The Cyclical Behavior of the Markups in the New Keynesian Models

The Cyclical Behavior of the Markups in the
New Keynesian Models
Jean Blaise Nlemfu M.
June 2015
Jean Blaise Nlemfu M. 1 / 39

Outline
1 Introduction
Background
What This Paper Does
Findings
2 The Model
Firms and Price setting
Households and Wage setting
Monetary Policy
Aggregation
3 Calibration
4 Results
Staggered Price-Setting Model
Staggered Wage - Setting Model
Staggered Price-Setting and Staggered Wage-Setting Model
5 Conclusion

Background
"How markups move, in response to what, and why, is however nearly terra
incognita for macro. ... Some of these theories imply pro-cyclical markups,
..... Some imply, however, counter-cyclical markups, with the opposite
implication. ... But we are a long way from having either a clear picture or
convincing theories and this is clearly an area where research is urgently
needed." Blanchard (2008), p.18

Role of price markup in the New Keynesian
Models
Inspired by evidence of countercyclical price markup which builds upon
earlier work by Bils (1987) and Rotemberg and Woodford (1999)
Price markup is a key part of the transmission mechanism :
A positive demand shock leads output and marginal cost to increase.
Because prices cannot adjust immediately, the markup falls.
A positive technology shock lowers marginal cost and raises output.
Because prices cannot adjust immediately, the markup rises.
Leading New Keynesian models with sticky prices and sticky wages
also predict countercyclical price markups in response to demand
shocks.

Evidence of procyclical price markup
Built upon recent work by Nekarda and Ramey (2013) and many
others
Evidence of acyclical or procyclical price markup conditional on supply
and demand shocks.
The question is :
what will happen in a model where monopolistically competitive
households set wages in staggered contracts ?
Wage markup varies
the focus on price markup in the literature is misplaced

Analyzes markup cyclicality using a medium-scale DSGE model
Inspired by Ascari, Phaneuf and Sims (2015) which built upon earlier
work by CEE (2005)
An extended version with :
Non-zero steady-state ination
Roundabout production structure
trend growth in IST and neutral technology
aggregate uctuations are driven by neutral technology, MEI and
monetary policy shocks
and most importantly both price and wage markups vary
assesses how positive trend ination aects the responses of price and
wage markups to shocks
Identies alternative sources of price and wage markups cyclical
behavior

Findings
The main result is that wage markup is more important than price
markup in our baseline model
When rising trend ination from 0 to 4 percent
wage markup change from countercyclical to procyclical movements
interaction with MEI/TFP shocks has greater impact on wage markup
cyclicality than with monetary shock.
with signicant increases ( in magnitude) in the wage markup than in
the price markup
price markup has a negligeable impact
These results put into question the focus on price markup cyclical
behavior in the literature.

Outline
1 Introduction
Background
Findings
2 The Model
Monetary Policy
Aggregation
3 Calibration
4 Results
5 Conclusion

Final Goods Producers
Composite gross output :
Xt =
1
0
Xt(j)
θ−1
θ dj
θ
θ−1
(1)
Input-demand function for the intermediate good :
Xt(j) =
Pt(j)
Pt
−θ
Xt, ∀j, (2)
Aggregate price indexe :
P1−θ
t =
1
0
Pt(j)1−θ
dj (3)

Intermediate Producers
The production function for a typical intermediate producer j :
Xt(j) = max AtΓt(j)φ
Kt(j)α
Lt(j)1−α
1−φ
− ΥtF, 0 , (4)
F is a xed cost, and production is required to be non-negative.
Υt is a growth factor and F is chosen to keep prots zero along a
balanced growth path.
At follows a process with both a trending and stationary component :
At = AtAτ
t , (5)
Aτ
t = gAAτ
t−1 (6)
The stochastic process driving the detrended level of technology At is
given by
At = At−1
ρA
exp sAuA
t , 0≤ ρA 1 (7)

Prot Maximization and Price Setting
Firms set their price according to Calvo pricing
Since all updating rms will choose the same reset price, the optimal
reset price relative to the aggregate price index is p∗
t ≡ P∗
t
Pt
.
The optimal pricing condition can be written:
p∗
t =
θ
θ − 1
x1,t
x2,t
. (8)
The auxiliary variables x1,t and x2,t can be written recursively :
x1,t = λr
t νtXt + βξpEt(πt+1)θ
x1,t+1, (9)
x2,t = λr
t Xt + βξpEt(πt+1)θ−1
x1,t+1. (10)

Labor Composite
The composite labor input is :
Lt =
1
0
Lt(i)
σ−1
σ di
σ
σ−1
(11)
The input demand for labor of type-i :
Lt(i) =
Wt(i)
Wt
−σ
Lt (12)
The aggregate wage indexe is :
W 1−σ
t =
1
0
Wt(i)1−σ
di (13)

Utility Maximization
The problem of a typical household :
maxCt ,Lt (i),Kt+1,Bt+1,It ,Zt
E0
∞
t=0
βt
ln(Ct − bCt−1) − η
Lt(i)1+χ
1+ χ
subject to
Pt Ct + It +
a(Zt)Kt
εI,τ
t
+
Bt+1
1+ it
≤ Wt(i)Lt(i) + Rk
t ZtKt + Πt + Bt + Tt
where
a(Zt) = γ1(Zt − 1) +
γ2
2 (Zt − 1)2

Utility Maximization
and the physical capital accumulation process,
Kt+1 = εI,τ
t ϑt 1− S
It
It−1
It + (1− δ)Kt. (14)
Investment adjustment cost
S
It
It−1
=
κ
2
It
It−1
− 1
2
, (15)
Two types of investment shocks (Justiniano et al., 2011)
IST, shocks map one-to-one into the relative price of investment goods
MEI, ϑt , shocks do not impact the relative price of investment
with
ϑt = (ϑt−1)ρI
exp sI uI
t , 0≤ ρI 1. (16)

Wage setting
Households update their wages each period with the probability
(1− ξw ).
The rst order condition gives the following optimal wage :
w∗
t =
σ
σ − 1
f1,t
f2,t
. (17)
Recursively the terms f1,t and f2,t give the following :
f1,t = η
wt
w∗
t
σ(1+χ)
L1+χ
t +βξw Et(πt+1)σ(1+χ) w∗
t+1
w∗
t
σ(1+χ)
f1,t+1,
(18)
and
f2,t = λr
t
wt
w∗
t
σ
Lt + βξw Et(πt+1)σ−1 w∗
t+1
w∗
t
σ
f2,t+1. (19)

Monetary Policy
Monetary policy consists of a talor-type rule
1+ it
1+ i
=
1+ it−1
1+ i
ρi
πt
π
απ Yt
Yt−1
g−1
Y
αy 1−ρi
εr
t . (20)
with it and i the nominal and steady state interest rate respectevely
πt
π the ination gap,Yt
Y the output gap and ρi the interest rate
smooting
απ and αy the control parameters
εr
t an exogenous shock to the policy rule, εr
t ∼iid 0, σ2
εr .

Aggregation
The aggregate input demands :
Γt(j) = φmct (stXt(j) + ΥtF) , (21)
Kt(j) = α(1− φ)
mct
rk
t
(stXt(j) + ΥtF) , (22)
Lt(j) = (1− α)(1− φ)
mct
wt
(stXt(j) + ΥtF) . (23)
The Real GDP or Aggregate net output, Yt is given by :
Yt = Xt − Γt (24)
The aggregate resource constraint is given by
Yt = Ct + It +
a(Zt)
εI,τ
t
Kt (25)

Outline
1 Introduction
Background
Findings
2 The Model
Monetary Policy
Aggregation
3 Calibration
4 Results
5 Conclusion

Calibration
Shock and Non-Shock Parameters borrowed from Ascari, Phaneuf and
Sims (2015)
Table: Non-Shock Parameters
β δ α η χ b κ γ2
0.99 0.025 1/3 6 1 0.7 3 0.05
θ σ ξp ξw φ ρi απ αy
6 6 0.66 0.66 0.61 0.8 1.5 0.2
Table: Shock Parameters
gA gI ρr sr ρI sI ρA sA
1.00221−φ 1.0047 0 0.0020 0.95 0.0272 0.95 0.0029

Moments
Moments borrowed from Ascari, Phaneuf and Sims (2015)
Table: Moments
E(∆Y ) σ(∆Y ) σ(∆I) σ(∆C) ρ1(∆Y )
Model 0.0057 0.0078 0.0247 0.0048 0.539
Data (0.0057) (0.0078) (0.0202) (0.0047) (0.363)
σ(Y hp) σ(Chp) σ(Ihp) σ(π) ρ1(π)
Model 0.0169 0.0089 0.0555 0.0064 0.892
Data (0.0162) (0.0086) (0.0386) (0.0064) (0.907)

Outline
1 Introduction
Background
Findings
2 The Model
Monetary Policy
Aggregation
3 Calibration
4 Results
5 Conclusion

Staggered Price -Setting
Staggered Price -setting

Staggered Wage -Setting
Staggered wage -setting

Staggered Price and Wage Setting
Staggered price and wage -setting

Outline
1 Introduction
Background
Findings
2 The Model
Monetary Policy
Aggregation
3 Calibration
4 Results
5 Conclusion

Conclusion
This paper analyzes markups cyclical behavior in a positive trend
ination medium-scale DSGE model
in a Staggered price-setting and staggered wage-setting model with
imperfect competition and trend ination rising from 0 to 4 percent,
wage markup is more important than price markup
The focus on the price markup in the literature is misplaced
More resarch is needed on the role of the wage markup

TFP Shock vs SPRPG Model
TFP Shock vs SPRPG Model

TFP Shock vs SWRPG Model
TFP Shock vs SWRPG Model

TFP Shock vs SPSWRPG Model
TFP Shock vs SPSWRPG Model

MEI Shock vs SPRPG Model
MEI Shock vs SPRPG Model

MEI Shock vs SWRPG Model
MEI Shock vs SWRPG Model

MEI Shock vs SPSWRPG Model
MEI Shock vs SPSWRPG Model

MP Shock vs SPRPG Model
MP Shock vs SPRPG Model

MP Shock vs SWRPG Model
MP Shock vs SWRPG Model

MP Shock vs SPSWRPG Model

Staggered Price -Setting (FD ltered)
Staggered Price -setting

Staggered Wage -Setting (FD ltered)
Staggered wage -setting

Staggered Price and Wage Setting (FD ltered)
Staggered price and wage -setting

The Cyclical Behavior of the Markups in the New Keynesian Models

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