
of
markup,
business
creation.
Producer
entry and product
creation
pose
an
interesting
question
for
304
the modeling
price-setting
preexisting
preserving
Bilbiie, Ghironi,
and Melitz
a new entrant makes
its first
rigidity. When
it operates as all
decision, we must take a stand on whether
do, subject to the same nominal
producers
rigidity?thus
across
the symmetry
that is a feature of the
producers
of nominal
it sets its price in flexible fashion,
whether
(1982) model?or
that itwill face a cost of adjusting
its price in all subsequent
our
We
that new entrants
inherit
periods.
begin
analysis by assuming
firms. This considerably
the same price rigidity as preexisting
simplifies
Rotemberg
but aware
the model
and allows
ical results. We
us to obtain
an initial set of
analytical and numer
in which new entrants set prices
then turn to the model
that they will be subject to a cost of price
fashion, but knowing
from the following period on.13 In this case, nominal
adjustment
rigidity
in price levels across cohorts of producers
that
results in heterogeneity
in flexible
at different points in time, and the aggregate
de
the economy
are
with
of
nominal
is
associated
gree
expansions
rigidity
endogenous:
the number of new entrants whose de
lower aggregate
rigidity because
entered
cision
is not influenced
version
by past price setting increases. We show that the
can still be solved in tractable
of this extended model
log-linear
in aggregate
of endogeneity
fashion, and we explore the consequences
means
Plausible
values
of numerical
parameter
examples.
rigidity by
are
to
that
from
shocks
virtually
indistinguishable
imply responses
that average product
Since we assume
those of the benchmark model.
in
small changes
is realistically
small at quarterly
frequency,
more
in
set
flexible
fashion
the fraction of firms that
triggered by
prices
and the benchmark
shocks have negligible
consequences,
aggregate
cost as
in which new entrants inherit the same price adjustment
model
turnover
yields robust conclusions.
in BGM, we explore the consequences
of non-CES preferences
by
a gen
with
familiar
the
(1977)
aggregator
variety
Dixit-Stiglitz
replacing
of symmetric preferences?parametrized
eral homothetic
specification
incumbents
As
This implies that the elas
in translog form for model
solution purposes.
across products
of
increases with
the number
ticity of substitution
an additional
effect of the number of available
introducing
producers,
curve. In our numeri
on inflation in the New Keynesian
Phillips
goods
that are similar to those
this extension yields conclusions
cal examples,
it further improves
model,
although
on the inflation persistence
front.
of the benchmark
of the model
the performance
(2006) develop mod
(2006) and Elkhoury and Mancini Griffoli
are closest to the one studied here. Lewis
that
nominal
rigidity
in fa
introduces monopoly
power in the labor market and sticky wages
Lewis
els with
Policy with Endogenous
Monetary
Entry & Product Variety
305
fashion into the BGM model.
respectively)
that monetary
result in
policy expansions
and she shows that
increased firm entry by boosting
aggregate demand,
this
evidence.
the sticky-wage model
reproduces
Elkhoury and Mancini
take the form of fees
Griffoli assume that entry costs in the BGM model
miliar
Calvo-Yun
She documents
(1983,1996,
VAR evidence
to lawyers with monopoly
nominal
the
power. Under
rigidity,
fashion and, as in Lewis, amon
lawyers set the entry fees in Calvo-Yun
that
boosts
the
results in increased firm entry.
economy
etary expansion
paid
boost firm entry in these models
because
Monetary
policy expansions
cost
to
creation
fall.14
induce
the
real
of
and
Corsetti
Bergin
product
they
on the consequences
VAR evidence
of exogenous
(2005) document
in monetary
for entry similar to that in Lewis' paper.
policy
changes
a
set
with
model
up
entry and one-period
price rigidity that repli
They
cates this evidence,
and they characterize
optimal monetary
policy and
the properties
of shock
transmission.
induce
monetary
counted
increased
In Bergin and Corsetti's model,
firm entry by increasing
dis
expansions
in
future profits. We show that a version of our model
which
of materials
rather than hiring
labor
entry requires purchases
in
to
increased
shocks
response
generates
entry
monetary
policy
by re
expected
the tight connection
moving
value of the firm embedded
Waller
(2007) contribute
cost and the
marginal
production
in the benchmark
Berentsen
and
setup.
on
to this literature
monetary
policy with firm
between
entry by introducing
entry subject to an entry fee in
endogenous-seller
in
and
which
informational
frictions moti
(2005) model,
Lagos
Wright's
as a medium
vate the existence of money
of exchange.
in
Price posting
a price
of entry constitutes
to Bergin and
similar
rigidity
Corsetti's model.
show
that
the
Friedman
in
rule
nominal
(zero
They
terest rate) is optimal
in their model with
fixed entry costs. But depar
tures from the Friedman
rule are optimal when
effects cause
congestion
costs
to
increase
with
the
number
of
firms.
entry
as follows. Section 2 presents
The rest of the paper is organized
our
advance
benchmark
model.
Section
policy
in the benchmark
model.
Section
3 obtains
the results
Section
4 discusses
on optimal
monetary
the implications
of
setup.
endogenous
entry and product variety for the New Keynesian
Phillips
curve. Section 5 studies
rate
interest
monetary
policy through
setting in
our model.
the business
Section 6 illustrates
of the
cycle properties
7 discusses
the main
results of the extensions
the assumption
that entry requires materials
on initial price
native assumptions
setting
CES preferences.
Section
8 concludes.
we
explore:
rather than labor, the alter
by new entrants, and non
306
Bilbiie, Ghironi,
and Melitz
2 The Model
2.1
Household
Preferences
Intratemporal
We
consider
populated
resentative
Consumption
and the
Choice
a cashless
is
economy, as inWoodford
(2003). The economy
a unit mass of atomistic,
identical
households.
The
rep
by
household
in each period Hna
supplies Lt hours of work
labor market
competitive
for the nominal
expected
intertemporal
utility
tion and p e (0,1) the subjective
tion takes the form U(Ct, Lt) =
> 0 is the Frisch
9
elasticity of
poral elasticity of substitution
wage
rate Wt and maximizes
Et[Z =tPS_'U(CS, Ls)], where Ct is consump
discount
factor. The period utility func
+ l/<p), X > 0, where
In Ct - x(L,)1+1/V(1
labor supply to wages,
and the intertem
in labor supply.
consumes
the basket of goods Ct, defined
t, the household
over a continuum
of goods ft: Ct = [ JweftcXw)e-1/etMe/(e_1)/ where
6 > 1 is
across
the symmetric
At
of
substitution
any given time
goods.
elasticity
At
time
t, only a subset of goods ft, c ft is available. Let pf(co) denote the nomi
nal price of a good co e ftr The consumption-based
price index for the
is then Pt =
home economy
and the household's
de
[Jwea^co)1_edco]1/(1~e)
mand
for each individual good co is c,(co) = [/?f(co)/PJ~eCr
2.2
Firms
There
is a continuum
of monopolistically
firms, each pro
competitive
coe ft. Production
variety
requires only one factor, la
is indexed by Zt, which
labor productivity
the
represents
a different
ducing
bor. Aggregate
and follows
is exogenous
effectiveness
of one unit of labor. Productivity
an AR(1) process in percent deviation
from its steady-state
level. Output
=
co is
Z,Z,(co), where
Z,(co) is the firm's labor de
y,(co)
supplied by firm
in units of
mand
The unit cost of production,
for productive
purposes.
=
is
is
where
the
real
the consumption
wt
wage.
wt/Zt,
Wt /Pt
good Ct,
Prior to entry, firms face a sunk entry cost of fE teffective
labor units,
are no fixed pro
equal to wJE t/Zt units of the consumption
good. There
in every
costs. Hence,
all firms that enter the economy produce
a "death" shock, which occurs with prob
are
hit
with
they
period,
g (0,1) in every
ex
period. We assume that the entry cost/Et is
ability 8
as
and treat changes in/?t
ogenous
changes inmarket
regulation.
duction
until
Firms
ing prices
a
cost of adjust
quadratic
rigidity in the form of
cost (in units
time (Rotemberg
the
real
1982). Specifically,
face nominal
over
Policy with Endogenous
Monetary
Entry & Product Variety
307
inflation volatility
of the composite
basket) of output-price
co is:
to
0
of
inflation
level
equal
facing firm
steady-state
around
a
k [ p,(a>) j2pt(co) ^n
jTyf(tt)'
w(tt)afe
is interpreted as the amount of marketing
that
materials
This expression
assume
a
We
the firm must purchase when
price change.
implementing
as the consumption
that this basket has the same composition
basket.
to the real revenue from out
The cost of adjusting prices is proportional
put sales, [pt(u)/Pt]y?(<&), where yf(co) is firm co's output demand.
Firms face demand
for their output from consumers
and from firms
themselves when
there is a mass Nt
they change prices. In each period,
a new firm
and setting prices in the economy. When
of firms producing
sets the price of its output
for the first time, we appeal to symmetry
across firms and interpret the t-l price in the expression
of the price ad
justment cost for that firm as the notional price that the firm would have
set at time t - 1 if it had been producing
in that period. An intuition for
this simplifying
is
that
all
firms
(even those that are setting
assumption
for the first time) must
a price decision.15
implementing
the price
buy the bundle of goods pact(u>)when
It should be noted, however,
that this
consistent
both with
the original Rotemberg
is entirely
and
with our timing assumption
that follows. Specifically,
(1982) setup
new entrants behave
as the (constant number
do in
of) price-setters
an initial condition
for the individual
framework, where
Rotemberg's
our
new
is
In
nature.
dictated
at any time
entrants
framework,
price
by
assumption
twho
and setting prices at t + 1 are subject to precisely
as price setters in
assumption
setup.
Rotemberg's
original
the assumption
that a new entrant, at the time of its first price
start producing
the same
Moreover,
knows the average product price last period is consis
setting decision,
tent with
the timing assumption
that an entrant starts producing
only
one period after entry, hence
being able to learn the average product
price during the entry period.16
The total demand
[pt(io)~\-e
yf(co)-
Zy-*-t
for the output
of firm co is thus
(Ct+ PACt),
=
across firms in the def
PACt
Ntpact(o>), and we used symmetry
inition of the aggregate demand of the consumption
basket for price ad
justment purposes
PACt.
Let p,(co) = pt(ixX)/Pt denote the real price of firm co'soutput. Then, firm
where
308
to households
K I P,(C0)
- - -
=
df(<o)
t (distributed
in period
co's real profit
as
written
p,(w)y?(co)z^(co)
The real value
Bilbiie, Ghironi,
as dividend)
pf(co)y?(co).
J
of the firm at time t (in units of consumption)
value of future profits from t +
discounted
stochastic
can be
2
1
z\_Pt-i\<?)
pected present
counted with the household's
and Melitz
discount
factor
is the ex
1 on, dis
the
follow
(see
ing):
vt{t?)
=
A,,sds(co), (1)
E, ?
s=t+l
=
factor ap
[(3(1 8)]S_'17C(CS, Ls)/Uc(Ct,
Lt) is the discount
A,s
co (which faces a
to
firm
future
from
households
proba
profits
plied by
bility 8 of being hit with the "death" shock in each period).
+ i?f(co)sub
At time t, firm co chooses
Z,(co)and p,(co) tomaximize
d,(co)
=
as given. Letting X^00)
ject to y,(co)
yf^co), taking wt, Pt,Ct, PACt, and Zt
on the constraint yt(u>) = yf(co), the first
denote the Lagrange multiplier
where
with
condition
order
, ,
respect
to Zf(co)yields:
wt
A
The
shadow
value
of an extra unit
common across
ginal cost,
The first-order condition
P,M
=
vMPM
is simply
of output
all firms in the economy.
with respect to pf(co) yields:
).
co sets the price as a markup
[|x,(co)] over nominal
the markup
where
|jLf(to)is given by
Firm
M-,(w) =-f-F?TT-TT-'
P,-i(a>) IP,^(<?)
cfA
the firm's mar
^
_\
P< [Pw(m)1{Pi?
,11
marginal
cost,
Monetary
Policy with Endogenous
Entry & Product Variety
As expected,
the markup
reduces to 6/(6 -1)
=
or
if
the
(k
0)
price pf(co) is constant.
rigidity
309
in the absence
of nominal
Firm Entry and Exit
mass of prospective
In every period,
entrants.
there is an unbounded
These entrants are forward looking, and correctly anticipate
their future
8 (in
expected profits d,(co) in every period as well as the probability
shock. We assume that en
every period) of incurring the exit-inducing
a
t only start producing
at time t + 1, which
introduces
oc
in
the
time-to-build
model.
The
exit
shock
exogenous
one-period
lag
curs at the very end of the time
and entry). A
(after production
period
8 of new entrants will therefore never produce.
proportion
Prospective
t compute
entrants
in period
their expected post-entry
value given by
trants at time
the present discounted
stream of profits vt(<u>).
value of their expected
This also represents
the average value of incumbent
firms after produc
tion has occurred
then face the
(since both new entrants and incumbents
same probability
1 8 of survival and production
in the subsequent
pe
riod). Entry occurs until firm value is equalized with the entry cost, lead
=
This condition holds so
ing to the free entry condition
vt(u>) wJ^/Z,.
long as the mass NEt of entrants is positive. We assume that macroeco
nomic shocks are small enough
to hold in every pe
for this condition
riod.17 Finally, the timing of entry and production
firms during
plies that the number of producing
=
+
(1-8)(NW
NE/M).
Symmetric
we have
period
assumed
t is given
im
by Nt
Firm Equilibrium
In equilibrium,
all firms make
identical choices. Hence, X,(co) = \, p,(co)
=
=
=
=
=
=
Vt> M'fM
IV fc(co)
ft, /,(<*>) lt, yt(u)
yt, pact(u)
pact, d,(a>)
dt,
=
and vt((o)
basket (used for
vt. The aggregate output of the consumption
and to pay price adjustment
costs) is
consumption
Yf
=
=
C( + PAC(
N(p,y,
=
N(P(Z(Zr
The expression
of the price index Pt implies that the relative price p, and
the number of producing
firms Nt are tied by the variety effect equation
=
=
p,
pt/Pt
(N,)1'".
Let i:t denote inflation in producer prices: irt =
ptlpt_x -1. Then, we can
write:
310 Bilbiie, Ghironi,
e
^ ~
(6
r 1) 1
-
k
(e -1)
fi -
-(irty
i-
+
yK)2
This can be simplified
=
[1 K(irf)2/2]Yf,
Ct
+ ir>t
P(l
-
kJ(1
further by noting
to obtain:
*
1 -m
+ K (i + irfK - p(i
r rc
8)E,
Household
Budget
Constraint,
*
Nt yfc+1 +ii
ir'+lK+1
cj;l^"^1
=
so that
that PACt
K(irf)2Yf/2,
Nt IT.
(2)
f [i1 (k/2)(it,)2
(i +vXi
(JnZ L
of this equation delivers our model's
Log-linearization
the effect of endogenous
curve, incorporating
Phillips
in detail in section 4.
which we discuss
2.3
and Melitz
Saving,
and Labor
New
Keynesian
product
variety,
Supply
hold two types of assets: shares in a mutual
fund of firms
Let xt be the share in the mutual
fund of firms held by the
t. The mutual
fund pays a to
household
representative
entering period
tal profit in each period
that is equal to the total
(in units of currency)
Households
and bonds.
in that period, PtNtdt. During period t, the
profit of all firms that produce
fund of NHt = Nt
household
representative
buys xt+1 shares in amutual
+
at time t and the new entrants).
NEtt firms (those already operating
=
at time t +
and pay dividends
(1 S)NHt firms will produce
Only Nt+1
1. Since the household
firms will be hit by the ex
does not know which
8 at the very end of period
t, it finances the continu
new
entrants during period
and
all
all
of
firms
preexisting
ing operation
t.The date tprice of a claim to the future profit stream of the mutual
fund
ogenous
exit shock
t firms is equal to the average nominal
price of claims to future
=
of
home
firms,
Vt
Ptvr
profits
twith nominal bond holdings
enters period
The household
BNt and
on
It
interest
income
bond
fund share holdings
receives gross
mutual
xt.
of NH
and the
fund share holdings
dividend
income on mutual
holdings,
and labor income. The house
value of selling its initial share position,
of bonds and shares to
hold allocates these resources between purchases
con
The period budget
be carried into next period and consumption.
is:
straint (in units of currency)
*Wi
+
VtNH,xt+1
+ PtCt =
(1 +
+
+
it_x)BNJt (Df Vt)Ntxt
+ (1 + T})WtLt+ T\,
Policy with Endogenous
Monetary
Entry & Product Variety
311
the nominal
interest rate on holdings
of bonds be
it_xdenotes
=
t-l and t,Dt denotes nominal dividends
(Dt
Ptdt), i\ is a labor
we
in
whose
role
discuss
the
and
T\ is a lump-sum
subsidy
following,
tax satisfying
the constraint TLt? -t[Wt Lt in equilibrium.
both
Dividing
sides by Pt and denoting holdings
of bonds in units of consumption
with
where
tween
-
BN,t + l/Pt'
Bt+1
We
Can Wrlte
=
(1 + rt)Bt +
Zt+1 + vtNHAxt+1 + C,
(dt
+
vt)Ntxt
+ (1 +
^)wtLt
+
t\,
(3)
1 + rt is the gross, consumption-based,
real interest rate on hold
+ rt= (1 4+ irf),
t
-1
of
bonds
1
between
and
defined
t,
ings
it_^)/(l
by
=
=
with irf
and
The
home
household
its
maximizes
Pt/Pt_x -1,
t\
T\/Pt.
to
this budget constraint.
expected
intertemporal
utility subject
where
The Euler equations
(Q-1
=
3E(
for bond
and share holdings
are:
-^HCf+1)-i
=
and*, 3(1 8)E,
("^J
.
V,+1 + dM)
As
forward iteration of the equation
for share holdings
and
expected,
absence of speculative
bubbles yield the asset price solution
in equa
tion (l).18
The first-order condition
for the optimal choice of labor effort requires
that the marginal
of labor be equal to the marginal
disutility
utility from
the real wage
received for an additional
unit of labor:
consuming
X(L,)V*
2.4
=
(1 + T;-A
Aggregate
Accounting
and Equilibrium
the budget constraint
and imposing
(3) across households
Aggregating
=
=
=
the equilibrium
conditions
0 and xt+1
1, Vf, yields the
Bt+1
xt
Bt
=
=
+
+
aggregate
accounting
Ct
identity Yt
NEtvt
wtLt
Ntdt, where we
defined GDP, Yt: Consumption
new
investment
(in
firms) must be
plus
to
income
income
(labor
equal
income).
plus dividend
=
Labor market
+
equilibrium
requires Ntlt
NEtfEt/Zt
Lt: The total
amount of labor used in
to
and
set
new
the
entrants'
production
up
must
labor
this
is
condition
plants
equal aggregate
supply. (Of course,
312 Bilbiie, Ghironi,
once
redundant
and Melitz
in goods and asset markets
is imposed.)
equilibrium
are summarized
in
conditions
of our benchmark model
The equilibrium
table 5.1.
a rule for nominal
interest rate set
by specifying
the setting of the labor subsidy iLt, and
ting by the monetary
authority,
for
the
processes
exogenous
entry cost/E, and productivity
Zt.
The model
3
is closed
Price Stability
with
Endogenous
Entry and Product
Variety
inflation in consumer and pro
and
because monetary
Pt
pt?indeterminate
no
real effect in the flexible-price,
cashless economy,
and we
policy has
in order
need not concern ourselves with the paths of nominal variables
The flexible-price
analysis
ducer prices?respectively,
of BGM leaves
prices are sticky, this is no longer the case.
in
the number of producers Nt and the asso
given
Specifically,
change
in
the relative price pt implied by the variety effect
ciated movement
=
=
pt
pJPt
(N,)176-1, the allocation of this relative price move
equation
ment to changes in producer or consumer prices is important for the dy
to solve
for real ones. When
a
In turn, producer price inflation is
a determinant
thus Nt?via
its impact on firm prof
of firm entry?and
and the
its. This section studies optimal monetary
policy in our model
versus
consumer
to
effects
allocation
of
prices.
producer
variety
optimal
on results in Bilbiie,
Our analysis of optimal monetary
policy builds
version
Ghironi, and Melitz
(2006). We show there that the flexible-price
namics
of real variables
and welfare.
is efficient?the
of the economy described previously
equi
competitive
labor
librium coincides with the social planner's
supply is
optimum?if
inelastic (cp= 0) and Lt = 1 Vr. The reason is that, with CES Dixit-Stiglitz
the profit destruction
by producer
externality
generated
preferences,
demand
for each individual
firm) is exactly
(which reduces
entry
determined
for
love
the
consumer's
matched
by the
variety?both
by
if 9
is
inefficient
6.
The
substitution
of
economy
flexible-price
elasticity
> 0 because
there is amisalignment
of markups
across
the items the con
a
over marginal
sumer cares about (consumption,
priced at markup
is restored if the
but efficiency
cost, and leisure, priced competitively),
of pricing over marginal
labor subsidy iLt is equal to the net markup
cost,
across
in
1 / (6 -1)
all periods. This subsidy aligns markups
consumption
of firm en
the
while
and
leisure
expected profitability
preserving
goods
the efficient equilibrium. We assume that t[ = 1/(0
try, thus inducing
1) yt below.
Sticky prices
imply
a time-varying
markup
whenever
producer
prices
Markup
^f
k1
f\~Ct
N.
Yf+1IT
_e_
JFq^^^1
KJ(1
-8)Ej
(0-1)
--(nf
+17it)7it-P(l
+
wt+iK+i
Ik
1
Yc
if.
]Nt
L
?2V
'^
[K
r1
_1
nf
+P*-i_
Euler
Pricing
V>t-y
Pt
=
equation
Number- (shares)
(1
firms
of=
Nt
d=
Profits
1-(O2
?
8)=8)(NM
+ NE/M)
|3(1
z>,
Et
I
-^-
J V,+1
+ d,+1)
Output
of
Yf= 1-(7it)2 Ct
sector
(bonds)
(Q^)"1
(Q)"1
Euler
$Et
equation
-~= consumption
Aggregate
+
accounting
tvt
Ct
wtEt
NE
=
N,df
+
(1
Intratemporal
xW1/(p
optimality
+T9?
=
Benchmark
Summary
Model,
(N,)1^
Variety
effect
p,
=
Free
entry
=
vt
wt
?
5.1
Table
w. ._
inflation
CPI
1?A
A_
=
314 Bilbiie, Ghironi,
are changing
over
and Melitz
in Bilbiie, Ghironi, and Melitz
(2006),
across
(aswell as across states and
periods
markup nonsynchronization
to
of the utility function) generates
arguments
inefficiency
compared
in
variation
the planner's
Since
this
model
time
of
optimum.
particular
time. As
shown
in the competitive
is due to producer
price in
equilibrium
we
a
zero
in
rate
to
be
the op
of
inflation
flation,
expect
producer prices
a planner. The
timal monetary
policy chosen by
following
proposition
the markup
that this is indeed the case. To isolate our main result, we prove
for the case of inelastic labor and then briefly discuss the
the proposition
case.
As in BGM (2006), we assume that the planner chooses
elastic labor
confirms
to producing
of labor that is allocated
existing varieties,
In addi
in
varieties.
the
of
number
determines
turn,
which,
produced
rate
in
also
the
of
this paper, the planner
chooses
tion,
producer price in
flation.
the amount
Proposition
cial planner,
1
The optimal rate of producer price inflation irt, chosen by a so
is zero.
1 is in an appendix,
available on request. The
The proof of Proposition
acts as a tax on firm
inflation
intuition is straightforward:
producer price
our model,
as can be seen directly
in the corresponding
in
equa
profits
tion in table 5.1 (inflation erodes the share of total profits in consump
It distorts
tion output both directly and by its impact on markups).
to
creation
labor
of new
and
the
allocation
of
decisions
entry
firm
firms
in suboptimal
of existing goods, resulting
consump
production
tion and lower welfare. Optimal
policy, therefore, aims to stabilize pro
while
ducer price inflation at zero. Importantly,
however,
producer
consumer
rate
of
must
the
be
stabilized,
price inflation
optimal
prices
in
the
number
of varieties:
must move
to
accommodate
changes
freely
versus
where
a star denotes
idence of bias
accounting
Weinstein
variables
in the measurement
in the efficient
Given
equilibrium.
of CPI inflation (precisely due
for new varieties),
convincingly
(2006), we view this normative
documented
the ev
to poor
Broda
and
by
as
of our model
implication
in producer
prices
good news. The central bank should target inflation
CPI inflation.
rather than (mismeasured)
labor supply is elastic, the subsidy t[ = 1 /(0 -1) ensures that the
When
the wedge
otherwise
is efficient,
removing
equilibrium
flexible-price
Entry & Product Variety
Policy with Endogenous
Monetary
315
rates of substitution
and transformation
the marginal
present between
In
and
leisure.
this
between
case, price stickiness distorts
consumption
to creation of
both the total amount of labor supplied and its allocation
of existing goods. It is easy to verify that a zero
firms and production
in producer prices is still the optimal monetary
policy.
The optimality
of producer price stability with inelastic labor supply
new
rate of inflation
a new
highlights
for price stability (at the producer
level) im
a
In
and
model
with
exoge
entry
product variety.
of firms and inelastic labor supply, time variation
have no impact on the equilibrium
path of con
argument
plied by endogenous
nously fixed number
in the markup would
and welfare:
would
be simply determined
sumption
consumption
by
the exogenous
and
labor
productivity
supply regardless of markup
dy
namics. Endogenous
vari
entry and product variety imply that markup
ation reduces welfare
and the allocation of
entry decisions
by distorting
of labor to firm creation versus production
of existing
in
maximiza
introduces a role for monetary
welfare
policy
the fixed amount
goods. This
at
tion by stabilizing producer price inflation at zero?and
the markup
mone
its flexible-price
of
the
level. We discuss
implementation
optimal
interest rate in the following.
tary policy by setting the nominal
4
The New
This
section
uct variety
describes
Phillips
The New
Curve
and the Log-Linear
Model
the implications
for the New
equations
log-linear
4.1
Keynesian
Keynesian
of the model.
Keynesian
Phillips
of endogenous
entry and prod
curve
and
the key
presents
Phillips
Curve
To study
the propagation
of shocks and compute second moments
of the
on
variables
the processes
for ex
endogenous
implied by assumptions
the model
around the efficient steady
shocks, we log-linearize
ogenous
state with zero inflation under assumptions
of log-normality
and ho
We
denote
from
state
deviations
with
percent
moskedasticity.
steady
sans
curve
serif
fonts. Our model's
follows
version
from log-linearizing
of the New
equation
Keynesian
Phillips
(2):
"
TT,= (3(1
where
gross
8)E/JT,+1-[Lt, K
irt and
inflation
(4)
|x,now denote percent
in the case of irt).
deviations
from steady
state
(of
316 Bilbiie, Ghironi,
=
^
Since pt = pt/Pt = (Nf )1/(e_1)and optimal firm pricing implies
=
ptZt/wt, it follows that |x,
(Nt)l/{*-l)Zt/wt, or, in log-linear
=
and Melitz
=
|x, pt/Xt
terms:
(5)
T-^7N<-(wt-Z,).
(With a constant number
relation between
negative
New
it,
Keynesian
=
0(1
-
of firms,
model.)
??
8)E/ir,+1 +
this relation
reduces
to the familiar
cost of the benchmark
and marginal
markup
into
(5)
(4) yields:
Substituting
(w, -Zt)--Nr
K
K
(6)
curve relation that ties firm
(6) is a New Keynesian
Phillips
Equation
tomarginal
cost in a standard fashion. Impor
level inflation dynamics
cost is adjusted to reflect the number of pro
tantly, the effect of marginal
state
in the economy.
This is a predetermined,
that operate
introduces directly a degree of endogenous
variable, which
persistence
in the dynamics
of product price inflation in the Phillips curve.
our model
links the dynamics
of inflation to asset prices
Furthermore,
the log
in an endogenous
(6) with
way, as can be seen by combining
ducers
linear free-entry
it,
=
0(1
-
to obtain:
condition
+
8)E,ir,+1 ?-(v,
-
f?,()
K
(7)
-N(.
K
to the relative price of investment
ties inflation dynamics
This equation
new
inflation and number
in
firms. It stipulates
that, for given expected
related to equity prices. Together with the
of firms, inflation is positively
bonds and equity implied by optimal
between
condition
no-arbitrage
inflation and equity prices
this connection between
behavior,
a crucial role for the
our
in
model)
(and thus capital accumulation
plays
of interest rate setting that we dis
and stability properties
determinacy
household
cuss
in the following.
Finally, using the definition
<
=
p(l
curve
Phillips
Keynesian
-
inflation, we can write
inflation:
for consumption-based
of CPI
-
8)?(<+1 + "^?V
K
-
-
~~
u
?^-IN,
1
N,_,
P(l
Zf)
-
-N,
K
-
8)(N,+1
the New
N,)],
(8)
of the gross CPI inflation
the percent deviation
irf now denotes
an ad
inflation displays
rate from the steady state. Consumption-based
to
inflation
firm-level
relative
ditional degree of endogenous
persistence
where
Policy with Endogenous
Monetary
Entry & Product Variety
317
in that it depends
directly on the number of firms that produced
in period t - 2.
t-l, which was determined
at time
Implications for Empirical Exercises
studies
the New
estimating
Keynesian
Existing
empirical
Phillips
curve (4), such as Sbordone
and
Gali
and Gertler
(2002)
(1999), proxy
the (unobservable)
variable with the inverse of the labor share.
markup
en
in a model without
that holds exactly
This is an approximation
this
variety. In our model with endogenous
variety, however,
one
no
if
holds.
believes
Indeed,
relationship
longer
product variety to
be important
that one
for business
cycles, the proxy for the markup
dogenous
should
use
is the inverse
the overhead
beyond
set up new product
of the share of labor (in consumption
output)
used to
(from an aggregate perspective)
quantity
=
measure
lines, \xt Yf/[wt(Lt
LEt)]. This markup
to the labor share measure
used by Rotemberg
and
closely
that takes
into account
overhead
labor. Log
(1999)
linearization
of this equation, when
replaced into (4), delivers a relation
testable.19 Alternatively,
that is empirically
the equation
for
exploiting
=
one
use
could
the
of
inverse
the
share,
(one minus)
jul^
profits,
profit
as a proxy for markups,
where Df = dtNt + k/2 (^t)2Yf
(1 Df/Yf)-1,
are profits gross of the costs of
that since these
price adjustment. Note
a
costs are zero when
around
zero-inflation
log-linearizing
steady-state
is equal to consumption
and gross
(and hence consumption
output
are
to
net
the
usable
profits
equal
profits),
equation will fea
empirically
ture only observable
that
and
total profit re
is, consumption
variables,
corresponds
Woodford
ceipts (or dividends).20
A further implication
of our framework
for empirical exercises comes
consumer
from the natural distinction
between
and producer
price in
our framework
flation in our model:
in
overcome
to
order
implies that,
measurement
issues inherent in using CPI inflation, empirical studies of
on producer price inflation (which
the Phillips curve should concentrate
is also the relevant objective
for monetary
of CPI
policy). Construction
data by statistical agencies does not adjust for availability
of new vari
eties in the specific functional
form dictated by the welfare-consistent
index.
cer
for variety, when
it happens,
Furthermore,
price
adjustment
not
at
does
the
our
in
tainly
happen
represented
frequency
by periods
model.
Actual
economy)
the model
moments
CPI data
are closer
to pt (the average price level in our
than Pt. For this reason, when
the properties
of
investigating
in relation to the data (for instance, when
second
computing
below or in the specification
of policy rules that allow for re
318 Bilbiie, Ghironi, and Melitz
one should focus on real variables
real quantities),
a data-consistent
index.
For any variable Xt in units of
price
by
the consumption
is obtained as
basket, such data-consistent
counterpart
to measured
action
deflated
an endo
issue, our framework
implies
in
shocks
much of the empirical
literature on
curve. An endogenous
term that depends
Phillips
to this measurement
Related
in cost-push
geneity bias
the New Keynesian
on Nt (due to the measurement
from not accounting
bias
to exogenous
attributed
shocks when
is
for variety)
the
estimating
Phillips
cost without
variety.
cost-push
curve equation
(6) using a proxy for marginal
the variety effect is removed from the welfare-consistent
When
tt,
=
curve
the Phillips
price,
8-1
0(1
8)E/irf+1
equity
(7) becomes:
"
+
-^?(Vk,,
U, (9)
of shares net of the variety effect.
of the firm/price
For given expectations
of future inflation, actual inflation is increasing
in the data-consistent
price of equity.
where
4.2
vRt is the value
The Log-Linear
Model
can be reduced
The log-linear model
New Keynesian
Phillips curve [4]):
N,+1
=
(1 + r +
+
f
-
(r + 8 +
i|*)N,
[(r + 8 + v|i)(9
1-8
1-hr
' '+1
=-E,C,+1-N,+1 C,
-
i|i)(6
1) + 8]Z,
1
(1 -8
+ r 6-1
\l
r+ 8
"1-8
to the following
1
-
-
-
i|i(6
1)C,
equations
(plus the
l)p,f
8f?>t, (10)
r + 8\
1+
r/
1
t+l+-ISL
0-1
*
(11)
V ;
1-8
Nt, (12)
Nf+1
Et>Kt+1+
-^
^-y
=
is zero when
where we defined
1), which
\\i
1) + 8]/(0
cp[(r+ 8)(0
the conduct
is closed by specifying
labor supply is inelastic. The model
rate
interest
the
nominal
the
of
of monetary
i,)over the
setting
policy (via
EA+i
business
=
Cf + it
-
cycle, which
we
discuss
in the following.
Policy with Endogenous
Monetary
5 Monetary
In this
Policy
the Business
319
Cycle
and stability properties
of
section, we discuss
determinacy
and
interest rate setting over the business
rules for nominal
cycle
simple
the implementation
5.1
over
Entry & Product Variety
of the optimal
the following
purposes, we consider
rules for interest rate setting:
For illustrative
flation-targeting
price
stability.
Rules
Simple Policy
+ TE.TT^ +
TcE^
i^^U
of producer
policy
+ g;,
1>T^0,T>0,TC^0,S
class of simple
=
0,1.
in
(13)
the nonsystematic
shock capturing
? j is an exogenous
component
assume that tc = 0when t > 0 and vice versa, re
We
of monetary
policy.
or consumer
the central bank to reacting to either producer
stricting
where
price
inflation.22
For the reasons we
have
previously
a re
discussed,
(and not feasible in
to welfare-based
CPI inflation is suboptimal
to
measurement
In consider
due
the
reality
problems we mentioned).
we
abstract from normative
and mea
ing this scenario,
prescriptions
surement
the response
issues; rather, we ask the question: what would
to various
of the economy
shocks be if the central bank could monitor
sponse
movements
volving
in welfare-consistent
CPI
Determinacy
and followed
a rule in
and Stability
In this section, we study the determinacy
under different monetary
policy
model
inflation
the latter?
and stability properties
of our
To
rules.
local determi
analyze
nacy and stability of the rational expectation
equilibrium, we can focus
on the perfect
version
of the system
no-fundamental-shock
foresight,
formed by (4), (10), (11), and the equation obtained by substituting
the
into
the
Euler equation
for bonds
(12). To be
monetary
policy rule (13)
in
consider
the
rule
which
the
central
bank
is
with,
gin
simple
respond
=
ing to expected producer price inflation with no smoothing:
\t TEtirt+1.
The following proposition
that the Taylor Principle holds in
establishes
our model
for all plausible
of parameter values.
combinations
economy
2 Lety = [l- (3(1- 8)J/[(3(2 - b)]. Assume that cp= 0, and (3,8,
Proposition
and 6 are such that 1 -7(6 -1) > 0, (3> 1/2, 6 > 2, andi < 7 = (k + 6 - 1)/(Q
-1). Then i>lis
necessary and sufficient for local determinacy and stability.
320
Bilbiie, Ghironi,
and Melitz
2 is in the appendix,
for Proposition
1, the proof of Proposition
on request. We
in
remark
that the parameter
restrictions
are
to
2
conditions
the
for
hold,
Proposition
sufficient
Taylor Principle
As
available
and they are extremely weak. For instance, the values of k and 0 that we
= 77 and 0
= 28.5: the sufficient condition
t <
consider
(k
3.8) imply t
28.5 is satisfied by any realistic parametrization
of interest rate setting.
while
Moreover,
that determinacy
we
cannot prove it analytically, we verify numerically
and stability hold for values of t well above the thresh
values we consider.
old t for the parameter
the
is an important
of
Taylor Principle
Validity
on the Taylor Principle
in models with physical
result given the debate
capital accumulations.
interest rate setting (t < 1) is necessary
(2001) shows that passive
Dupor
and stability in a continuous-time
and sufficient
for local determinacy
and Fuerst (2005) study the issue
model with physical capital. Carlstrom
in a discrete-time
that it is essentially
capital and conclude
with
interest rate
forward-looking
determinacy
is restored
shows that the standard Taylor Principle
model
with
to achieve
impossible
setting. Our result
when capital accumulation
new production
takes the form of the endogenous
creation
of
lines.
Intuition: The Role of Asset Prices
inMonetary
Policy Transmission
in our setup is in striking con
the validity of the Taylor Principle
trast to results of models with
traditional physical
capital, an intuitive
for this
in
the
mechanism
is
order.
of
this
difference
Indeed,
explanation
on
our
the
the
role
of
model
is centered precisely
result in
endogenous
Since
our New Keynesian
model
value of the firm?in
price of equity?the
the explanation
relies on one hand on
with free entry. As we anticipated,
the Phillips curve in (9) that relates inflation and asset prices (net of the
on the other hand on the no-arbitrage
condition
variety effect) vR tand
can
for bonds and shares. This condition
implied by the Euler equations
as:
be written
"
',
r+8
1-8
=
E,ir,+1
-vRA
+
y--y
E,vR,+1
+
(14)
Y~---;Efd^+1.
the rele
first on the policy rule studied in Proposition
2, where
and
consider
is
expected product price inflation,
objective
to
shock unrelated
that a sunspot
the following
Suppose
experiment.
Focus
vant
inflation
hits the economy, and that (without losing generality)
any fundamental
so that all other expected values
it is located in inflationary expectations,
Policy with Endogenous
Monetary
Entry & Product Variety
321
are taken as given. We wish to show that if the
(the
policy rule is passive
this sunspot shock will have real effects,
is violated),
Taylor Principle
if the policy rule is active the sunspot has no effect. When
the
an
increase
in
is
inflation
violated,
Taylor Principle
expected
triggers a
fall in the real interest rate. From the no-arbitrage
condition
(14), this im
whereas
rise (a fall in the real
plies that the data-consistent
price of shares must
a fall in the real return on shares,
return on bonds must be matched
by
an increase
for fixed expected dividend
and future price, means
which,
in the share price today). But an increase in the share
price implies, by
(9), that actual inflation today will rise, and hence that the sunspot is self
the Taylor Principle
is satisfied, the opposite holds: the
fulfilling. When
an
in
increase
the
real interest rate, a fall in today's
sunspot
triggers
share price by no-arbitrage,
and a fall in today's inflation by the Phillips
the sunspot vanish.23
curve, making
can be
The same mechanism
easily verified
to contemporaneous
sponding
or expected)
(contemporaneous
we
omit
those
the formal
cases,
to save
statements
producer
inflation
for a policy rule re
inflation, and indeed to
to hold
price
in consumer
and proofs
prices. Therefore,
of the Taylor Principle
for
space.24
A comparison
of our results and intuition with those of Carlstrom
and
Fuerst (2005) allows us to further emphasize
the crucial role of the dif
ferent type of capital at the core of our model.
Carlstrom
and Fuerst
occurs in a discrete-time
that indeterminacy
model with physical
the central bank responds
to expected
future inflation be
capital when
cause the
condition
between
bonds
and
no-arbitrage
capital contains no
show
t. This happens
because
return to
the expected
future
variables
the
capital depends
only
determining
marginal
product of capital at time t + 1. In turn, this implies that there is a zero
root in the system, and
the ex
Instead, in our model,
indeterminacy.25
variable
dated
at time
on
5.2
return
on shares
on the price of shares
depends
today (an en
hence
this
zero-root
variable),
Indeed,
dogenous
removing
problem.
a
link
novel
be
through
today's price of equity, our model
provides
tween the no-arbitrage
condition
and the Phillips curve that is absent in
models
that do not feature endogenous
variety and free entry.
pected
Implementing
Endogenous
The
Entry
Price Stability with
and Product Variety
the nominal
efficient, flexible-price
equilibrium
requires
rate to be equal to the Wicksellian
interest rate (inWoodford's
interest
2003 ter
322
Bilbiie, Ghironi, and Melitz
that is the interest rate if that prevails when prices are flex
minology),
ible and producer
terms, the Wick
price inflation is zero. In log-linear
sellian interest rate is:
-
i*= EC*
C* -_(N*
1
-N*^
= FC*
-
C* 4- ttc*
EtC*+1 C* is the risk-free, real interest rate of BGM and nf *a is
the optimal consumer price inflation that accommodates
changes in va
+
t and t
1 (known at time t). Note, however,
that com
riety between
to the policy rule \t= \fwould
mitment
result in equilibrium
indetermi
a fixed number
with
of producers
nacy, as in the standard model
where
in Woodford
discussed
contain
would
sticky-price
A simple
no
(2003), because
to variables
feedback
equilibrium.
interest rate rule that implements
is
equilibrium
rate setting
in the
that are endogenous
nominal
interest
the efficient,
flexible-price
T>1,
(15)
TIT,+ EfY?( + 1 %,
= - i* is the interest rate
where
gap relative to the what is interest rate,
it
\t
=
=
is the
and
(C* [1/(6
[1/(6
1)]N*}
l)]Nt
C,
CR,( C*f
CKt
%
f,
=
gap
measured
between
output
consumption
and
its
flexible-price
level.
to track
the monetary
(15) requires
authority
in
rate
in
interest
and
the
Wicksellian
expected growth of the
changes
more
to
to
than proportionally
respond
output gap, and
consumption
to verify that the following
inflation. It is possible
equation holds for the
The
interest
dynamics
rate rule
of the consumption
output
gap:
=
(15) into this equation yields tit,
=
is
0 Vf, since the Taylor Principle
has unique solution irt
satisfied. In turn, zero producer price inflation in all periods
implies YRt
=
=
0, and therefore,
ifVr.26
i,
Substituting
EtiTt+1,which
the interest
6
Cycles:
Business
rate rule
Propagation
and Second Moments
of our benchmark model
In this section, we explore the properties
by
to
means
We
of numerical
pro
responses
compute
impulse
examples.
we compute
and monetary
policy shocks. Next,
ductivity, deregulation,
and compare them to second
of our artificial economy
second moments
moments
with
those produced
by the baseline BGM model
As shown in BGM, these mo
and CES preferences.
in the data and
flexible
prices
Monetary
Entry & Product Variety
Policy with Endogenous
323
to those under the optimal monetary
(which also correspond
pol
are very close to those
in
the
economy)
generated by the
icy
sticky-price
standard RBC model.
ments
6.1
Calibration
=
calibration, we interpret periods as quarters and set (3
0.99?a
standard choice for quarterly business
cycle models. We set the
=
size of the exogenous
firm exit shock 8
0.025 tomatch
the U.S. empir
use
We
ical level of 10 percent
the value of 6
destruction
per year.27
job
=
set
6
and
from Bernard, Eaton, Jensen, and Kortum
3.8, which
(2003)
was calibrated to fit U.S. plant and macro
trade data.28 We set initial pro
= 1. The initial
to
Z
entry cost/? does not affect
ductivity
steady-state
= 1without
we
loss of generality.
therefore
any impulse response;
set/?
In our baseline
for the elasticity of labor supply, cp,and we
set the weight
of the disutility
of labor in the period utility function, X/
so that the steady-state
level of labor effort is 1?and
levels
steady-state
are the same?regardless
of all variables
of cp.29
We set the price sticki
k = 77, the value estimated
ness parameter
by Ireland (2001). Although
We
consider
different
values
Ireland obtained
this estimate using a different model, without
and endogenous
to changes
variety, our results are not sensitive
a
value of this parameter within
range.
plausible
6.2
Impulse
entry
in the
Responses
Productivity
from steady state) to
Figure 5.1 shows the responses
(percent deviations
a 1 percent increase in
for
the
inelastic
labor case. For con
productivity
sistence with
the second-moment
results in the following, we assume
0.979, as in King and Rebelo
(1999). The figure
persistence
the
efficient
obtained
under opti
compares
flexible-price
equilibrium
mal monetary
with
three
alternative
(round markers)
parame
policy
productivity
first is a simple rule re
=
sponding
price inflation,
it
1.5Et7Tt+1 (cross
=
a
is
the
second
rule
rate
interest
markers);
involving
\t
smoothing,
features the same long-run re
0.81^ + 03Et7Tt+1 (square markers), which
to
as
inflation (1.5)
the previous
rule; and the third is a
sponse
expected
=
rule responding
to expected
welfare-consistent
CPI inflation,
i,
that the difference
between
the responses
1.5E/nf+1 (star markers). Note
under each of the simple rules and the optimal policy measures
the gap
trizations
of the monetary
policy
to expected
producer
rule (13). The
324
ptoZ itoZ
0.03
0.02
\1
rtoZ
fftoZ
\
CtoZ
??j
| \ 0.6J f
j
([
^^k
|
'
0
5
10 15*""20
0
5" 10 15 20'"
l /Z*^
06
2
\f\
0.4
1.5
\
0 0U?^^^J
5 10 15
I
1
0.2
/V
0ii-1
0 5
20
_wtoZ_
o:4
0
08
^DtoZ
?'6
' 25l\
2
06!,1/V
if
5
X.
10 15 20
Figure
?0
j
^^
5
10 15 20
-?ir-
.1L_i5
15 20 0
v
0.11
10 15 20
toZ
^
>.
0U-^??....l
5 10 15 20 0
:
.0.15 JL-_0 5 10 15 20 0
10 15 20
i o.5!
dtoZ^_
\0.2v\
?-3\ I015/
BJ I
0.05
Q4-1 5
10 15 20
YtoZ
ytoZ
\'
\ ?4I
02
]_1 0.511
?0
0.1
_
^toZ
____
_
_
_mtoZ
0.05/ i02
J-1 0 ll-1
0 5 10 15 20
20
5
?0
LtoZ
-?-3
.05
\ / Qb!
f
If?__J
0 5 10
0 5\^W^
\^/I -0.4
o-15
oe!%J"005V
\ I
/
^ ! _0,/
0.1/
10 15 20
A
0.5
oil?^n^^nJ
0 5 10 15
r!oZ___
\.
5
1
l8' 15 iQ~
orr ^n.
j -oi
/^
-0.2
ftol.
ft-1
I 14
1
%J
0 ~5
LctoZ
LEtoZ
;
10 15 20
'
0 T"" To"l5"~2Ci
NtoZ NEtoZ
il?"~;
and Melitz
Bilbiie, Ghironi,
0.8
^\,
V0.6'
0?2l_W**??.
0 5 10 15
20
02J_
?0
5
10 15 20
5.1
shock, persistence
responses:
Impulse
productivity
= 1.5
=
Cross markers:
i,
Etnt+r Square markets:
i,
.979. Round
+
.8i,_L
markers:
optimal
.3E/irf+1. Star markers:
policy.
= 1.5
i,
to the flexible-price
under the alternative
rules. The
equilibrium
of years after the shock is on the horizontal
axis, and responses
are normalized
so that 0.3 (for instance) denotes 0.3 percent.
relative
number
Focus
ductivity
on the responses under the
optimal policy. The increase in pro
makes
the business
environment
temporarily more attractive,
a
entrants
number
of
which
translates into a grad
(NEt),
higher
drawing
ual increase
in the number of producers
(Nt) before entry and the stock
of production
lines return to the steady state. The larger number of pro
cost (wt/Zt - not shown) and the relative
ducers induces the marginal
pt to increase gradually with unchanged
price of each product
markup.
The GDP (Yt) and consumption
in
(Q) increase, and so does investment
as the fixed labor
new firms (vf =
is
reallocated
toward
supply
vtNEtt)
of new products.
firm-level output
(yt) is below
Interestingly,
an
the steady state during most of the transition,
for
initial ex
except
a
on
The
effect
of
relative
the
pansion.
price prevails
higher
expansion
creation
in consumption
demand
to push
individual
firm output
below
the
Policy with Endogenous
Monetary
steady
Entry & Product Variety
325
state for much
in the number of
of the transition, with expansion
in new firms responsible
for GDP remaining
state throughout
the transition. Notably,
the dynamics
and investment
producers
above the steady
of firm entry result
exogenous
shock,
in responses
that persist beyond
the duration of the
some
a
for
and,
key variables,
display
hump-shaped
pattern.30
across
a remarkable
When
feature
responses
comparing
policy rules,
of the results is that the dynamics
of macroeconomic
under
aggregates
the first two simple policy rules are strikingly similar to those in the flex
indis
Indeed, the responses of GDP are virtually
equilibrium.
are
and
the
those
of
and
number
of
tinguishable,
consumption
producers
also very close. Equivalently,
the changes in producer price inflation and
ible-price
the markup
induced by technology
shocks under these policy rules are
in the fixed
small. It isworth stressing that this is in contrast to responses
are
New
benchmark
where
there
model,
variety,
Keynesian
quantita
deviations
from the flexible-price
under
tively significant
equilibrium
=
such simple policy rules. In our model,
instead, a simple rule such as \t
response to inflation,
1.5Et7it+1, despite not featuring an overly aggressive
to
to
the
close
its
first-best
manages
economy quite
bring
optimum. This
no
is
to welfare-consistent
longer true when monetary
policy responds
CPI inflation:
there are more
in the responses of con
evident differences
of
from the suboptimal
sumption
producers,
stemming
to
central
bank
movements
in
of
the
CPI inflation
welfare-based
response
that reflect fluctuations
in the number of products.31
our
with entry can induce inflation and counter
model
Importantly,
and the number
and potentially
to tech
labor, in response
cyclical markups,
procyclical
shocks.
To
this
in
understand
recall
the
stan
intuition
the
result,
nology
dard New Keynesian
which
and procyclical
model,
implies deflation
in response
to productivity
increases: marginal
cost falls,
markups
as
decrease
is
not
but
much
because
of stick
(there
deflation),
prices
by
and markups
increases
too?that
iness, so output
increase,
is, the
our
is
an
In
with
model
is
additional
markup
procyclical.
entry, there
channel
of shock transmission working
in the opposite
direction: posi
tive productivity
shocks increase future profits and the value of the firm
to create new goods).
on la
(it ismore productive
Entry puts pressure
bor demand,
cost to increase in order to
inducing marginal
satisfy free
and output
entry. By this channel, prices increase, but not by as much,
increases
and
investment
There
is infla
(both consumption
increase).
tion and the markup
is countercyclical.
Otherwise
the
put, through
usual channel, labor demand by existing firms falls, the real wage
falls,
326
Bilbiie, Ghironi,
and Melitz
and the markup
increases. Through
the new channel,
labor demand by
it can overturn
increases and, if it increases enough,
the usual
an
a
in total labor demand,
effect and generate
increase
real
higher
entrants
and a countercyclical
Which
channel dominates
de
markup.
on
shock
values
As
shown
(for instance,
parameter
pends
persistence).
on impact with the persistence
in figure 5.1, the new channel dominates
that we use to compute
in the following discussion.
second moments
wage,
Deregulation
to a 1 percent, permanent
Figure 5.2 shows the responses
deregulation
shock (a lowering of the entry cost/?,) with inelastic labor supply under
the same policy scenarios discussed
earlier.
itoL
ptofE
1
0
006[l
o,A
o,\
5
101?T 2cT*0
?0
-v
0.02
!\\ ,\
*
5~ ^rcr?1%U^6l
5
?0
5
10 15 20
05
$r~
J_[
0.2^_j
?0
5
0.3
0.3
/^
-I_Vt_"L_
?0
5
j&^
10 15 20
?0
5
5
?0
w
E f toto
10 15 20
0
5
DtofE
vEtofE
-?-2
0
5
Figure
Impulse
markers:
?0
5
:f
| ^
-0.3|y
0
d
5
10 15 20
4.4!
j
10 15 20
iL.
0
10 15 20
t^
*1
(T~5T(Pf5?20~J
rv
fto
fE
to
I -02
"0-2
5
10 15 20 0
5
10 15 20
i
iV?
5
10 15 20
ytofE
Yto%
?-1
!/
W0.5^^'shh^^^ "06
\\ !
10 15 20
5
10 15 20 0
L?tofE
LtofE
fE m tofE
f {/
5
f?
10 15 20
FS^
-??5
0.2/0,
0
-S~
||
X^J
10 15 20
r
oLZ
0.02^
10 15 20
LEto
^
f
A
\
0
CtofE
O-CMli
:-^^^
-1
to
NtofE
NE
%
i?a
rtofE
pPtofE
I0.06
^[t?-"I
10 15 20
0
5
10 15 20
0
5.2
responses:
permanent
= 1.5
i,
Et tt(+1 Square
deregulation.
=
markers:
if
Round
.81^ +
markers:
optimal
policy; Cross
= 1.5
.3E/ir/+1. Star markers:
i,
EtT:f+v
Monetary
Policy with Endogenous
Entry & Product Variety
327
at
again on responses under the optimal policy. Deregulation
tracts new entrants and firm value decreases
(the relative price of the in
Focus
vestment
good
is relatively more attractive than
falls). Since investment
labor reallocation
from the latter to
there is intersectoral
consumption,
as households
now postpone
the former. Consumption
initially falls,
to invest more
in firms whose
has not in
productivity
consumption
creased. The number of firms starts increasing, but GDP initially falls as
the decline
variables
in consumption
the increase in investment.
dominates
toward their new steady-state
then move monotonically
All
lev
is that the long-run expansion
of CES preferences
of
els. A consequence
driven
the
in
is
extensive
(the long-run
consumption
entirely
margin
by
crease in the number of producers), with output per firm back at the ini
tial steady-state
level.
As in the case of a productivity
for the first two
shock, the responses
alternative policy rules, where
the targeted measure
of inflation is pro
re
ducer price inflation, are again very similar to the flexible-price
As
when
the
difference
is
for
the
sponses.
monetary
productivity,
larger
authority
discussed
to welfare-based
responds
CPI
inflation,
difference
for the same reasons
with
The most notable
respect to the
previously.
case
more
so
in
all
when
the
rule
(but
responses
flexible-price
responds
to welfare-based
CPI inflation) concerns the dynamics
of the consumer
the optimal policy, deregulation
in
induces deflation
price index. Under
rate in absolute
(at a decreasing
terms) precisely
because
there is an increase in the number of products
(at a decreasing
the alternative
rules, this response changes sign?positive
rate). Under
inflation in the welfare-based
CPI occurs?because
the increase in pro
the welfare-based
ducer
crease
CPI
to compensate
the effect of the in
enough
of available varieties. This effect is strongest when
to welfare-based
CPI inflation.
responds
price inflation
in the number
the central bank
is high
Monetary
The next
Policy
set of responses,
in figure 5.3, shows
plotted
to
shock
the
nominal
interest rate?a
transitory
purely
crease with
zero exogenous
the effects
1 percent
of a
de
Because of the assumption
of
persistence.
zero exogenous
are plotted
all responses
for the policy rule
persistence,
interest rate smoothing
the effect of the shock is
(otherwise,
involving
short
but
for
different
values
of
the
labor supply elasticity,
cp
lived),
very
=
and
An
interest
rate
cut generates
inflation and
0, 2,
4, respectively.32
a positive
of GDP
both by Yt and the data
(as measured
response
328
ptocsiitocsi
jfi
if~
N to
csi
NEtocsi
0
5
10
15
0
10
5
15
if
?
b
0 n-^^tej-fl-o
a?*;*??
1
in
15
-el]_._j
s
m
Figure
ifi
5
,_._J
n
10
10
15
mtocsi
t]_._J
0
5
15
n
-2QIj
n
5
I
m
ir
iV
11 Nfesg^-^
u
n
s
m
10"
15
-61]_._._J
0
5
Y
to
csicsi
to
YR
1-5rt-'-'-^
Qj
is
15
0
5
TO
o
10
150
5
10
consistent
rate shock,
elasticity
persistence
= 2.
Square
0. Round
markers:
markers:
! 1
m
is
v?^--t
Q1^
o
s
t-m
inelastic
labor supply
labor.
= 4.
elasticity
rise, consistent with conventional
YRt). Wages
of empirical
evidence
for the post-1980 United
States (for instance, Christiano,
and Evans 1999). How
Eichenbaum,
effect on GDP is combined with a contractionary
ever, the expansionary
in the number of pro
impact effect on entry (and a gradual decrease
counterpart,
and the bulk
wisdom
in Bergin and Corsetti
ducers) that conflicts with the evidence
(2005) and
occurs
Lewis
of entrants
because no
(2006).33 The fall in the number
return on equity to fall along with the ex
arbitrage requires the expected
ante real return on bonds. The decrease
in the expected
return on equity
is brought
future:
about by an increase
the procyclical
in today's
an increase
impact
in the price of shares today relative to the
into
translates
response of the real wage
price via the free-entry condition. The cost
re
and its expected
requires labor?increases,
turn falls, inducing investment
in new products
to fall (the combination
it relatively more attractive
to
of prices that the household
faces makes
of firm creation?which
equity
15
-n
1-5rt-
11
DLJ?i
LV_^_I_J
n
S?h>
Ol'V^^ho
5
5.3
interest
responses:
Impulse
Cross markers:
labor supply
15
v csi
to
csi
to
d
10
0 ^>
3
/
f~
Ltocsi
iPtocsi
v Eto
to
D
csi
csi
y tocsi
I j^b^- -n
4a 1-"-'-T
0
/^h? . . ? ? u ?
j
5
I
n
\V
0
5
and Melitz
Ctocsi
-:ip
LEtocsi
w
rtocsicsi
to
0 1'V^rt^jwJ
TO
0
5
rtocsi
pctocsi
rn
Bilbiie, Ghironi,
15
Policy with Endogenous
Monetary
Entry & Product Variety
329
than invest). This effect changes sign after a few years,
the steady state,
the real wage
falls and share prices are below
when
in
to
attractive
The
it
invest
creation.
ef
contractionary
product
making
on
on
link
relies
the
between
fect of monetary
entry
expansions
crucially
consume
rather
firm value
cost implied by free entry. In section 7,we study
and marginal
that breaks this link and implies an expansionary
of the model
a version
effect of monetary
6.3
policy
on firm entry.34
expansions
Second Moments
To further evaluate
the properties
of the sticky-price model, we compute
of our artificial economy
for
second moments
variables
and compare
them to those of the
the implied unconditional
some key macroeconomic
data
and
those produced
model with CES
by the BGM flexible-price
we
on
to Zt as the
In
this
focus
random
shocks
exercise,
preferences.
source of business
that sunk entry costs are
cycle fluctuations,
assuming
constant at fEt = 1 and abstracting
from exogenous
monetary
policy
in
shocks.35 To start with, we compute moments
of GDP, consumption,
and hours worked. We use the same productivity
vestment,
process as
0.979 and a standard deviation
King and Rebelo (1999), with persistence
to
to
of innovations
facilitate
of results with
0.0072,
comparison
equal
setup and BGM. As in King and Rebelo's benchmark
=
set
that mone
cp 2.36 Under
calibration,
sticky prices, we assume
=
tary policy follows the rule \t 0.8it_a 4- 03Etirt+1. This rule is empirically
based on the findings of a large empirical
literature, which
plausible,
documents
the importance of interest rate smoothing
in Federal Reserve
the baseline
RBC
we
its focus on inflation
targeting since the 1980s, and the marginal
of GDP responses.
Table 5.2 presents
the results. For each
significance
the first number
moment,
(bold font) is the empirical moment
implied
(1999), the second number
by the U.S. data reported in King and Rebelo
policy,
(normal
optimal
Table
font)
is the moment
monetary
policy
generated
under sticky
model
(or
by the flexible-price
and the third number
prices),
5.2
Moments
for Data,
BGM CES Model,
axt
Investment,
and Sticky
Variable
Xt
Prices
<jxt/aYRt
E(XtKt_1)
1.81
YRt
1.34
CR/t 1.35
5.30
0.65
0.66
0.74
0.48
5.23
5.20
2.93
3.90
Lt 1.79
0.63
0.63
0.99
0.47
0.46
vRtNEt
Source for data moments:
King
2.36
and Rebelo
1.00
(1999).
corr(Xt,YRt)
0.84
0.70
0.70
1.00
0.48
0.80
0.75
0.74
0.88
0.97
0.98
3.82
0.87
0.69
0.69
0.80
0.99
0.99
0.88
0.69
0.69
0.88
0.98
0.98
330
Bilbiie, Ghironi, and Melitz
under the
(italics) is the moment
generated
by the sticky-price model
mo
rule discussed
We
second
compute model-implied
previously.
ments
for HP-filtered
variables
for consistency with data and standard
RBC practice, and we measure
investment
value of household
investment
in new
in our model
with
the real
firms
(vRtNEt).
is virtually
The performance
of the sticky-price model
indistinguish
re
able from that of the flexible-price
turn?is
economy, which?in
some
in reproducing
close to that of a benchmark
RBC model
markably
in BGM. The simi
of U.S. business
cycles as documented
across
in
is not sur
and
models
flexible-price
larity
performance
stickyin light of the similarity of impulse responses between
the rule
prising
we discussed
we are
that
and
the
previously.
considering
optimal policy
An empirically
plausible
degree of nominal
rigidity does not signifi
key
features
of the model
relative to the flexible-price
the performance
once one takes into account that Federal Reserve policy ap
alter
cantly
counterpart
in the recent past. Un
pears not to have been too distant from optimal
a
the
baseline
of monetary
der plausible
sticky-price
policy,
specification
faces the same well-known
framework
one)
(as the flexible-price
and hours are too
of the standard RBC model:
difficulties
consumption
relative to output; there is not enough endogenous
persistence
and all real variables
indicated
(as
by the first-order autocorrelations);
are too procyclical
relative to the data. As far as inflation is concerned,
a standard deviation
of product
the model
price inflation
produces
smooth
0.82, and correlation with GDP -0.87. The
equal to 0.01, autocorrelation
to the
in the number of producers
contributes
effect of slow movement
as
of inflation,
explained.
previously
persistence
correlation of the markup with
5.4
the
shows
model-generated
Figure
GDP
at various
lags and
and Woodford
it to that documented
by
comparing
and
that
(1999)
generated by the BGM model
model with translog pref
The flexible-price
leads,
Rotemberg
with translog preferences.37
Counter
erences
the contemporaneous
almost perfectly
reproduces
its
correlation
time
of
the
of
the
furthermore,
profile
markup;
cyclicality
with the business
by Rotemberg
cycle is very similar to that documented
with translog preferences
is countercyclical
The markup
across goods is tied to the number
the elasticity of substitution
The time profile of the
increases during expansions.
of producers, which
to
of producers
the
stock
to
of
is
the
slow
due
correlation
response
on
shocks, with GDP increasing
impact, and the number of producers
and Woodford.
because
responding
preferences
gradually
and with
generates
excessive
a
lag. The sticky-price
contemporaneous
model
with
CES
Countercyclicality
Policy with Endogenous
Monetary
Entry & Product Variety
331
0.6-j-1
0.4-?^^^-?--j-p.--O
-0.6-^^^^
.0.8 -I-
\-^^*
~~Q
D
Y*^^
-1-I-1-1-1-1-1-1-1-1-1-1
-5-4-3-2-1012345
-A5.4
Figure
The Cyclicality
of the Markup
Data -D-
BGM Translog ? ? Sticky Prices
(1).
to replicate
the time profile of the correlation
because
the
of producer
determined
by the dynamics
price infla
markup?now
no longer tied to the number of producers.
tion?is
On the bright side,
the sticky-price model with endogenous
entry and product variety gen
and
fails
erates procyclical
in line with empirical ev
producer entry, qualitatively
corre
The
idence, and procyclical
aggregate profits:
contemporaneous
=
lation between
and
is
if
0.95.
Even
the
falls
DRt
YRt
markup
NtdRA
increase
to
in
due
the
aggregate
during expansions,
profits
expansion
the number
of
producers.38
In sum, given
flation-sensitive
model
close
for in
rigidity and policy behavior
the
of
the
policymakers,
performance
sticky-price
at replicating key business
is?not
cycle moments
surprisingly?
to the flexible-price
The sticky price model
fails to
counterpart.
plausible
nominal
match
the cyclicality of the markup,
though endogenous
variety gener
ates procyclical
and
consistent
with
the presence
profits. Interestingly,
of an endogenous-state
in the New Keynesian
curve
variable
Phillips
a
the
model
rate.
in
delivers
inflation
This
the
direc
(6),
goes
persistent
tion of ameliorating
the inability of the standard setup to generate
cient persistence,
(1995).
highlighted
by Fuhrer and Moore
7
suffi
Extensions
In this section, we discuss
benchmark model discussed
model
inwhich
the implications
of three extensions
of the
we
a
our
version
of
First,
previously.
study
the tight link between
firm value and marginal
produc
332
Bilbiie, Ghironi, and Melitz
tion cost implied by free entry is broken by assuming
that entry requires
units
the
of
basket
rather
than
purchasing
consumption
hiring labor. We
show that this version of the model
increased
generates
entry
producer
to expansionary
in response
monetary
policy shocks. Second, returning
to the benchmark
of the entry cost, we remove
the as
specification
new
same
entrants
that
the
stickiness
inherit
of
sumption
price
degree
as incumbents
and we
in flexible
decision
allow new
fashion. We
entrants
consider
to take their first price-setting
two alternative
one
in
assumptions:
but take into ac
case, new entrants set their initial price flexibly,
that they will face a cost of price adjustment
from next period on.
In the other case, we simply assume that new entrants charge a constant
over
cost. We show that these versions
of the model
markup
marginal
count
that are virtually
identical to those
values.
parameter
Finally, return
on the cost of price adjustment, we ex
to shocks
responses
for plausible
model
deliver
dynamic
of the benchmark
assumption
ing to the benchmark
the
of departing
from CES preferences,
the
implications
plore
extending
to a general, homothetic
benchmark
model
of
consump
specification
in translog form and
this specification
tion preferences. We parametrize
show
also
roughly
7.1
that this extension
leaves
the key properties
of the model
unchanged.
Entry Cost
Our benchmark
in Units
model
of Consumption
reductions
generates
to
in firm entry in response
of the in
is a consequence
monetary
expansionary
policy shocks. This
in
crease in the entry cost evaluated
in units of consumption,
wtfEt/Zt,
of
the
duced by the shock. The countercyclical
impact response
markup
a
response of the real wage.
procyclical
in the cost of hiring labor for firm creation and,
thus discouraging
via the free-entry condition,
the price of investment,
on the response of
evidence
with
This
conflicts
result
entry.
empirical
in Bergin and Corsetti
shocks
firm entry to monetary
(2005) and
policy
in figure 5.3 is associated
This induces an increase
Lewis
model
terest
with
of our benchmark
(2006). Here, we present a simple modification
in the in
to
reductions
of
that delivers a positive
response
entry
rate.
rather
that the entry cost/E,,
of assuming
in units of the
of effective
labor, is defined
basket, Ct: Instead of hiring labor, entry now requires pur
consumption
a
in the
this basket has ex
where
basket
of materials
chasing
amount/"^,
as consumption,
same composition
and we introduce
the su
actly the
The modification
than being
defined
consists
in units
Monetary
Policy with Endogenous
Entry & Product Variety
333
case.
the notation
relative to the benchmark
perscript C to differentiate
As a consequence
the
of this modification,
of
sector
output
consumption
now coincides with GDP: Yt = Nt ptyt = wtLt +Ntdt, and there is no
longer
of labor between product creation and produc
any sectoral reallocation
tion of existing
The new assumption
the following
goods.
implies
in
the
model
of
table
5.1:
in
the
for
Yt replaces Yf
changes
expressions
no
an
and
to
is
have
defin
markup
profits (it
equation
longer necessary
ing Yf), and the free-entry condition equates the value of the firm tofEt.
In log-linear
The new
new
firms
Keynesian
Phillips curve is unaffected.
condition
in
free-entry
implies that the price of investment
in units of consumption
is now constant absent exogenous
terms,
the New
such shocks,
changes
in/-f, due to changes inmarket
regulation. Absent
to 1, the model
and
to one in which
reduces
the con
normalizing/^
in
of
investment
firm
creation
is
constant
and
sumption-based
price
one
as
to
of
in
unit
the standard RBC setup
equal
consumption?exactly
without
costs of capital adjustment.
this does not imply
Importantly,
=
that the price of investment
in data-consistent
evaluated
units, vRt
vj
pt, or the nominal
price of investment,
Vt, are constant. But the even
our entry model
between
and the familiar RBC
tighter isomorphism
in welfare-consistent
we now discuss.
framework
which
from regulation
Abstracting
free entry, no-arbitrage
between
(1
b)Et[(CM)-\l
+ dt+1)\ =
Et
units
has
important
implications,
=
1, and imposing
changes,
setting/^
bonds and shares now implies:
(Ct+1)-\\+tc
(16)
In log-linear terms, amonetary
policy shock that reduces the ex ante real
+
t and t
interest rate between
1 lowers expected profits for period
t+
1.However,
it necessarily
leaves the expected present discounted
value
of profits over the infinite future unchanged,
to preserve
the free-entry
= 1.
condition^
We log-linearize
the modified
model
around the zero-inflation
steady
state. Figure 5.5 presents
the impulse
of the log-linearized
responses
to a zero-persistence
1 percent decrease
model
in the interest rate under
three alternative parametrizations
for interest rate setting: Round mark
ers denote
the responses under the rule it=
+
0.81^
0.3irt + ?}, cross
markers denote the case \t= 0.81^ + 0.3tt, + 0.1YR t+
and
square mark
?j,
=
ers denote the case
+
+
In
all
three cases, the central
it 1.5irt
0.5YRt
?j.
bank is responding
to current rather than expected
inflation. By tying the
stock
market
of
in
investment
equilibrium
price
product creation to the
334
itocsi
ptocsi
-0.4
p^tocsi
tocsi
Ntocsi
NE
4
Ltocsi w
i i5i
*T\
0
10
15
m
tocsi
' ' ' ' '
""'
5
u0
l[
0
10
d tocsi
A
\?f
5
01|f>j^?-^-?"0
.
5
I -151j
0
5
15
10
to
_V
10
15
g
0
A
T
|
15
rtocsi
csi
to
,1
5
10
15
u0
11/
5
5
15
u0
I -15lj_|
15
0
5
10
5
15
^ ,,,,?
JH,
0
5
10 15
15' 1515
o^?
0
5
Figure
4_j
u0
^V^maul
L^V^L-.-_J
10
15
5
10
15
Q U^?-4M^_1-JLI-JLJ
0
5
10
15
5.5
interest rate shock, persistence
responses:
Impulse
=
+ .3irr Cross markers:
Round markers:
it M^
ers: i, = 1.5tt, + .5YRr
exogenous
framework
0, entry cost in units of consumption.
=
+
+
it
.81^
3irt
TYR,. Square mark
the model behave exactly as the RBC
entry cost and making
in the investment
the modified
dimension,
setup reintro
and Fuerst (2005): if interest
the problem highlighted
by Carlstrom
rate setting responds only to expected
inflation, the no arbitrage condi
the economy
tion (16) features only expected
future variables,
exposing
to indeterminacy.39
For this reason, we restrict attention to rules inwhich
duces
to current
the conse
inflation,
responds
studying
a
rate
to
data-consistent
and/or
quences
response
smoothing
in figure 5.5 are computed
GDP. The responses
for the same parameter
values as the responses above, focusing on the case in which
the elastic
= 2.
that
of
labor
is
the
shows
the re
of
cp
ity
Inspection
supply
figure
the central
bank
of interest
15
n-^
Y to csi YR'?csi
csi
10
vEtocsi
"? ? ?m
Oii^-Q8
10
10
?5
^\
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0
\\\
i ,on
5
5
1 \
20
rtocsi
Ctocsi
Vi>_
i)' 5 10 \t 'fj 5 10IB oLH?fc='M
0I! 5 1C?15'"IfT'W'ls'
]
and Melitz
0.2 -02
\
^.'?'3
-0?2
0.4
| ?'2
-06
L_
I
Bilbiie, Ghironi,
Monetary
Policy with Endogenous
Entry & Product Variety
several key features of those
sponses preserve
lowers the real interest rate and has expansionary
in figure
335
5.3: the shock
for
consequences
and
GDP.
and
The
the
real
falls
increases.
wage
sumption
markup
the price of investment no longer rises. Even if
portantly, however,
in consumption
demand with unchanged
profits fall, the expansion
con
Im
firm
firm
draws more
firms into the market,
and the number of entrants in
all policy rules.40 Labor effort expands because
there is no
a
use
as
in
contraction
in figure 5.3.
the
of labor for firm creation,
longer
The response of the number of entrants is very large under the rule \t
=
over 80
in investment
0.8i^_1 + 0.3TTt + ?j, with an impact expansion
a
above
the
state?and
percent
steady
large expansion
correspondingly
in GDP. This result is another consequence
of reducing
the investment
value
creases under
side of the model
it is a familiar
costs,
volatile. When
to the standard
RBC setup: absent capital adjustment
that investment
is excessively
value of the firm is tied to 1, our model
result of RBC models
the equilibrium
a re
this
result. Policy, however,
reproduces
plays a role: introducing
to
rate
GDP
in
interest
the
of
invest
sponse
setting dampens
volatility
=
ment and GDP, as highlighted
by the responses under the rule \t 0.8if_a
+ 0.3tt, + 0.1
+
and GDP is fur
1.Finally, the volatility of investment
Y^
ther dampened
interest rate smoothing
thus reducing
the
by removing
as
rate
of
the
interest
shown
the
movement,
persistence
responses
by
under the rule \t= 1.5irf + 0.5YR, + ?j.
or
We omit the responses
to productivity
shocks in this
deregulation
on request).
under
the three
(they are available
Importantly,
=
a
discussed
rules
and
with
cp 2, positive productiv
previously
policy
0.979 now causes
to fall and the
inflation
ity shock with persistence
scenario
markup
to rise on impact, as in the benchmark
because
the link between
precisely
happens
cost (which was providing
the extra channel
sults in our baseline model)
is absent when
fixed-variety model. This
firm value and marginal
re
the opposite
generating
entry requires purchasing
The markup moves
in countercyclical
fashion only under the
=
policy rule i, 0.8i,_a + 0.3ir, + 0.1 YRt + ?j because YRJails on impact un
der this rule.41
materials.
To conclude, assuming
that the entry cost is in the form of
purchasing
materials
rather than hiring labor brings the predictions
of the model
in
to
shocks
closer
the
in
evidence
and
response tomonetary
policy
Bergin
Corsetti
(2005) and Lewis
However,
(2006), at least qualitatively.
pre
the
feature
that
this result also has some less appealing
generates
cisely
the link between monetary
implications:
policy and inflation through eq
the
that
uity prices disappears,
undermining
properties
determinacy
on
this
link.
More
the
crucial
role
of
movements
allocative
rely
generally,
336
Bilbiie, Ghironi,
and Melitz
in (welfare-consistent)
firm value (the relative price of investment)
dis
this version of the
appears in this variation of the model.42 Additionally,
sec
model
introduces an important asymmetry
between
the investment
tor (creating new product varieties) and the production
sector in terms of
the consequences
in the defini
of the "love of variety" effect embedded
tion of the consumption
basket. Ceteris paribus, an increase in variety in
creases
in
sector while
the investment
productivity
leaving that in the
sector unchanged.
In the benchmark model,
any changes due
production
to the variety effect did not have such relative productivity
implica
tions.43 Ifwe
business
benchmark
7.2
discount
cycles,
exogenous monetary
these features of the modified
specification
Endogenous
as a starting point
Aggregate
Stickiness
a source of
policy shocks as
model
lead us to prefer our
for analysis.44
and Producer
Entry
So far, we have assumed
that new entrants are subject to the same nom
inal rigidity as incumbent
firms. It is plausible,
that new en
however,
trants in period twill make their first price-setting
in period t +
decision
a
to a past
1 without
to
relative
pay
cost-of-price
adjustment
having
in
In this case, heterogeneity
decision
price-setting
they did not make.
price levels arises across cohorts of firms that entered at different points
on the mar
in time, as their price-level
decisions will differ depending
at
cost
time
of
thus
de
conditions
the
entry,
affecting price-setting
ginal
cisions in subsequent
The
of
aggregate price rigidity in
periods.
degree
as
the number of new price-setters
the economy becomes
endogenous,
relative to a past price decision varies with
that face no cost of adjusting
the business
cycle.45
on re
in the appendix
the extended model
(available
present
an
features
infinite number
the model
quest).46 Prior to log-linearization,
of state variables
(we assume that the economy has existed since the in
finite past; thus, the set of currently producing
firms, Nt, includes repre
We
sentatives
that in log-linear
in period
entered
us
we show
cohorts). However,
decisions
the time-t price-setting
of firms that
of an infinite number
of entrant
terms,
r- 2 and further
to characterize
in the past are identical.47 This allows
firms in
behavior
of producing
of only two sets of firms: those that
the log-linearized
terms of the representative
members
are one period old at time t (and thus are taking their first price-setting
on the timing of entry and production)
decision, given our assumptions
and those who are two or more periods old.
Under
the assumption
that new
price-setters
take into account
that
Policy with Endogenous
Monetary
Entry & Product Variety
337
a
they will be subject to cost of adjusting prices relative to their previous
choice from their second period of price setting on, optimal behavior
over marginal
cost in the first pe
does not result in a constant markup
riod of price setting, since new price-setters
the incentive to
incorporate
the initial choice and the next pe
smooth price movements
between
costs. For
riod's price implied by the expectation
of future adjustment
of comparison, we also consider the scenario inwhich we
completeness
assume
the constant
that new price-setters
simply
charge
elasticity
over
cost.
0/(6-1)
markup
marginal
to a 1 percent productivity
increase
the responses
Figure 5.6 presents
with
0.979
persistence
in which
model
new
for the benchmark
model
the
(round markers),
do not pay a cost of price adjustment
but
in
future costs (cross markers),
and the model
entrants
take into account
optimal
entrants
charge
new
which
it 0-01
0-005!
| 0'01[[.".
I ?-005
LArtP
5 TtT15?20
x103
0
.
5
Figure 5.6
Alternative
Shock,
future
5
\
\
\J
10 15 20
LEtoZ
LctoZ_
'--^?^3
0
10 15 20
.^.0.005 \
?Xj "?-01fX**"^ i -001\
*S**
t^r^tTT^?20
10 15 20
0 5
10 15 20
J \^0.1
10M5~*20
?0 5
1I
\
0-5!
0lU
|
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j-0.0051
15
o.2
0
LI-,
5
001II" _~!
NtoZ
NEtoZ
8
; 0.35
1.5
r
0
?
0.01
f
rtoZCtoZ
J \
-5 j
1
-0.01\
yS
|_I
o
j p=p^?
\-0.1/
/
"?'2
\ -?-3
j \ /
-0.4 J??-?
0
5
cost
1
0.005
!0.005
j-0.005\
\
marginal
pCtoZPAtoZ
j
0 jl_|Q
-0.005
j\ \
-0.01
-0.015\
over
markup
itoZ
ptoZ
~
0
a constant
\ ns\ \ UI) / \
15
1\
\
V
0.2
! Q
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I 5 10
?0
15 20
?-4
\0.3//>
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wtoZ YtoZ
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08[T\
I 0.8
j
\
I \?6 \
06 \
04
\?-4
X
/0.20.2
^
u
10 15 20
0Ju0
10 15 20
5
on Initial Price Setting:
Assumptions
Impulse
Variables.
Round markers:
Benchmark;
Aggregate
cost into account; Square markers:
Entrants
charge
(T-'-'
0
10 15 20
to
Responses
Cross markers:
constant
a
5
"i
10 15 20
Productivity
Entrants
take
markups.
338
(square markers).
exercises and we
Bilbiie, Ghironi,
and Melitz
We keep the same parameter values as in the previous
assume that labor supply is inelastic. For simplicity, we
rule inwhich
the central bank responds with coefficient
a
policy
In
1.5 to expected
inflation in producer prices in the benchmark model.
are
in
two
the alternative
there
models,
producer price
(log-linearized)
flation rates: one that measures
the change in the initial price set for time
assume
tby firms that entered at t-1 relative to the initial choice at t-1 by those
that entered ait-2,
and the other measuring
inflation in producer prices
to producer
prices in the bench
by older firms. However,
responding
to the empirically
amounts
to responding
mark model
consistent mea
sure of consumer
in
context
inflation
the
of
that
model
(since pro
price
consumer
is equal to welfare-consistent
inflation
price
price
the product variety effect that is not captured by avail
inflation minus
that in the alternative mod
able CPI data). For this reason, we assume
ducer
1.5 to inflation in an
els, the central bank is responding with coefficient
removes
consumer
that
the
level
pure product variety
average
Pt
price
=
Under
effect from the welfare-consistent
(Nt)1/{Q'1}Pt,48
price index Pt: Pt
to the empirically
rel
the central bank is thus responding
all scenarios,
evant measure
of expected consumer price inflation in the context of the
on aggregate quantities,
the nominal
relevant model.
Figure 5.6 focuses
consistent price index, in
and real interest rates, inflation in the welfare
inflation in Pt (de
in producer
prices in the benchmark model,
in the alternative models,
and the real wage. The responses
tt^)
are virtually
In
identical across models.
variables
of nonmodel-specific
to
in
of
the
that
identical
of tt^ is virtually
the response
addition,
irt
flation
noted
To explore the intuition for this result, figure 5.7 pres
that are specific to cohorts of firms. For
of variables
1
indexed by a superscript
than firm values, variables
and variables
firms in the alternative models,
refer to one-period-old
and the
refer to older firms in the alternative models
without
superscript
of
The
in
benchmark
firm
the
model.49
vt is the
response
representative
The
model.
firm
in
value
the
benchmark
of
response of v\ is
response
benchmark
model.
ents
the responses
all variables other
the response of the value
asset price that determines
of new
entrants
the allocation
in the alternative
of resources
models
(the
of firms
to creation
the responses
of existing goods). Although
point to
production
new
in
across
incumbents
and
of behavior
price-setters
heterogeneity
firm of the
of the representative
the behavior
the extended models,
versus
benchmark
bents
Given
model
from
is virtually
indistinguishable
is
models?and
vt
essentially
in the alternative
the assumption
=
0.025,
implied by 8
of a small
the virtual
incum
that of
to v\.
turnover
identical
rate of product
steady-state
across
identity of behavior
the repre
Monetary
Policy with Endogenous
Entry & Product Variety
toZ
ptoZ
p1
?'?6
339
r1toZ
rtoZ
0.005
?'2
/ //
?-15l
|
0.04
0 j\_j
0.2/ \
0.15
\\
\
^ lj
0-02
,-0.005 j
\
\
ai|?05
0
-0.01\
*S* 005f
jIL_^_J 0" 5^ltr*15?20?
0lTj10 "imT"^
?0 5' 10 15 20
mtoZ
m1toZ
"?02
-0.03/
-0.04
/
-?05lL
0 5
0
5
5
\
0'2\
0.3
M\\ \
>
?0
5
0.1I\\o.f\
~**A -?-1'
V ^~?~~
1 -01\
10 15 20
0
5
Figure 5.7
Alternative
Shock,
future
10 15 20
on Initial Price
Assumptions
Setting:
Impulse
Firm-Level
Variables.
Round markers:
Benchmark;
to
Responses
Cross markers:
cost
constant
sentative
into account;
Square markers:
firm of the benchmark
10 15 20
y1 toZ_ytoZ
0.151/ \
10 15 20
oil_^?
u0 5
15 20
1
05
?-5l
0.4
/ \ ^
\ 0.2j /X
0.1
^0.11/
\
\
-J
0U_^u0 5 10
10 15 20
a05
i0051
?0
V 0.1
0.1
'
\
vtoZ
_vt toZ_
I
\
\
l -Q06'y i
10 15 20
/\ /
0.2
M*/
_005/ ]
?-3\
a3\
?-2
02
02
V
1
11) 15 2U
H?b
d1toZ dtoZ
?,
m\f-o.oiF/ I
' -002
?-2
I/
/ /-0-03
\
-004 /
/
J
j
/
Entrants
model
charge
and
0
a
5
10 15 20
Productivity
Entrants
take
markups.
incumbents
that small departures
of the number of new
from
the
price-setters)
steady state have negligible
for aggregate dynamics
relative to the benchmark model.
in the alterna
tive implies
entrants
new
consequences
The
role of 8 for the differences
(and
across nominal
rigidity assumptions
by the extreme example of figure 5.8. There we present
as in
a
the responses
of the same variables
de
figure 5.6 to permanent
crease in the nominal
interest rate with the rate of product destruction
= 0.25. The shock causes a
set to the unrealistically
per
high value of 8
manent
in
increase in inflation and thus a permanent
the
number
drop
is best
illustrated
of producers,
to production
consequences
and a permanent
reallocation
of labor from firm creation
of incumbent
with
Consistent
the real
intuition,
goods.
smaller as we move
of the shock become
the
bench
from
340
(-
.
I TC0O0OOO0O00
"j?
|
'
1.5
csi
i to
csi
p to
y*> COO'0O:'00OOOir
,
1.5 /
j
0-5
rtocsi
tocsi
10 15 20
5
10 15 20
12
__?
I-10
10
'
"20 3' -2
!
-40
0
,^
00
5
0
Figure 5.8
Alternative
"
?
?0
5
'
0
10 15 20^
Assumptions
Shock. Round
terest Rate
into account;
Square
0
to
csi
_
n lP csi_iPto
ooooo
'S-oooooop
14
i .30
H
|\.........E..
,
IAr.
-30|?s# )( )( )( )( )( )( )( )' )( )( X )CV*\ \ l OeOOOOOOOOOOOO
J_\_-_ -40
ln ^k
I .
0
NE tocsiNtocsi
n
\J
p?-,-,-,
pj-.-,
'20
I
(\
U
'"
4
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^ ? Ll .
10 15 20
5
10 15 20
0
)()()< mX )( )( )( )l )( )i
^u0
5
10 15 20
I 2
5 I
A I'
o4-1
H... IIIIMn Mu IIn Mu
5
10 15 20
on Initial Price
'
-A _. >^H ji H ]nH S S n L^ r
0
5
to a Permanent
Setting:
Impulse Responses
Cross markers:
Entrants
take future
Benchmark;
Entrants
charge constant markups.
10 15 ~20
In
cost
to the model
in which new price-setters
take into account
the future cost of price adjustment,
inwhich
and from this to the model
new price-setters
a constant
This is in line with de
charge
markup.
as
we
move
nominal
to the
from one model
creasing aggregate
rigidity
mark model
next. Nevertheless,
turnover (and
unrealistically
large average product
are
our
in
shock
for any no
model
extremely high
persistence)
required
as a consequence
to emerge in shock transmission
ticeable difference
of
more
7.5
flexible price-setting
Non-CES
Having
yields
by new
entrants.
Preferences
verified
results
behavior
that our benchmark
that are robust
I
w to csi
Ytocsi_
*>
markers:
markers:
?l) b' 10 1b 20
: -io.-io|
m
.3 4
5
\
?(j b" 10 1b 20
(J
/.1
\l
I
2.5!
] 05
nC
AA r-9-,-.-.-]
(J |-r- -.0 ODO 0 OOODO O
tocsi
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PA
i\f\ 411
5|
2;
1 1 1.5^
3|l 000000008BO
L
0.51
?0 5' 10' 15'20'
?0 5 10 15 20
^0
-.-.-.
r-ip-r-.--.-.-,
and Melitz
Bilbiie, Ghironi,
on price stickiness
assumption
to alternative
of pricing be
specifications
Monetary
Policy with Endogenous
Entry & Product Variety
341
on
assumption
by new entrants, we return to the benchmark
we
a
in
and
the
of
the
dif
model
consequences
pricing,
study
extending
ferent direction?allowing
for non-CES preferences.
the con
Suppose
form with elas
sumption basket takes a general, symmetric, homothetic
havior
A
derivation
across
in the
6(Nt) increasing
products
> 0]. This is the
BGM.
of
[Q'(Nt)
goods
assumption
a
that for CES preferences
delivers
mirroring
markup
ticity of substitution
number of available
individual
similar to (2), with d(Nt) replacing
9. The only other equation
equation
is the one governing
from table 5.1 that is affected
the variety effect,
=
=
which now becomes
pt
p(Nt)
p'(Nt)Nt/p(Nt).
We prove in the appendix
(available on request) that the (first-best)
price inflation remains zero under this general
The same policy rule (15) as in the CES case
preference
specification.
the
implements
optimal allocation, when combined with appropriately
fiscal instruments
studied in detail
(and lump-sum
financed)
designed
in Bilbiie, Ghironi,
and Melitz
We
the markup
(2006).50
log-linearize
for
this
around
the steady
equation
general preference
specification
optimal
rate of producer
zero
state with
in the translog
inflation, and parametrize
preferences
form introduced
(2003) and explored by BGM (with sym
by Feenstra
metric price elasticity of demand - [1 + crNJ, a > 0). Assuming
the cal
ensures
ibration scheme 6 (N) = 1 + crN = 6, which
of the
equality
state
across
we
CES and translog preferences,
obtain the New
steady
curve
for
inflation
under
Keynesian
producer
Phillips
price
translog
preferences:
it,
=
P(l
-
e-i
8)Efirf+1 +-(wt
Zt)
e-i\
- ?( i
+ ??
K
OK Nr
^2k
J
(17)
curve with CES
the difference
from the Phillips
(6):
preferences
the steady-state
benefit of additional variety is now half of its CES coun
in the number of firms has an
effect
terpart, and variation
independent
on the
via its effect on the elasticity of substitu
flexible-price markup
an additional
effect of the number of firms on inflation.
tion, generating
Notice
Figure 5.9 shows the impulse responses
crease with persistence
0.979 under CES
to a 1 percent
in
productivity
and
(round markers)
translog
for the benchmark
parameter values. We as
(cross markers)
preferences
sume that
to expected
inflation
policy responds
are
coefficient
1.5. Most
responses
qualitatively
ence
in producer
similar
prices with
across prefer
are noticeable.
differences
specifications,
quantitative
although
The most pronounced
are in the
differences
qualitative
markup
firm-level
The
is
below
the steady
responses.
output
markup
the horizon of the response under
throughout
translog preferences
and
state
due
342
itoZ
on?
ptoZ
I
Ne*oZ
NtoZ
Q25
08
V
0:6
?0 5 10 15 20
PtoZ
lr_vEJoZ_
0-2 ^C
|
015|
^^^J
?0 5 10 15 20
?0 5 10 15 20
Figure 5.9
CES versus
Round
10 15 20
T/
X-O.OSI/
?-15j/
X.I
0.1
/ < X\
1^^^^J ^ -0.1 /
0.05l[^
^*
0.2
5
10
15
20
?0
to the effect
i;
l4f^?r?1
j"0-5
|-?f
0 5 10 15 20
0 5 10 15 20
d toZvtoZ
! ?-2LrC\ I
\\
0.15/
Tj 0.4
0.2
0 5 10 15 20
\\
Q I \X^C.,J
j
0 5 10 15 ~20~' ?0 5 10 15 20
YtoZ
vtoZ
_^
~0| V _^Jj
"0 5 10 15 2cT
|
j \X
^
0.1|
0.05
! 0. \\
^
0.2i
to a Productivity
Translog:
Impulse Responses
=
markers:
CES Cross-markers:
it
Translog.
Policy:
substitution.
"
0r y1''j^a^
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.-.,
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002n
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and Melitz
Bilbiie, Ghironi,
?0 5 10 15 20
Shock, Persistence
1.5 Etirt+V
.979.
firms on the elasticity
of a larger number of producing
benefit of product variety
At the same time, the welfare
of
is
and so the response of the number
relative to the CES scenario. This
smaller under translog preferences,
to the shock is muted
of producers
the
response of the relative price and keeps
dampens
the transition.
above the steady state throughout
firm-level
To verify whether
have noticeable
translog preferences
we repeat the experiment
of table 5.2 under
implications,
output
quantitative
the translog
moments
of table
Table 5.3 replaces the model-generated
specification.
5.2 with the results of the flexible-price
model with translog preferences
are largely
(BGM translog) and its sticky-price version. The conclusions
to table 5.2, although?consistent
with what we
relative
unchanged
increase
the persist
noted previously?translog
noticeably
preferences
ence of producer price inflation: standard deviation,
and
autocorrelation,
are
now
and -0.61, respectively.
correlation of irtwith GDP
0.02,0.94,
Finally,
figure 5.10 augments
figure 5.4 by including
the model-based
Entry & Product Variety
Policy with Endogenous
Monetary
343
5.3
Table
Moments
BGM Translog
for Data,
Model,
and Sticky
Variable
X,
<rXt
YRt1.81
Investment,
E(^A-i) corr{Xt,
<VarRf
0.84
1.00
1.29
0.70
0.70
YRt)
1.00
CRt 1.35
0.75
0.81
0.74
0.60
0.63
0.80
0.78
0.74
0.88
0.95
5.30
4.27
4.01
2.93
3.42
3.11
0.87
0.66
0.69
0.80
0.96
0.98
Et 1.79
0.49
0.49
0.99
0.39
0.38
0.88
0.66
0.68
0.88
0.95
0.97
vRtNEt
Source for data moments:
0.6
1.25
Prices
King
and Rebelo
(1999).
-|-1
-1.2
-
-I-,-,-,-5-4-3-2-1012345
-A-Data
Figure
-D-
BGMTranslog
-,-,-,-,-,-1
- ?
Sticky CES -X-Sticky
Translog
5.10
The Cyclicality of theMarkup (2)
markup
cyclicality
in the translog model with sticky prices.
shifts the correlation between markup
Introducing
and GDP at
translog preferences
in
in the
leads and lags
the right direction
through the effect of variation
on the elasticity of substitution. However,
number of producers
the con
becomes even more excessively
negative. The
we consid
best
model
remains
the
those
flexible-price
translog
(among
at
the
of
the
ered)
reproducing
cyclicality
markup.51
temporaneous
8
correlation
Conclusions
This paper studied the implications
of introducing
endogenous
product
creation in a sticky-price model
of the business
cycle suitable for mone
is endogenous
and the price-setting
tary policy analysis. When variety
to
individual
distortion
first-best
pertains
prices,
producer
optimal
monetary
policy should aim at stabilizing product price inflation and let
consumer
to accommodate
the welfare-relevant
price index fluctuate
a novel mo
in
the
number
of
Our
model
changes
products.
highlights
0.98
344
Bilbiie, Ghironi,
and Melitz
occurs because
tive for price stability, which
inflation acts as a distor
on
tax
to firms for
firm
and
incentives
tionary
profits,
profits provide
creation.
product
Our model
also
identifies
a new
channel
for monetary
policy
trans
the price of equity (the value of a firm or product). This
in a way that is ab
in the inflation-dynamics
price
equation
sent from standard
to the connec
due
models,
fixed-variety
precisely
tion between
the markup
(and marginal
cost) and the price of equity via
mission
through
is featured
since our model
the free-entry condition. Moreover,
embeds a portfolio
decision between holding equity and bonds, monetary
policy influences
that relates the real
the price of equity through a no-arbitrage
condition
return on bonds
to the expected
real
(which the central bank influences)
on equity. This link between
and monetary
inflation dynamics
policy through assets prices is central to the validity of the Taylor Prin
in the
model with capital accumulation
ciple in our endogenous-variety
new
lines. This is unlike results from fixed-variety
form of
production
return
models
with
physical
capital.
for inflation dynamics
product variety has implications
Endogenous
curve
New
and the estimation
of
Empiri
Keynesian
equations.
Phillips
in
to
to
order
need
be
amended
cal proxies for (unobservable)
markups
estimate
Phillips
curves
in
the
presence
of product
creation.
Moreover,
curve in the presence
of endogenous
that the Phillips
variety
that
features an extra term (with respect to its fixed-variety
counterpart)
a
on
state
variable.
This
the number of available varieties,
goes
depends
in the direction of alleviating
the notorious
difficulty of New Keynesian
we
show
with
forward-looking
persistence
an
bias that is present
endogeneity
identify
price setting. Finally,
curve ignore product
and
estimates
of the Phillips
whenever
variety
on
hence attribute the endogenous
component
coming from its impact
models
in accounting
for inflation
we
shocks.
to exogenous
cost-push
dynamics
simi
exercises show that the sticky-price model performs
Numerical
in terms of matching
several fea
counterpart
larly to the flexible-price
inflation
a policy
that is plaus
specification
with
the
Consistent
presence of
policymakers.
an
in
the
model
variable
the
generates
Phillips curve,
endogenous-state
are confirmed by two
results
These
inflation
persistent
dynamics.
fairly
tures of the U.S. business
cycle, given
ible for inflation-sensitive
alternative
of the benchmark
assumptions
setup: studying
new
entrants
and the conse
decision
for the initial price-setting
by
exten
Another
quences of non-CES
translog) preferences.
(specifically,
a
in which
version of the model
sion studies
entry requires purchasing
extensions
Monetary
Policy with Endogenous
Entry & Product Variety
345
firm
labor. In that model,
the link between
cost implied by free entry disappears:
value and marginal
production
an
in entry, but technology
induce
increase
shocks
monetary
expansions
a
and
immediate
wider
deflation
for
generate
procyclical
markups
materials
range
rather
of parameter
than hiring
values.
Recent
literature has documented
the pervasiveness
of
empirical
a
at
that
is
relevant
busi
creation
and
destruction
for
product
frequency
ness cycle
a
This paper provides
propagation.
starting point for incor
inmonetary
models
of the business
poration of this phenomenon
cycle
suitable
for policy analysis. Like the benchmark New Keynesian model
fixed product
the benchmark
model
of this paper has
variety,
an
from
Combined
empirical,
quantitative
shortcomings
perspective.
with
the procyclical
of entry to productivity
shocks, price
response
with
stickiness
induces excessive
of markups
relative to
countercyclicality
the data. However,
the model highlights
realistic consequences
of prod
a
new
uct creation subject to sunk costs (persistence),
motive
for price
a
new
and
connection
between
and
stability,
monetary
equity
policy
literature. The
prices that is not featured in the previous New Keynesian
to generate procyclical
ability of the model
entry and profits
producer
in
the presence of such countercyclical
im
(even
markups)
significantly
benchmark with respect to these stylized
proves on the New Keynesian
facts. Quantitative
extensions
to address
the introduction
short
remaining
empirical
of congestion
in
effects
entry
and the counter
of real wages
instance,
the procyclicality
dampen
of
be easy to pursue.52 Thus, we view the
cyclicality
markups?would
model
of this paper as a promising
stepping stone for future research on
a variety of positive
and normative
in potentially
richer mon
questions
with
models
etary
endogenous
entry.
producer
comings?for
that would
Acknowledgments
For helpful
comments, we thank Daron Acemoglu,
Virgiliu Midrigan,
Gemot Muller,
and participants
in
Julio Rotemberg, Michael Woodford,
the Twenty-second
NBER Annual Conference
on Macroeconomics,
the
Konstanz
Seminar on Monetary
Thirty-eighth
Theory and Policy, and a
at
are
seminar
Boston College. We
Mar
Giovannini,
grateful toMassimo
and
Frank
for
excellent
research
assistance.
Remain
Rubio,
garita
Virga
Bilbiie thanks the NBER for hospitality
ing errors are our responsibility.
as a Visiting
Fellow while
this paper was written.
Ghironi
and Melitz
thank the NSF for financial support
through a grant to the NBER.
346 Bilbii, Ghironi,
and Melitz
Endnotes
1. See, for instance,
the IMF's GEM model
and the Federal Reserve
Board's
others)
and Gust 2005, among others).
2003, among
(illustrated
by Laxton and Pesenti
SIGMA model
(illustrated
by Erceg, Guerrieri,
2. Rotemberg
and Woodford
the implausibility
of positive
(1995) addressed
returns
to scale induced
profits by assuming
increasing
by fixed, per-period
to fall below
zero
this assumption,
ever, under
any shock that causes profits
erate exit and induce a nonlinearity
in firm decisions.
steady-state
costs. How
should
gen
and Cooper
3. See Campbell
and Lapham
Head,
(1998), Chatterjee
(1993), and Devereux,
in Bilbiie, Ghironi,
similar evidence
and Melitz
(1996a, b). We illustrate
(2005).
4. Bernard,
disaggregation:
new
and Schott
(2006) measure
Redding,
a 5-digit U.S. SIC code. Contributions
level would
be substantially
aggregated
further details.
higher.
at a relatively
goods
creation
of product
See Bilbiie,
Ghironi,
coarse
and Melitz
can be very
the level of product
high in the Broda
substitutability
that product
their evidence
creation
is concentrated
suggests
sample,
uct categories
that are much more differentiated
(nonfood
products).
5. Although
stein (2007)
over
level of
at a more
dis
(2005)
for
and Wein
in prod
to
Calvo-Yun
(1983, 1996) setup
at dif
that entered
of price-setters
with monopolistic
business
competition
cycle models
flexible-price
and Cardia
and endogenous
(1998) and Cook
(2001). Comin
entry also include Ambler
re
and Gertler
(2006) are more
(2004), Jovanovic
(2006), and Stebunovs
(2006), Jaimovich
choose
6. We
model
the Rotemberg
in prices within
avoid
heterogeneity
ferent dates. Earlier
cent
with
to the theoretical
contributions
the familiar
and across
literature.
cohorts
for a discussion
See BGM
of the relation
our model.
a product,
a producer,
and a firm, in our model.
7. There is a one-to-one
between
mapping
use the word firm to refer to an indi
recent literature, we routinely
For consistency
with
with
line associated
The latter is best thought of as a production
vidual unit of production.
a
can potentially
within
be introduced
incumbent
firms, where
specific good. These goods
for their production
decisions
make profit-maximizing
independently
product managers
lines. Our model,
thus, does
not
address
the boundaries
of the firm.
in production
we augment
to include
of existing
the model
capital
physical
new
than the standard RBC
the
does
better
model
and
of
creation
lines,
production
goods
a
and persistence
of U.S. GDP. However,
at matching
framework
high rate of
volatility
to have a unique,
solution.
for
the
is
model
nonexplosive
required
capital depreciation
8. When
to an em
is also related
be targeted
by policy
for
CPI data do not account
that occurs because
problem
manner
in the welfare-consistent
by the model.
prescribed
of the welfare-based
CPI is a biased measure
cost-of-living
a recent and growing
Broda and
for example,
literature?see,
index, as documented
by
stabilize CPI inflation.
that the central bank should
Weinstein
(2006). Broda
(2004) argues
is
ifmeasured
CPI inflation
of our model
with
the prescription
This is not inconsistent
9. The
issue
of what
inflation
rate should
relevant measurement
pirically
the introduction
of new goods
the observed
As a consequence,
closer
to average
product
price
inflation
than
to welfare-based
consumer
price
inflation.
Monetary
(2000) were
and Gertler
and King
(1996) and Clarida, Gali,
in the now-standard
New Keynesian
10. Kerr
result
347
Entry & Product Variety
Policy with Endogenous
framework.
the first to derive
this
a related
(1991) has
Leeper
dis
cussion.
same
11. The
sumer
12. Sbordone
mates
(2002)
when
obtained
calibration
scheme
of labor used
share
monetary
analysis?that
in our model.
prices
inflation,
subject to the caveat
implied by
con
should not target welfare-consistent
CPI
for welfare-consistent
holds
our normative
policy
does not affect the esti
that using
this corrected measure
a
Our
framework
the
baseline
proxy.
suggests
markup
specific
using
in this correction,
labor used
based on the
for the share of overhead
showed
for creating
new
products.
a version
we also consider
of comparison,
13. For completeness
new price-setters
set their initial price as a constant markup
simply
in which
of the model
over
marginal
cost.
in Lewis
and Mancini
Griffoli
(2006) and Elkhoury
(2006) are in principle
on
to one of the problems
that our approach
aims to address:
they rely
monopoly
as a
stone
nominal
but
abstract
from
for
entry
stepping
they
rigidity,
(by workers
14. The models
subject
power
or
lawyers)
15. We
in the presence
relax
17.
will
of the equilibrium
If vt(u>) < wJEt/Zt,
prospective
in zero entry.
resulting
18. We
omit
profits.
in the following.
this assumption
16. Symmetry
cost,
of monopoly
the transversality
/?,_i(w)
imply
entrants
conditions
=
Pt-i^^
not be
willing
will
for bonds
to incur
that must
and shares
the sunk-entry
to en
be satisfied
sure optimality.
that using
this corrected measure
does not affect the
(2002) indeed showed
a spe
obtained when
the baseline markup
proxy. Our framework
using
suggests
cific calibration
for the share of overhead
scheme
labor used in this correction,
LJ
namely:
L = 8( |x-1) / (r + 8|jl), where we denote
levels of variables
the sub
steady-state
by dropping
our baseline
that follows,
this is approximately
0.20; the
script t. Under
parameterization
19. Sbordone
estimates
upper
bound
20. We
suggested
leave
the markup
estimation
for future
by the empirical
of Phillips
research.
curves
results
using
of Basu
these
and Kimball
alternative
(1997)
profit-based
is 0.25.
proxies
for
21. Returning
to the normative
the central bank should
stabilize pro
prescription?that
ducer prices?our
model
that if the central bank targeted CPI inflation,
the bias in
implies
itsmeasurement
to the extent that biased CPI inflation
would
indeed be beneficial
is closer
to producer
22. We
price
consider
inflation
rules
consumer
than welfare-consistent
featuring
a response
to GDP
inflation.
price
YRt in section
7.
removed
does not hinge on having
the variety
effect
argument
can be made
and dividends.
The same argument
the Phillips
by using
and the no-arbitrage
in welfare-consistent
condition
terms.
23. This
24. Details
are available
from equity
curve
prices
equation
(7)
on request.
25. The problem
is only partially
in order to endogenize
(introduced
solved
by
the price
the introduction
of capital).
of capital adjustment
costs
and Fuerst show that
Carlstrom
348 Bilbii, Ghironi,
the Taylor
is restored
Principle
for forward-looking
cost.
the only interest
(15) is by no means
to design
It is, of course, possible
implausible
rate rule that implements
the optimal mon
rules that achieve
this goal.
alternative
etary policy.
27.
job destruction
8 takes place
Empirically,
the death shock
ance
for empirically
of the adjustment
parametrizations
26. Rule
rules only
and Melitz
of a product
explicit modeling
a
higher 8 implies
stating the ability
is induced
at the product
job destruction
generates
of multiproduct
less-persistent
of the model
firms, we
dynamics,
to generate
by both
level.
firm exit and contraction.
In our model,
In a multiproduct
firm, the disappear
firm exit. Since we abstract
from the
without
include
our choice
this portion
of job destruction
with
of 8 is also consistent
in 5. As
not over
persistence.
that is too high,
that the value of 6 results
in a steady-state
Itmay be argued
markup
to observe
to the evidence.
it is important
without
relative
However,
that, in models
any
over
cost. In
cost and average
fixed cost, 0/(6
of both markup
1) is a measure
marginal
our model with
that firms earn zero profits net of the entry
entry costs, free entry ensures
al
cost (inclusive
cost. This means
of the entry cost). Thus,
that firms price at average
= 3.8
a
over
de
cost, our parametrization
fairly high markup
marginal
though 0
implies
to pricing
costs. The main
and average
results with
livers reasonable
respect
qualitative
in a
ifwe set 0 = 6, resulting
that follow are not affected
features of the impulse
responses
and
and Woodford
of price over marginal
20 percent markup
cost, as in Rotemberg
(1992)
several other studies.
28.
29. This
requires
x
= 0.924271.
variables
deflated
of several macroeconomic
(the pro
responses
by average prices
are
the consumption-based
price index
qualitatively
price level pt) rather than with
re
similar. For instance, CRt increases with a hump-shaped
response,
except when
policy
a
to welfare-based
CPI inflation. YRt also rises, although without
hump.
sponds
30. The
ducer
31. Results
32. The
from policy
labor
inelastic
rules
case
featuring
a response
is in round markers;
to GDP
are available
on request.
=
cp 2 in cross markers;
and
=
cp 4 is in
square markers.
a
between
correlations
find that unconditional
that Bergin and Corsetti
33. Note, however,
or
are
measures
measure
and
of
of expansionary
net)
entry (gross
negative.
monetary
policy
34. We
should
note,
however,
condition
the free-entry
which
expansion
enough monetary
to the entry region studied
mass
a
ity and there is positive
omy
policy
would
have
of zero entry (in
started from a situation
that if the economy
v <
and NE = 0), a strong
holds with
wfE/Z,
inequality,
that brings
the econ
in share prices
could induce an increase
holds with equal
in this paper (in which
the entry condition
of entrants at all times). In that case, expansionary
monetary
as well.
an
of the model
effect on entry in this version
expansionary
as a
the role of exogenous
literature has downplayed
monetary
policy
empirical
eco
to
on the role of
in
instead
of fluctuations,
response
policy
systematic
focusing
as a mechanism
of the cycle (see, for instance, Leeper,
for propagation
conditions
and Zha [1996]).
35. The
source
nomic
Sims,
36. The period utility
the endowment
where
function
is defined
over
(1999),
(1 Et) in King and Rebelo
to 1. The elasticity
of labor
is normalized
cali
in leisure
(set to 1 in their benchmark
leisure
of time in each period
to variations
the risk aversion
L is steady-state
bration) multiplied
by (1 L)/E, where
=
cp 2 in our specifications.
yields
supply
is then
effort,
calibrated
to 0.33.
This
Policy with Endogenous
Monetary
the various
37. Of
measures
considered
of the markup
by
empirical
in our model
that ismost
closely related to the markup
2 of their table
is reported
in column
labor, whose
cyclicality
this is because
in figure 5.4. As mentioned
previously,
share-based
labor
the one
and Woodford,
Rotemberg
is the version with overhead
2
(p. 1066), and reproduced
can be written
in our model
as the inverse
markups
of the share
of labor (in consumption
=
lines, |x( Yf /[wt(Lt
product
as a share of con
is specified
the overhead
used to set up new
quantity
beyond
an additional
issue: this measure
There
of
course,
is,
EEt)].
as in
and Woodford.
output, not GDP,
Rotemberg
sumption
output)
little difference,
this makes
cality, however,
since
the share
to cycli
For issues pertaining
in GDP
of consumption
is rel
acyclical.
atively
real profits dR t increase on
0.979, but quickly
drop
persistence
in Nt that boosts DRt
low. It is expansion
a
with
response
hump-shaped
(figure is
38.
349
Entry & Product Variety
Firm-level
with
link between
39. The
the baseline
inflation
now
model
a favorable
shock
following
productivity
state and return to it from be
the steady
the transition,
above the steady state throughout
on
available
request).
impact
below
in (9) and discussed
at length in
prices reflected
no
cost
to the
because
is
marginal
precisely
longer tied
and equity
disappears,
of the firm.
value
of vRt, which
of vt, which
does not move, we report the response
in response
to the shock. Note
in the data-consistent
price of investment
that of NEi, since vE = vtNEr
sponse of vE coincides with
40.
Instead
cline
41. Computing
in no significant
42. Unless
we
improvement
introduce
costs
lines of familiar
relative
additional
ad hoc
of adjusting
correlation
to the benchmark
(purged
division
changes
product
costs of adjusting
the number
of firms along
the
capital.
further
alternative
specification
a
would
thus
lowers
is invariant
this cost of
to the latter.
combine
the two assumptions
by positing
of labor and materials.
The properties
of
on the relative
share of these two inputs in firm
combination
requires
Cobb-Douglas
to shocks would
then depend
responses
creation. We leave the development
of this version
traditional
for future work.
physical
capital)
tors,
in this case results
understand
that entry
of the model
(and the incorporation
of
and Sabbatini
and Stockman
(2004), Gautier
(2006), and Hoeberichts
more
in
of higher
sectors
of the econ
price flexibility
competitive
To the extent
that entry is more
sec
in more
they consider.
prevalent
competitive
this evidence may be suggestive
of a connection
between
and
stickiness.
entry
price
Fabiani, Gattulli,
find evidence
(2004)
omies
the cycle
model.
in product
of the variety
effect is l/pr Expansion
variety
creation
the pure variety
effect, while wRJEt /Zt
through
purged
45.
with
a de
that the re
that the cost of creating a new product
in real units
this, observe
=
of the variety
and
model, where wRt
effect) is wRtfEt /Zt in the benchmark
wt/pt,
=
removes
In
the
modified
the
effect.
absent
model,
pt
)1/(e_1)
pure
(Nf
variety
by
=
a new
in market
(i.e., setting/?f
1), the cost of creating
regulation
product
43. To further
44. A
of the markup
the time profile
shows
consumer
and Kurz-Kim
over the
in Germany
(2006) analyze
prices
period
account
into
the
effect
of
1998-2003,
taking
product
replacements.
They report that the in
are taken into account
cidence of price changes
increases when
it
replacements
(although
are
new
or
is not clear that replacements
in a
truly
products
just newly
adopted
products
Hoffmann
outlet).
particular
46. As
model
a
by-product,
by removing
the model
the assumption
in the appendix
also extends Rotemberg's
of a nature-given
initial price.
(1982) original
350 Bilbii, Ghironi,
47. We
the same
around
the model
log-linearize
as the benchmark
model,
prices
steady
the comparison
to facilitate
state with
zero
and Melitz
in all
inflation
to shocks.
of responses
48. The price index Pt is closer than Pt to empirical
CPI data for the reason previously
dis
that data do not account
of new products
at the frequency
for availability
relevant
cussed,
and in the form tied to our preference
for our model
Given
any variable Xt
specification.
in units of consumption,
in the extended
is thus
the data-consistent
models
counterpart
as: XR, = PtXt
defined
and Melitz
(2005) for further discussion.
/Pt. See Ghironi
rate tv]measures
49. The inflation
the change
at t - 2.
at t - 1 relative
to those that entered
rate of inflation
50. The
ment
trade
optimal
(Ramsey)
in which
lump sum
costs
the welfare
from both a time-varying
elasticity
extra variety with
the profit incentive
future research.
would
the welfare
against
of substitution
and
set by
those
The monetary
costs of markup
environ
authority
variation
would
coming
of the benefit
of
the misalignment
the
by
markup. We leave
provided
that entered
in a second-best
be non-zero
are unavailable.
instruments
of inflation
in the initial price
this extension
for
k below
the value of the nominal
Ire
rigidity parameter
surprisingly,
lowering
in
the performance
of the sticky-price
(2001) estimate
improves
translog model
at
terms of markup
leads
and
the
correlation
However,
contemporaneous
cyclicality
lags.
k as low as 5.
with GDP remains excessively
(-0.81), even with
negative
51. Not
land's
52. Congestion
when
pansions
effects would
entry
requires
also dampen
materials.
the positive
response
of entry
to monetary
ex
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