International Trade Elasticity Puzzle & Dynamic market ...gsme.sharif.edu/~madanizadeh/Files/TradeDynamics_slides.pdf · Seyed Ali Madanizadeh International Trade Elasticity Puzzle

IntroductionModelResults

Numerical ResultsAppendix

International Trade Elasticity Puzzle & Dynamicmarket penetration

Seyed Ali Madanizadeh

April 2012

Seyed Ali Madanizadeh International Trade Elasticity Puzzle & Dynamic market penetration



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?




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?




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.




QuestionMotivation


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.




QuestionMotivation


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.




QuestionMotivation


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.




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




QuestionMotivation







QuestionMotivation







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.




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.




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.




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.




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)




ConsumersProducers

Consumers:

Same as EKK:

maxCj =

∑i

Z Mij

0xij (ν)

σ�1σ dµ (ν)

! σσ�1

s.t.∑i

Z Mij




�pij (v)Pj

��(σ�1)




ConsumersProducers

Consumers:

Same as EKK:

maxCj =

∑i

Z Mij

0xij (ν)

σ�1σ dµ (ν)

! σσ�1

s.t.∑i

Z Mij


Each buyer will be reached with probability fij (v) by aproducer.

Demand function for good v is :


�pij (v)Pj

��(σ�1)




ConsumersProducers

Consumers:

Same as EKK:

maxCj =

∑i

Z Mij

0xij (ν)

σ�1σ dµ (ν)

! σσ�1

s.t.∑i

Z Mij




�pij (v)Pj

��(σ�1)




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)




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)




ConsumersProducers

Entry

Firms enter if V � 0) ct � ct

Free Entry:Vi � Mei fei




ConsumersProducers

Entry






ConsumersProducers

Entry






ConsumersProducers

Xijt = MeiZ cj

0Xijt (ct ) d Pr

ij(c)




ConsumersProducers

Pjt =

∑iMeit

Z cjt

0fijt (c) p1�σ

ijt (c) d Prij(c)

! 11�σ




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 )




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




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




Steady StateSmall Open Economy DynamicsCalibration

Productivity

Pr (cij (v) � c) = Φijcθ

EntrydijwiAiz (v)

= cij (v) � cij =�1+ rrDij

� 1σ�1

(3)





Productivity

Pr (cij (v) � c) = Φijcθ

EntrydijwiAiz (v)

= cij (v) � cij =�1+ rrDij

� 1σ�1

(3)





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)





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





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





Equilirium

wiLi = ∑j

0B@ 1φi

�dijwiAi

��θ

∑n1

φn

�dnjwnAn

��θ

1CAwjLjwhere:

φi =feiwiLi





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





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





Productivity Structure:

Pr (Z � z) = z�θ

cij =dijwiAiz

� cij

Following EKK de�ne

Φij =

�Aidijwi

�θ

Pr (cij � c) = Φijcθ





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




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





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 )

�





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




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.




Convergence of policy and value functions




Values Functions/Policy Functions




Evolution of f over time for each c .




f over c for each time t.




Evolution of Agregate sale/pro�t/�xed costs over time.




Evolution of sale/pro�t/�xed costs over time for each c .




Distribution of pro�t over c




Half time for each c




Value and policy functions vs β




Evolution of Agregate sale/pro�t/�xed costs over time vs β




Distribution of pro�t over c vs β




Half time vs β




Value and policy functions vs r




Evolution of Agregate sale/pro�t/�xed costs over time vs r




Distribution of pro�t over c vs r




Half time vs r




Evolution of Agregate sale/pro�t/�xed costs over time vs F orX ,P




Distribution of pro�t over c vs F or X ,P




Half time vs F




Show Stedy states for c

Aggregate SS vs β, r ,F ,X (,P)




Results of going from Autarki to (free) trade




Results of reducing trade costs by 10% and show the long runand short run elasticities.




Show fraction of exporters




show graphically what happens in GE (show things aremonotone)




Estimate trade elasticity.




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


Πij =Xijσ

�1� Ξt (Dij )

DijΓt (Dij )

�Πi =

Xiσ�∑

j

Xijσ





Trade Balance Equation:

Xi = ∑j

MeiΦijΓt (Dij )∑nMenΦnjΓt (Dnj )

Xj

Income and Expenditure

Xi =σ

σ� 1

wiLi �∑

jMei θΦijFijΞt (Dij )

!


Documents

International Trade Elasticity Puzzle & Dynamic market ...gsme.sharif.edu/~madanizadeh/Files/TradeDynamics_slides.pdf · Seyed Ali Madanizadeh International Trade Elasticity Puzzle