International Trade Elasticity Puzzle & Dynamic market...
Transcript of International Trade Elasticity Puzzle & Dynamic market...
IntroductionModelResults
Numerical ResultsAppendix
International Trade Elasticity Puzzle & Dynamicmarket penetration
Seyed Ali Madanizadeh
April 2012
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
How can we explain the low short run trade elasticity andlarge long run elasticity.
Why do we see large unemployment after trade liberalizationsor large currency devalutions?
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
How can we explain the low short run trade elasticity andlarge long run elasticity.
Why do we see large unemployment after trade liberalizationsor large currency devalutions?
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Propose a dynamic Market Penetration model (Extended EKKtype model)
Firms need to pay convex adjustment cost to penetrate intomarket. So it takes time for them to get into a new market,especially the new �rms.Due to the sluggish adjustment, we do not observe largechanges in trade shares in the short run.Most of the labor movements and changes in �rm sizes happenin the long run.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Propose a dynamic Market Penetration model (Extended EKKtype model)
Firms need to pay convex adjustment cost to penetrate intomarket. So it takes time for them to get into a new market,especially the new �rms.
Due to the sluggish adjustment, we do not observe largechanges in trade shares in the short run.Most of the labor movements and changes in �rm sizes happenin the long run.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Propose a dynamic Market Penetration model (Extended EKKtype model)
Firms need to pay convex adjustment cost to penetrate intomarket. So it takes time for them to get into a new market,especially the new �rms.Due to the sluggish adjustment, we do not observe largechanges in trade shares in the short run.
Most of the labor movements and changes in �rm sizes happenin the long run.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Propose a dynamic Market Penetration model (Extended EKKtype model)
Firms need to pay convex adjustment cost to penetrate intomarket. So it takes time for them to get into a new market,especially the new �rms.Due to the sluggish adjustment, we do not observe largechanges in trade shares in the short run.Most of the labor movements and changes in �rm sizes happenin the long run.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
introducing labor market frictions.
It takes time for the �rms to adjust and worker to re-allocate.
We get large unemployment in the short run
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
introducing labor market frictions.
It takes time for the �rms to adjust and worker to re-allocate.
We get large unemployment in the short run
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
introducing labor market frictions.
It takes time for the �rms to adjust and worker to re-allocate.
We get large unemployment in the short run
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Sticky Wages:
This would magnify the frictions in the labor market to preventwages to adjust to its optimal levelThis friciton prevents labor movement toward more productive�rms.Unemployment magni�es.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Sticky Wages:
This would magnify the frictions in the labor market to preventwages to adjust to its optimal level
This friciton prevents labor movement toward more productive�rms.Unemployment magni�es.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Sticky Wages:
This would magnify the frictions in the labor market to preventwages to adjust to its optimal levelThis friciton prevents labor movement toward more productive�rms.
Unemployment magni�es.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
QuestionMotivation
Sticky Wages:
This would magnify the frictions in the labor market to preventwages to adjust to its optimal levelThis friciton prevents labor movement toward more productive�rms.Unemployment magni�es.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Consumers:
Same as EKK:
maxCj =
∑i
Z Mij
0xij (ν)
σ�1σ dµ (ν)
! σσ�1
s.t.∑i
Z Mij
0pij (v) xij (ν) dµ (ν) = Xj = wjLj +Πj
Each buyer will be reached with probability fij (v) by aproducer.Demand function for good v is :
Xij (v) = pij (v) xij (ν) = fij (v)Xj
�pij (v)Pj
��(σ�1)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Consumers:
Same as EKK:
maxCj =
∑i
Z Mij
0xij (ν)
σ�1σ dµ (ν)
! σσ�1
s.t.∑i
Z Mij
0pij (v) xij (ν) dµ (ν) = Xj = wjLj +Πj
Each buyer will be reached with probability fij (v) by aproducer.Demand function for good v is :
Xij (v) = pij (v) xij (ν) = fij (v)Xj
�pij (v)Pj
��(σ�1)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Consumers:
Same as EKK:
maxCj =
∑i
Z Mij
0xij (ν)
σ�1σ dµ (ν)
! σσ�1
s.t.∑i
Z Mij
0pij (v) xij (ν) dµ (ν) = Xj = wjLj +Πj
Each buyer will be reached with probability fij (v) by aproducer.
Demand function for good v is :
Xij (v) = pij (v) xij (ν) = fij (v)Xj
�pij (v)Pj
��(σ�1)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Consumers:
Same as EKK:
maxCj =
∑i
Z Mij
0xij (ν)
σ�1σ dµ (ν)
! σσ�1
s.t.∑i
Z Mij
0pij (v) xij (ν) dµ (ν) = Xj = wjLj +Πj
Each buyer will be reached with probability fij (v) by aproducer.Demand function for good v is :
Xij (v) = pij (v) xij (ν) = fij (v)Xj
�pij (v)Pj
��(σ�1)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Producer: with Cost c and market share f
invests C (f 0; f ) to increase its share to f 0.
V (f ; c ,P,X ) = maxp,f 0
�0,Π (p; c ,P 0,X 0) f 0 � C (f 0; f ) +
11+r V (f
0; c 0,P 0,X 0)
�where:
Π�f 0, p; c ,P,X
�=
�1� c
p
�X� pP
��(σ�1)(1)
C�f 0, f
�= max
(0,F
γ+ αf +
f 0 � f(1� f 0)β
!)(2)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Producer: with Cost c and market share f
invests C (f 0; f ) to increase its share to f 0.
V (f ; c ,P,X ) = maxp,f 0
�0,Π (p; c ,P 0,X 0) f 0 � C (f 0; f ) +
11+r V (f
0; c 0,P 0,X 0)
�where:
Π�f 0, p; c ,P,X
�=
�1� c
p
�X� pP
��(σ�1)(1)
C�f 0, f
�= max
(0,F
γ+ αf +
f 0 � f(1� f 0)β
!)(2)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Entry
Firms enter if V � 0) ct � ct
Free Entry:Vi � Mei fei
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Entry
Firms enter if V � 0) ct � ct
Free Entry:Vi � Mei fei
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Entry
Firms enter if V � 0) ct � ct
Free Entry:Vi � Mei fei
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Xijt = MeiZ cj
0Xijt (ct ) d Pr
ij(c)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Pjt =
∑iMeit
Z cjt
0fijt (c) p1�σ
ijt (c) d Prij(c)
! 11�σ
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
Recursuve Competitive Equilibrium:
f 0 = f�f , c ;P 0,X 0,F
�E 0 = E
�f , c ;P 0,X 0,F
�X 0j = X (fPgk , fXgk , fFgk )P 0j = P (fPgk , fXgk , fFgk )
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
FOC :p =
σ
σ� 1c
π (c) +1
1+ rV 0�f 0, c 0;P 0,X 0
�=
F
(1� f 0)β
�1+ β
f 0 � f1� f 0
�
V 0�f , c ;P 0,X 0
�=
1
(1� f 0)β� α
!F
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
ConsumersProducers
FOC :p =
σ
σ� 1c
π (c) +1
1+ rV 0�f 0, c 0;P 0,X 0
�=
F
(1� f 0)β
�1+ β
f 0 � f1� f 0
�
V 0�f , c ;P 0,X 0
�=
1
(1� f 0)β� α
!F
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Productivity
Pr (cij (v) � c) = Φijcθ
EntrydijwiAiz (v)
= cij (v) � cij =�1+ rrDij
� 1σ�1
(3)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Productivity
Pr (cij (v) � c) = Φijcθ
EntrydijwiAiz (v)
= cij (v) � cij =�1+ rrDij
� 1σ�1
(3)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
π (c) =XPσ�1
σmσ�1 c�(σ�1)
f � (c) = 1��
rF(1+ r) π (c)
�1/β
= 1��ccij
� σ�1β
V =1+ rr
π (c) f � (c)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Γ� (Dij ) = ζ
�1+ rrDij
� θσ�1�1
Ξ (Dij ) = 0
Fij = 0
Xij = ζθσ
�1+ rr
� θσ�1�1
MeiΦijFijDθ
σ�1ij
Pj = m�1+ rr
Xjσ
� 1θ�
1σ�1
∑i
θζMeiΦijF1� θ
σ�1ij
!� 1θ
ζ =1
θ � σ+ 1� 1
σ�1β + θ � σ+ 1
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Trade Balance Equation:
Xi = ∑j
0@ MeiΦijF1� θ
σ�1ij
∑nMenΦnjF1� θ
σ�1nj
1AXjXi =
σ
σ� 1wiLi
Free Entry:
Mei fei � Vi = ∑jVij = ∑
j
1+ rr
Xijσ=1+ rr
Xiσ
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Equilirium
wiLi = ∑j
0B@ 1φi
�dijwiAi
��θ
∑n1
φn
�dnjwnAn
��θ
1CAwjLjwhere:
φi =feiwiLi
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Entry Decision:
E 0 (c , f ) =�1 if c � c (P 0,X 0,F )
0 OW
f 00 = f 0 = f = 0)
cij�P 0j ,X
0j ,Fij
�=
�1+ rα+ r
X 0P 0σ�1
σmσ�1Fij
� 1σ�1
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Entry Decision:
E 0 (c , f ) =�1 if c � c (P 0,X 0,F )
0 OW
f 00 = f 0 = f = 0)
cij�P 0j ,X
0j ,Fij
�=
�1+ rα+ r
X 0P 0σ�1
σmσ�1Fij
� 1σ�1
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Productivity Structure:
Pr (Z � z) = z�θ
cij =dijwiAiz
� cij
Following EKK de�ne
Φij =
�Aidijwi
�θ
Pr (cij � c) = Φijcθ
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Equivalence theorem:
W (g ;A) = maxg 0
(0,Ag 0 �
γ+ αg +
g 0 � g(1� g 0)β
!+
11+ r
W�g 0;A
�)(4)
where the policy function is
g 0 = g (g ,A)
V (f ; c ,P,X ) = FW�f ;XPσ�1
σmσ�1Fc1�σ
�f (f ; c ,P,X ) = g
�f ;XPσ�1
σmσ�1Fc1�σ
�Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
De�ne
Dij =XjPσ�1
j
σmσ�1Fij
cij =
�1+ rα+ r
Dij
� 1σ�1
ft (c) = f�ft�1 (c) ,Dijc1�σ
�Γt (Dij ) =
Z c (Dij )
0ft (c) cθ�σdc
Ξt (Dij ) =Z c (Dij )
0
γ+ αft�1 (c) +
ft (c)� ft�1 (c)(1� ft (c))β
!cθ�1dc
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Agreagte Sale of i in j :
X 0ij ,t (Dij ) = θσMeiΦijFijDijΓt (Dij )
Fij =Xijσ
Ξt (Dij )DijΓt (Dij )
Πij =Xijσ
�1� Ξt (Dij )
DijΓt (Dij )
�
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Steady StateSmall Open Economy DynamicsCalibration
Based on EKK we calibrate the parameters as below:
β =1λ=
1.91
= 1. 098 9
θ
σ� 1 = 2.46
σ = 2.98
θ = 4.87
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Numerical Tricks
Use the sum of the value functionsSolve for an interval of f instead of just one point or the wholeinterval.Provide the Jacobian and Hessian functions (patterns)Using a compact set instead of (0, 1) : There�s discontinuitySolve for A0s �rst, and then do the iterations and integrations.Writing the costs in terms of destination.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Convergence of policy and value functions
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Values Functions/Policy Functions
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Evolution of f over time for each c .
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
f over c for each time t.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Evolution of Agregate sale/pro�t/�xed costs over time.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Evolution of sale/pro�t/�xed costs over time for each c .
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Distribution of pro�t over c
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Half time for each c
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Value and policy functions vs β
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Evolution of Agregate sale/pro�t/�xed costs over time vs β
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Distribution of pro�t over c vs β
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Half time vs β
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Value and policy functions vs r
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Evolution of Agregate sale/pro�t/�xed costs over time vs r
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Distribution of pro�t over c vs r
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Half time vs r
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Evolution of Agregate sale/pro�t/�xed costs over time vs F orX ,P
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Distribution of pro�t over c vs F or X ,P
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Half time vs F
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Show Stedy states for c
Aggregate SS vs β, r ,F ,X (,P)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Results of going from Autarki to (free) trade
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Results of reducing trade costs by 10% and show the long runand short run elasticities.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Show fraction of exporters
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
show graphically what happens in GE (show things aremonotone)
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Estimate trade elasticity.
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Agreagte Sale of i in j :
X 0ij ,t (Dij ) = θσMeiΦijFijDijΓt (Dij )
πni =MeiΦijΓt (Dij )
∑nMenΦnjΓt (Dnj )
P 0j = m
θ ∑iMeiΦijΓt (Dij )
! 11�σ
Fij =Xijσ
Ξt (Dij )DijΓt (Dij )
Πij =Xijσ
�1� Ξt (Dij )
DijΓt (Dij )
�Πi =
Xiσ�∑
j
Xijσ
Ξt (Dij )DijΓt (Dij )
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration
IntroductionModelResults
Numerical ResultsAppendix
Trade Balance Equation:
Xi = ∑j
MeiΦijΓt (Dij )∑nMenΦnjΓt (Dnj )
Xj
Income and Expenditure
Xi =σ
σ� 1
wiLi �∑
jMei θΦijFijΞt (Dij )
!
Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration