Download Optimal Monetary Policy with Endogenous Entry and Product Variety

Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Optimal Monetary Policy with Endogenous
Entry and Product Variety
Florin Bilbiie
Paris School of Economics, Univ. Paris 1 Panthéon-Sorbonne and CEPR
Ippei Fujiwara
Australian National University, CAMA and EABCN
Fabio Ghironi
Boston College, Boston Fed, EABCN and NBER
Conclusion
October 9 2012
1 / 62
Endogenous
Product Variety
Target Level of In‡ation in Practice
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
2 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
3 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Friedman Rule
I
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
If there exists no nominal frictions, in‡ation plays no
role in the determination of the real economic variables.
I
I
There is no concept for the optimal rate of in‡ation,
since in‡ation does not matter at all.
If there exists a nominal friction in the form of the
money as a transaction purpose, such as the Cash in
Advance (CIA) constraint, the optimal in‡ation is
negative.
I
I
Conclusion
I
This is the prescription known as the Friedman Rule.
When the nominal interest rate is zero, the opportunity
cost of holding money (cash) becomes the smallest.
Thus, the optimal in‡ation rate should be negative so
that the nominal interest rate is zero.
This classic idea is very intuitive but very much at odds
with current practices in central banks.
4 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Aims of this Presentation
I
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
To …rst show that zero in‡ation rate is the optimal
monetary policy in the standard New Keynesian Model,
which is the workhorse model in many central banks.
I
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
I
To also show why price stability (or in‡ation targeting)
is welfare-improving.
To show that in a model with endogenous product
variety, the Ramsey planner uses non-zero in‡ation (and
so trade o¤ some of the costs associated with it) in
order to close some of the ine¢ ciency wedges, namely
I
Conclusion
I
I
to minimize the gap between marginal rate of
substitution and transformation between consumption
and labor;
to smooth the intertemporal path of the markup;
to bring the pro…t incentives for …rm entry and product
creation closer to the bene…t of variety to consumers.
5 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Related literature
I Endogenous Product Variety
I
I
I
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
Positive analysis
Bilbiie, Ghironi and Melitz (2006)
Normative analysis
I
Bilbiie, Ghironi and Melitz (2008a, b, c); Bergin and
Corsetti (2008); Ghironi and Chugh (2009)
I Price Stability in a Standard New Keynesian Model
I
Adao, Correia, and Teles (2003); Khan, King, and Wollman
(2003); Schmitt-Grohe and Uribe (2007, 2011)
I Internalizing Externality (Ramsey Tax)
I
Ljungqvist and Uhlig (2000); Choudhary and Levine (2006); and
Faia (2006)
I No work of optimal non-zero in‡ation rate under endogenous
product variety!
6 / 62
Endogenous
Product Variety
Outline
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
1. Introduction
2. New Keynesian Model and Optimal In‡ation Rate
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
3. Model
Ramsey Optimal
Monetary Policy
5. Ramsey Optimal Monetary Policy
Optimal In‡ation
Rate
Conclusion
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
6. Optimal In‡ation Rate
7. Conclusion
7 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1. Introduction
Model
3. Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
Ramsey Optimal
Monetary Policy
6. Optimal In‡ation Rate
Optimal In‡ation
Rate
7. Conclusion
2. New Keynesian Model and Optimal In‡ation Rate
5. Ramsey Optimal Monetary Policy
Conclusion
8 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
What is the new Keynesian Model?
I
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
The new Keynesian model is a DSGE model where
prices are not adjusted immediately.
I
I
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
I
I
This is called nominal rigidities, or sticky prices.
Usually, we use time-dependent nominal rigidities as in
Calvo (1983), Rotemberg (1982) or Taylor (1980).
In this paper, we assume Rotemberg (1982) adjustment
cost, where …rms needs to pay the cost of price changes.
As a result, changes in nominal variables, such as
money supply or nominal interest rates by central
banks, can a¤ect real variables.
I
Note
MV = PY ,
or
M
= kY .
P
9 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
New Keynesian Model
I
Introduction
Each household in a complete market (or representative
household) maximizes the utility:
New Keynesian
Model and
Optimal In‡ation
Rate
χ 2
h ,
2 t
log (Ct )
Model
subject to the budget constraint:
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
At + Pt Ct = (1 + it
I
1 ) At 1
+ W t ht .
FONCs are
Pt
1
1
= β (1 + it )
,
Ct
Pt + 1 Ct + 1
Conclusion
and
χht =
1 Wt
.
Ct Pt
(1)
(2)
10 / 62
Endogenous
Product Variety
I
Bilbiie, Fujiwara,
Ghironi
Each …rm i under monopolistic competition maximizes
the pro…t:
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Pt (i ) Yt (i )
W t ht ( i )
φ Pt ( i )
2 Pt 1 ( i )
P t ( i ) Yt ( i )
Wt
Yt ( i )
Zt
φ Pt ( i )
2 Pt 1 ( i )
2
1
Pt Ct ,
or
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
2
1
Pt Ct ,
since the production technology is de…ned as
Ramsey Optimal
Monetary Policy
Yt (i ) = Zt ht (i ) ,
Optimal In‡ation
Rate
(3)
subject to the downward sloping demand curve:
Conclusion
Yt ( i ) =
I
Pt ( i )
Pt
θ
Yt
Firms need to pay adjustment cost when changing
prices. This creates nominal rigidity.
11 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
I
As a result, each …rm i set its price optimally to
maximize the present discounted value of real pro…t:
8
9
h
i θ
P t (i )
>
>
Yt
>
>
Pt ( i ) P t
>
>
Pt
>
>
<
=
∞
h
i
θ
C
t
t
P t (i )
W
Y
t
t
,
∑ β Ct + 1 >
Z
Pt
P
>
>
ht
i2 t >
t =0
>
>
>
>
: φ P t (i )
1 Ct ;
2 P t 1 (i )
where pro…t should be discounted by the household’s
marginal rate of substitution.
12 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
I
The FONC is
(1
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
θ ) Pt ( i )
θ
1
Pt
θ
Wt
+θ
Pt Zt
Pt ( i )
Pt
θ 1
Pt ( i )
1
1
Pt 1 ( i )
Pt 1 ( i )
Pt Pt + 1 ( i )
Pt + 1 ( i )
+ βφ
1
Pt ( i )
Pt2 (i )
= 0.
φ
Conclusion
13 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
I
Under symmetric equilibrium where Pt = Pt (i ) ,
Wt
φπ t (1 + π t )
Pt Zt
+ βφπ t +1 (1 + π t +1 )
(1
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
θ) + θ
(4)
= 0.
where
πt =
Pt
Pt 1
1.
Conclusion
14 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
I
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
it =
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
I
Conclusion
1
β
1 + απ t + ut .
(5)
The …nancial market clearing condition is
At = 0.
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
The central bank sets nominal interest rate following
Taylor type monetary policy rule as
I
The goods market clearing condition is
Yt = C t +
φ 2
π Ct .
2 t
(6)
15 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
I
The model consists of six equations for Ct , wt =
π t , ht and Yt from equations (1) to (6):
Wt
P t , it ,
1
1 + it
1
=β
,
Ct
1 + π t + 1 Ct + 1
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1
wt ,
Ct
Yt = Zt ht ,
χht =
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
wt
φπ t (1 + π t )
Zt
+ βφπ t +1 (1 + π t +1 )
θ) + θ
(1
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
= 0.
Conclusion
it =
1
β
1 + απ t + ut ,
and
Yt = C t +
φ 2
π Ct .
2 t
16 / 62
Endogenous
Product Variety
Price Stability
Bilbiie, Fujiwara,
Ghironi
Introduction
I
The resource constraint:
New Keynesian
Model and
Optimal In‡ation
Rate
Zt ht =
Model
or
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Conclusion
Zt
1 + 2 π 2t
φ
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
1+
φ 2
π Ct ,
2 t
ht = Ct ,
tells that any in‡ation is costly. In‡ation acts like a
negative technology shock.
I
Hence, the price stability should de…nitely be
welfare-improving.
I
If there exists no distortion other than nominal rigidities,
price stability is the sole aim of any stabilization policy.
17 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Price Stability (Calvo Pricing)
I
The resource constraint is
Introduction
ct (i ) = Zt ht (i ) ,
New Keynesian
Model and
Optimal In‡ation
Rate
or
Z 1
Pt ( i )
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
0
Pt
θ
diCt = Zt
Z 1
0
ht (i ) di = Zt ht ,
or
Zt
ht ,
∆t
where the price dispersion term is expressed as
Ramsey Optimal
Monetary Policy
Ct =
Optimal In‡ation
Rate
Conclusion
∆t =
I
Z 1
Pt ( i )
0
Pt
θ
di
Again, the price stability should de…nitely be
welfare-improving.
18 / 62
Endogenous
Product Variety
Distortions
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
I
1. (abovementioned) nominal rigidities
2. monopolistic rent
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
There exist two distortions in the above model.
I
Hence, it is not obvious whether it is optimal to achieve
zero in‡ation all the time.
I
We need to solve the Ramsey problem to derive the
optimal monetary policy.
Conclusion
19 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
Ramsey Optimal Policy
I
Given initial conditions, we should maximize the social
welfare
h
∞
χ 2i
t
β
log
C
h ,
(
)
t
∑
2 t
t =0
subject to the above system excluding monetary policy
rule:
1 + it
1
1
=β
,
Ct
1 + π t + 1 Ct + 1
1
χht =
wt ,
Ct
Yt = Zt ht ,
wt
0 = (1 θ ) + θ
φπ t (1 + π t )
Zt
+ βφπ t +1 (1 + π t +1 ) .
and
Yt = C t +
φ 2
π Ct .
2 t
20 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Divine Coincidence
I
I
CtMCE
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
I
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
Ramsey policy recommends complete price stability,
keeping the in‡ation rate always zero.
If price is ‡exible and no cost push shock is given to a
standard new Keynesian model,
=
I
χθ
Zt2
1
1 +σ
.
Under the Pareto optimal allocation,
CtPO
I
1
θ
=
1 2
Z
χ t
1
1 +σ
.
The log di¤erence between C MCE and C PO is always
constant irrespective of any policy.
This property of the standard new Keynesian model is
named as the divine coincidence by Blanchard and Gali
(2006). If the di¤erence is time-varying and can be
a¤ected by policy. Such a situation is called real
imperfections.
21 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
22 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
23 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Price Stability in New Keynesian Models
Proposition
In a model with …xed variety, CES-DS preferences, elastic
labor, and quadratic price adjustment costs, optimal in‡ation
in the Ramsey equilibrium is zero both in steady state and
over the business cycle.
I
The distortionary costs associated with in‡ation
outweigh the potential bene…ts obtained by even slight
variations in in‡ation that would lead to markup
erosion; hence, in‡ation is optimally not used.
I
Despite the ‡exible-price equilibrium being ine¢ cient,
Ramsey-optimal policy should still aim for price
stability, in the long run and over the cycle, in a variety
of setups (Schmitt-Grohé and Uribe, 2007, Adao,
Correia, and Teles, 2003, Khan, King, and Wollman,
2003, and others).
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
24 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1. Introduction
Model
3. Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
Ramsey Optimal
Monetary Policy
6. Optimal In‡ation Rate
Optimal In‡ation
Rate
7. Conclusion
2. New Keynesian Model and Optimal In‡ation Rate
5. Ramsey Optimal Monetary Policy
Conclusion
25 / 62
Endogenous
Product Variety
Endogenous Entry
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
I
Monopolistically competitive …rms can maintain positive
pro…ts forever is unrealistic.
I
Strong pro-cyclical behavior of net producer entry
(extensive margin), that cannot be explained without
…rm dynamics.
Ramsey Optimal
Monetary Policy
I
Optimal In‡ation
Rate
Conclusion
I
Endogenous entry is particularly popular in trade theory
after Krugman (1980) and Melitz (2003).
It is a simple model for real imperfections.
26 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Household
I
The representative household maximizes
∞
Introduction
Et
New Keynesian
Model and
Optimal In‡ation
Rate
∑ βs
t
U (Cs , Ls ) ,
s =t
where
1+ 1
Model
U (Ct , Lt ) = ln Ct
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
subject to
Ramsey Optimal
Monetary Policy
Bt +1 + vt NH ,t xt +1 + Ct
Optimal In‡ation
Rate
Conclusion
Lt ϕ
,
1 + ϕ1
= (1 + rt )Bt + (dt + vt ) Nt xt + wt Lt .
I
Firm dynamics are
NH ,t
Nt + NE ,t ,
and
Nt +1 = (1
δ) NH ,t .
27 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Firm
I
Firm ω maximizes the real value of the …rm:
∞
vt (ω ) = Et
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
∑
Λt,s ds (ω ) ,
s =t +1
where
dt (ω ) = ρt (ω ) ytD (ω ) wt lt (ω )
κ
(pt (ω )/pt 1 (ω ) 1)2 ρt (ω ) ytD (ω ) ,
2
and
ρt (ω ) pt (ω ) /Pt .
subject to the demand used for both consumption and
costly price changes:
∂ ytD (ω ) / (Ct + PACt )
∂ [pt (ω ) /Pt ]
θ (Nt ) ,
and production function:
yt (ω ) = Zt lt (ω ) .
28 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Symmetric Equilibrium
I
The free entry condition is
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
vt =
I
wt fE ,t
.
Zt
The resource constraint (goods market clearing) is
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
YtC
I
Ct + PACt = Nt ρt yt = Nt ρt Zt lt .
Financial market clearing requires
Ramsey Optimal
Monetary Policy
Bt = 0 8t,
Optimal In‡ation
Rate
and
Conclusion
I
xt = 1 8t.
Labor market clearing requires
Nt lt +
NE ,t fE ,t
= Lt .
Zt
29 / 62
Endogenous
Product Variety
Benchmark Model
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
I
Monetary Policy maximizes the welfare subject to the
above equilibrium conditions.
30 / 62
Endogenous
Product Variety
Pareto Optimal Allocation
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
I
Pareto optimal allocation is determined by the social
planner to maximize the welfare subject to the …rm
dynamics and resource constraint:
∞
max
L t ,C t ,N t +1
E0
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
∑ βt fln Ct
h ( Lt )
t =0
+ ψ1,t Nt
(1
+ ψ2,t (Ct
Zt Nt ρt ht )g.
δ ) Nt
1
+
Zt 1 ht
fE ,t 1
1
Ct 1
ρt 1 fE ,t
1
31 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Preferences
I
CES-DS is de…ned as
Z
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Ct =
I
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
ω 2Ω
ct ( ω )
(θ 1 )/θ
θ/(θ 1 )
dω
.
CES-Benassy is de…ned as
C t = ( Nt )
e
1
θ 1
Z
ω 2Ω
ct ( ω ) ( θ
1 )/θ
θ/(θ 1 )
dω
.
I
Summary
I
The results with CES preferences will be only shown in
this presentation.
Optimal In‡ation
Rate
Conclusion
32 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1. Introduction
Model
3. Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
Ramsey Optimal
Monetary Policy
6. Optimal In‡ation Rate
Optimal In‡ation
Rate
7. Conclusion
2. New Keynesian Model and Optimal In‡ation Rate
5. Ramsey Optimal Monetary Policy
Conclusion
33 / 62
Endogenous
Product Variety
Three Distortions
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
I
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
1. Labor supply is inelastic.
2. The bene…t of variety in elasticity form is equal to the
net markup.
3. Markups are constant over time and across states of
nature.
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
In a model with ‡exible prices, the competitive
equilibrium is e¢ cient if and only if the following three
conditions are satis…ed.
I
The last two conditions imply that preferences ought to
be of the CES-DS form.
34 / 62
Endogenous
Product Variety
Constant Markup across States
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
I
With labor priced at no markup in a competitive labor
market and consumption goods priced at a markup over
marginal cost, the heterogeneity in markups across the
arguments of utility results in distortion of labor supply
decisions.
I
The household “buys too much of the cheaper good”
(leisure), and so it ends up working and consuming too
little.
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
35 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
I
Model
1
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
The intratemporal optimality conditions for the labor
supply in the monopolistically competitive ‡exible price
equilibrium is
χhtϕ = Ct σ Zt ρt
I
θ (Nt ) 1
.
θ (Nt )
That under the Pareto e¢ cient allocation is
1
χhtϕ = Ct σ Zt ρt .
Conclusion
36 / 62
Endogenous
Product Variety
Bene…t of Variety vs Markup
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
I
When the welfare bene…t of variety e (Nt ) and the net
markup µ (Nt ) 1 (which measures the pro…t
incentives for …rms to enter the market) are not aligned,
there is either too much (if e (Nt ) < µ (Nt ) 1) or
too little (if e (Nt ) > µ (Nt ) 1) producer entry
relative to the social optimum.
Conclusion
37 / 62
Endogenous
Product Variety
Constant Markup over Time
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
I
Markup ‡uctuations over time and across states,
induced by changes in the elasticity of substitution as
the product space changes, are ine¢ cient because there
are not enough entry incentives in low-markup
times/states and too strong incentives for entry in
high-markup times/states.
Conclusion
38 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
I
The intertemporal optimality conditions in the
monopolistically competitive ‡exible price equilibrium is
Introduction
θ ( Nt ) 1
ρt fE ,t
θ (Nt )
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
= (1
I
δ) β
Ct + 1
Ct
σ
"
C t +1
1
θ (N t +1 ) N t +1
+ θ (θN(Nt +t1+)1 ) 1 ρt +1 fE ,t +1
#
.
That under the Pareto e¢ cient allocation with the CES
preference is
ρt fE ,t
= (1
δ) β
Ct + 1
Ct
σ
C t +1
θ (N t +1 ) 1 N t +1
1
+ρt +1 fE ,t +1
!
.
39 / 62
Endogenous
Product Variety
Discussion on Constant Markup
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
I
Conditions 1 and 3 together state that markups must
be aligned across items the consumer cares about, over
time, and across states.
I
Lerner (1934) documents that “If the social degree of
monopoly is the same for all …nal products there is no
monopolistic alteration from the optimum at all.”
Conclusion
40 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1. Introduction
Model
3. Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
Ramsey Optimal
Monetary Policy
6. Optimal In‡ation Rate
Optimal In‡ation
Rate
7. Conclusion
2. New Keynesian Model and Optimal In‡ation Rate
5. Ramsey Optimal Monetary Policy
Conclusion
41 / 62
Endogenous
Product Variety
Ramsey Optimal Monetary Policy
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
h
i
κ 2
π
Z
ρ
N
L
h ( Lt )
(
)
t
t
C ,t
∑
L t ,π t ,L C ,t ,N t +1
2 t
t =0
"
!#
Lt LCt Zt
+ η 1,t Nt +1 (1 δ) Nt +
fE ,t
κ 2
π
+ η 2,t [(1 θ (Nt )) 1
2 t
κ 2
+ θ ( Nt ) 1
π LC ,t hL (Lt ) κπ (1 + π t )
2 t
Nt 1 2κ π 2t
+ β (1 δ) κπ t +1 (1 + π t +1 )
]
Nt +1 1 2κ π 2t +1
"
!#
f
hL (Lt +1 ) ZE t,t++11
fE ,t
g.
+ η 3,t hL (Lt )
β (1 δ )
Zt
+ 1 LC ,tN+1 hL (Lt +1 )
∞
max
E0
βt fln
1
t +1
42 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Bene…t of Variety vs Markup
Proposition
In a model with endogenous entry, homothetic preferences
for variety, elastic labor, and quadratic price adjustment
costs, optimal in‡ation in the Ramsey equilibrium is zero in
steady-state only if preferences are such that the bene…t of
variety is equal to the steady-state net markup:
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
e (N ) =
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
I
Conclusion
I
1
θ (N )
1
.
As long as the above condition holds, zero long-run
in‡ation is optimal regardless of labor supply elasticity.
Since the product creation margin is e¢ cient, and the
planner was already not using in‡ation in the
…xed-variety case, endogenous entry does not give the
planner any additional incentive to resort to this
distortionary instrument.
43 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
In‡ation vs Markup
I
When the above condition does not hold, a non-zero
optimal long-run rate of in‡ation may emerge: Long-run
in‡ation a¤ects the steady-state markup and can be
used by the central bank to close the gap between the
pro…t incentive for …rm entry (the steady-state markup)
and the bene…t of variety e¤ect for consumers (e).
I
The central bank must weigh the bene…ts of this policy
against the welfare costs of in‡ation.
I
Note that the relationship between steady-state gross
markup and steady-state in‡ation (under the
assumption θ (N ) = θ) is given by
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
µ=
θ
(θ
1) 1
κ 2
2π
δ
+ κ 1r +
+r (1 + π ) π
.
44 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
I
When the bene…t of variety is always lower than the
markup (1 + e < θ/ (θ 1)), there is always too much
entry in the monopolistically competitive equilibrium.
I
The central bank cannot close this gap perfectly, but it
can use in‡ation to minimize it by choosing the value of
in‡ation that minimizes the steady-state markup and
hence reduce entry.
I
Using in‡ation entails welfare costs, though, so the
optimal value of in‡ation will balance these costs with
the bene…t obtained from moving closer to the lower
markup level (measured roughly by the distance
between the markup curve and the lower horizontal
curve in the …gure).
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
45 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1. Introduction
Model
3. Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
Ramsey Optimal
Monetary Policy
6. Optimal In‡ation Rate
Optimal In‡ation
Rate
7. Conclusion
2. New Keynesian Model and Optimal In‡ation Rate
5. Ramsey Optimal Monetary Policy
Conclusion
46 / 62
Endogenous
Product Variety
Parameters
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
47 / 62
Endogenous
Product Variety
Optimal Long Run In‡ation
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
48 / 62
Endogenous
Product Variety
I
Unless taste for variety and monopoly power coincide
(CES-DS preferences) and the steady state is e¢ cient,
the optimal rate of in‡ation in the Ramsey steady state
is non-zero.
I
With CES-Benassy preferences, the optimal steady-state
in‡ation rate is positive (negative) when the taste for
variety is smaller (larger) than the net markup.
I
When the number of …rms is suboptimally larger
(smaller) than in the Pareto optimal equilibrium, the
Ramsey-optimal steady-state in‡ation rate becomes
positive (negative) to reduce (increase) the markup, so
that less (more) …rms are attracted to enter the market
by less (more) pro…t opportunities.
I
The central bank chooses a non-zero optimal level of
steady-state in‡ation by trading o¤ the welfare costs of
in‡ation and the bene…t of reducing the misalignment
of taste for variety and pro…t incentive.
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
49 / 62
Endogenous
Product Variety
I
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
I
I
Sizeable deviations from price stability occur, ranging
from an annual in‡ation rate of almost 4 percent, when
the bene…t of variety is nil, to an annual de‡ation rate
of 8 percent, when the bene…t of variety is 1.
This new role of the steady-state in‡ation rate is absent
in the standard New Keynesian model with …xed variety.
Insofar as they pertain to the inability of the market
economy to internalize an externality and align
incentives and bene…ts between groups of agents in the
economy, our results are also related to those in
Ljungqvist and Uhlig (2000), Choudhary and Levine
(2006), and Faia (2006). Ljungqvist and Uhlig (2000)
and Choudhary and Levine (2006) study tax policies
purported to help internalize the externality stemming
from external habits (preferences that exhibit
catching-up-with-the-Joneses incentives). Faia (2006)
analyzes optimal monetary policy under matching
frictions that feature a congestion externality.
50 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
I
The quantitative signi…cance of these results hinges
upon one’s view of a plausible value for the parameter
governing taste for variety. Unfortunately, to the best of
our knowledge, decisive evidence as to a reasonable
value for this parameter is hitherto unavailable.
I
Therefore, our exercise should be viewed as on the one
hand providing a novel argument for potentially
signi…cant deviations from long-run price stability, and
on the other pointing to the need for more empirical
investigation into the nature of preferences for variety.
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
51 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Optimal In‡ation Rate over the Business Cycle
I
What is the optimal path of in‡ation over the business
cycle, in response to productivity shocks?
I
Over the business cycle, another distortion may emerge
in the ‡exible price equilibrium: the intertemporal
misalignment of markups. The central bank uses
in‡ation over the cycle to smooth markup dynamics and
undo the implied intertemporal distortion. The
‡exible-price response to shocks is ine¢ cient, and so
optimal in‡ation will vary over the business cycle.
I
This intertemporal distortion resembles the logic of
cost-push shocks in the plain vanilla New Keynesian
model; however, in our framework cost-push shocks
occur because of variations in the set of products.
Therefore, our framework can be viewed as providing a
way to endogenize cost-push shocks.
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
52 / 62
Endogenous
Product Variety
CES-DS
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
53 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
I
Optimal policy under CES-DS preferences consists of
replicating the ‡exible-price solution.
I
Although ‡uctuations in the ‡exible-price equilibrium
are not optimal (because of the presence of a
steady-state distortion driven by monopolistic
competition in the goods market combined with elastic
labor supply), the central bank should not try to
smooth these ‡uctuations using in‡ation.
I
Under CES-DS preferences, the previous literature’s
…nding that price stability is optimal both in the long
run and over the (productivity shocks-driven) business
cycle is robust to the introduction of endogenous entry
and variety.
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
54 / 62
Endogenous
Product Variety
CES-Benassy (low bene…t of variety)
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
55 / 62
Endogenous
Product Variety
CES-Benassy (high bene…t of variety)
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
56 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
I
Price stability is not the sole aim of monetary policy
under commitment unless the taste for variety equals
the markup and the steady state is e¢ cient.
I
The Ramsey-optimal monetary policy sets the
short-term nominal interest rate to reduce (increase)
in‡ation so that the markup becomes higher when the
di¤erence in the number of …rms between the Pareto
optimal and the ‡exible-price equilibrium allocations in
negative (positive). This is a new feature of optimal
stabilization policy that arises with endogenous …rm
entry and a distorted steady state.
57 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
I
Many previous studies with …xed-variety models (such
as Adao, Correia, and Teles, 2003, Khan, King, and
Wollman, 2003, Schmitt-Grohé and Uribe, 2007, and
others) show that Ramsey-optimal policy should still
aim for price stability, in the long run and over the
business cycle, despite the ‡exible-price equilibrium
being ine¢ cient.
I
This result no longer holds when variety changes
endogenously and the market economy does not
properly align incentives for product creation and the
bene…t of product variety.
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
58 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Welfare Cost in Consumption Unit
I
Since we use the utility function:
Introduction
1+ 1
L ϕ
,
u (C , L) = log (C ) + χ
1 + ϕ1
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
V0a =
∞
∑ βt u [(1
λc ) Ctr , Lrt ]
t =0
Ramsey Optimal
Monetary Policy
=
Optimal In‡ation
Rate
log (1 λc )
+ V0r ,
1 β
where V0r and V0a denote the welfare under Ramsey and
alternative policy.
Conclusion
I
Hence, the welfare loss in consumption unit is computed
as
r
a
λc = 1 e ( β 1 )(V 0 V 0 )
59 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
Ramsey Optimal
Monetary Policy
Optimal In‡ation
Rate
Conclusion
60 / 62
Endogenous
Product Variety
Bilbiie, Fujiwara,
Ghironi
Introduction
New Keynesian
Model and
Optimal In‡ation
Rate
1. Introduction
Model
3. Model
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
4. Sources of Ine¢ ciency in the Flexible Price Equilibrium
Ramsey Optimal
Monetary Policy
6. Optimal In‡ation in the Long and in the Short Run
Optimal In‡ation
Rate
7. Conclusion
2. New Keynesian Model and Optimal In‡ation Rate
5. Ramsey Optimal Monetary Policy
Conclusion
61 / 62
Endogenous
Product Variety
Conclusion
Bilbiie, Fujiwara,
Ghironi
Introduction
I
New Keynesian
Model and
Optimal In‡ation
Rate
We show that in a model with endogenous product
variety, a Ramsey planner use non-zero in‡ation (and so
trade o¤ some of the costs associated with it) in order
to close some of the ine¢ ciency wedges, namely
Model
I
Sources of
Ine¢ ciency in the
Flexible Price
Equilibrium
I
Ramsey Optimal
Monetary Policy
I
Optimal In‡ation
Rate
Conclusion
I
to minimize the gap between marginal rate of
substitution and transformation between consumption
and labor;
to smooth the intertemporal path of the markup;
to bring the pro…t incentives for …rm entry and product
creation closer to the bene…t of variety to consumers.
The non-zero optimal in‡ation rate is a unique result,
compared to the previous studies on the robustness of
the price stability with the standard new Keynesian
Model
62 / 62