Analyzing and Testing the Structure ofChina’s Imports for Cotton – A Bayesian

System Approach

Ruochen WuRuochen WuMaster Thesis Prepared for the Erasmus Mundus Master Thesis Prepared for the Erasmus Mundus

AFEPA ProgrammeAFEPA ProgrammeThesis DefenseThesis Defense

Corvinus University of BudapestCorvinus University of BudapestBudapest, HungaryBudapest, Hungary

09/08/201309/08/2013

2

Organization BackgroundBackground Statement of problemsStatement of problems ObjectivesObjectives Research hypothesesResearch hypotheses Former studiesFormer studies Theoretical modelTheoretical model CDE cost functionCDE cost function

Weak separabilityWeak separability Model specificationModel specification MethodologyMethodology DataData ResultsResults ConclusionConclusion Further researchFurther research

3

Background Largest producer and importer of cottonLargest producer and importer of cotton

43% of total import in 200543% of total import in 2005 TRQ and STETRQ and STE

Six major sources:Six major sources: West Africa, Egypt and Sudan, Central Asia, Indo-West Africa, Egypt and Sudan, Central Asia, Indo-

Subcontinent, Australia and USASubcontinent, Australia and USA ROWROW

4

Statement of problems What are the distributions of Allen What are the distributions of Allen

elasticities of substitution: sample mean and elasticities of substitution: sample mean and standard deviation?standard deviation?

Which separable structures are more Which separable structures are more plausible?plausible?

5

Objectives To estimate the Chinese import demand for To estimate the Chinese import demand for

cotton with Bayesian bootstrapcotton with Bayesian bootstrap To estimate the posterior distribution of the To estimate the posterior distribution of the

Allen elasticities of substitutionAllen elasticities of substitution To test the separable structures among To test the separable structures among

different sources of import (success rate)different sources of import (success rate)

6

Research hypotheses Cotton is an intermediate product as input in Cotton is an intermediate product as input in

textile industrytextile industry The Chinese Government has the power to The Chinese Government has the power to

determine the cotton import quantitydetermine the cotton import quantity The cotton imports are used to close the gap The cotton imports are used to close the gap

between domestic production and total demandbetween domestic production and total demand

7

Former studies Armington and its problemArmington and its problem

HomotheticityHomotheticity constant elasticity, no separability allowedconstant elasticity, no separability allowed Constant Difference of Elasticity (CDE)Constant Difference of Elasticity (CDE)

The cotton trade is still heavily influenced by trade The cotton trade is still heavily influenced by trade barriers, including that of Chinabarriers, including that of China

Different results deeming agricultural products as Different results deeming agricultural products as intermediate onesintermediate ones

8

Theoretical model

An Armington – type model: differentiation An Armington – type model: differentiation by originsby origins

Two stage cost minimizationTwo stage cost minimization The textile industryThe textile industry The cotton importsThe cotton imports

9

Theoretical model – stage 1 Textile industry produces under the Textile industry produces under the

production function as:production function as:

Cost minimization:Cost minimization:

1,,,,,,,,, 21 mqqqTITDLKfTITDLKfY

YpppwwwwC mIDLK ,,,,,, 21

2,,,..}min{ TITDLKfYtsTIwTDwLwKw IDLK

10

Theoretical model – stage 2 Cost minimization on imported cottonCost minimization on imported cotton

Unit cost function on imported cotton:Unit cost function on imported cotton:

PricePrice

},,min{,,,, 221121 mmm qpqpqpTIpppCI

3,,,.. 21 mqqqTITIts

4,,,,,,, 2121 TIpppcTIpppCI mm

51,,,,,, 2121

pp

pp

ppcpppcp m

m

11

CDE cost function (1) Indirectly implicit additive CDE functional Indirectly implicit additive CDE functional

form:form:

According to characters of cost functionsAccording to characters of cost functions

61,1

1

11

m

i

ii

m

i

bii

m

iii

i

i

ppBwBcwG

miallforbandB ii ,,2,100

7,,2,1100 miallforbandBor ii

12

CDE cost function (2) With Roy’s IdentityWith Roy’s Identity

Allen elasticities of substitutionAllen elasticities of substitution

8logloglog

ppb

ppbA

SS m

mi

iim

i

i

iij

m

lllji

j

i

jj

jiiij

SS

pq

Spcpq

cq

1

loglog1

loglogloglog

loglog

90;1 jiifjiif ijij

13

Weak separability Definition:Definition:

If the m products are separated If the m products are separated into k subsets into k subsets (Moschini et al., 2004)(Moschini et al., 2004)

In CDE, and in the same subset meansIn CDE, and in the same subset means

10,,,,,, 11111 1

kknkkn ppcppccc

mxxx ,,, 21

kSSS ,,, 21

11,,,,

,,,,,

nmslallforji

SxxSxx jnmislsnlm

ix jx

ji bb

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Model specification To capture affairs in the world cotton market, the To capture affairs in the world cotton market, the

model is specified as:model is specified as:

Reduced form: p on all exogenous variablesReduced form: p on all exogenous variables

126,,2,1log

log

93log

77

654

3217

iforppb

ppbTDMFATDWTOT

DMFADWTODSS

iiiii

iiiii

15

Methodology (1) Bayesian Bootstrap Multivariate RegressionBayesian Bootstrap Multivariate Regression Bayesian methodsBayesian methods

Bayesian TheoremBayesian Theorem

Parameters as random variablesParameters as random variables Allows to study the distribution of parametersAllows to study the distribution of parameters Prior informationPrior information

13Pr|Pr

PrPr|Pr|Pr yy

yy

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Methodology (2) Algorithm to bootstrapAlgorithm to bootstrap

1. OLS on reduced form1. OLS on reduced form

2. Generate N bootstraps of the rows in 2. Generate N bootstraps of the rows in the estimated residuals matrix to the estimated residuals matrix to

obtain obtain N matricesN matrices

1411 mnmkknmllnmnmn UZXY

15 knkppnkn VTZ

16',,''^^^^

1^

VVSTZVZTTT

NiVi ,,2,1,*

17

Methodology (3)

3. Obtain N bootstrap samples3. Obtain N bootstrap samples

4. Obtain N bootstrap samples4. Obtain N bootstrap samples

5. Insert the Z*s and 3SLS the structural 5. Insert the Z*s and 3SLS the structural equations, combining the prior restrictionsequations, combining the prior restrictions

NiSSSSVV iii ,,2,1,211*21***

17''' 1*** TTTTIMandMVVSWith iii

Nii ,,2,1,*

18,,2,1,'' **1^

* NiVTTT ii

NiZi ,,2,1,*

19,,2,1,** NiTZ ii

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Methodology (4)

In the context, testing for separability is In the context, testing for separability is equivalent to testingequivalent to testing

Frequentist econometrics: Quasi Likelihood Frequentist econometrics: Quasi Likelihood Ratio (Gallant and Jorgenson, 1979)Ratio (Gallant and Jorgenson, 1979)

Bayesian econometrics: HPDI or HPDBayesian econometrics: HPDI or HPD

ji bb

20|Pr|Pr dyy

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Data FAO dataset 1992 – 2011, relatively shortFAO dataset 1992 – 2011, relatively short Quantity and total expenditure on cotton Quantity and total expenditure on cotton

from different sourcesfrom different sources Both prices and expenditure shares were Both prices and expenditure shares were

volatilevolatile The U.S. cotton always had a large shareThe U.S. cotton always had a large share

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Results (1)““Africa”, “Asia” and “Australia, the U.S.A. and the ROW” Africa”, “Asia” and “Australia, the U.S.A. and the ROW”

, and (success rate 22.4%), and (success rate 22.4%) ““Africa”, “Asia and the U.S.A.” and “Australia and the Africa”, “Asia and the U.S.A.” and “Australia and the

ROW” ROW”

, and (success rate 39.4%), and (success rate 39.4%) ““Africa and the U.S.A.”, “Asia” and “Australia and the Africa and the U.S.A.”, “Asia” and “Australia and the

ROW” ROW”

, and (success rate 41.4%), and (success rate 41.4%)

21 bb 43 bb 765 bbb

21 bb 643 bbb 75 bb

621 bbb 43 bb 75 bb

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Results (2) Own-price AESOwn-price AES

U.S. has minimum mean in all three separable structures, Egypt U.S. has minimum mean in all three separable structures, Egypt and Sudan maximumand Sudan maximum

For the S.D., more dependent on separable structuresFor the S.D., more dependent on separable structures Cross-price AESCross-price AES

The mean is between 0 and 1 for the 1The mean is between 0 and 1 for the 1stst and 3 and 3rdrd structures; structures; clustered into 3 groups in the 2clustered into 3 groups in the 2ndnd: slightly more than 1, around 0.55 : slightly more than 1, around 0.55 and around 0.1and around 0.1

The S.D. in the 1The S.D. in the 1stst and 3 and 3rdrd structures are relatively large to the structures are relatively large to the mean, and smaller in the 2mean, and smaller in the 2ndnd; Central Asia and Indo Subcontinent ; Central Asia and Indo Subcontinent is rather variableis rather variable

Should not be over interpretedShould not be over interpreted

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Results (3)

Shared Hypothesis 95% HPDI Smallest HPD Probability

[-0.10854, 7.41145] 0.940

[-6.03060, 0.053560] 0.948

[-6.48984, -0.94374] 0.976

[-2.55294, 4.20667] 0.536

[-7.09208, 1.54325] 0.878

[-2.80300, 2.58693] 0.082

021 bb

061 bb

063 bb

076 bb

075 bb

043 bb

Testing for separable structuresTesting for separable structures

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Conclusion Generalized Armington model on China’s cotton Generalized Armington model on China’s cotton

import demandimport demand

Sensitive Allen elasticities of substitution to Sensitive Allen elasticities of substitution to

separable structuresseparable structures

““Africa and the U.S.A.”, “Asia” and “Australia and Africa and the U.S.A.”, “Asia” and “Australia and

the ROW” is the most plausible separable structurethe ROW” is the most plausible separable structure

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Further research

Success rate relatively lowSuccess rate relatively low

The generalized Armington model may still The generalized Armington model may still

be too restrictive, may improve with a more be too restrictive, may improve with a more

flexible model if data permit thatflexible model if data permit that

Thank you for your attention

Ruochen WuRuochen Wu

Master Thesis Prepared for the Erasmus Mundus Master Thesis Prepared for the Erasmus Mundus AFEPA ProgrammeAFEPA Programme

Thesis DefenseThesis Defense

Corvinus University of BudapestCorvinus University of Budapest

Budapest, HungaryBudapest, Hungary

09/08/201309/08/2013

26

First separable structure (1)

Parameter Posterior Mean Posterior S.D. Min Max

b1 0.24216 0.15092 0.00067083 0.65765

b3 0.53014 0.25587 0.012523 0.99099

b7 0.45514 0.24910 0.012216 0.99669

Success Rate 22.4%

Table 6.4 BBMR results with separability between “Africa”, “Asia” and “Australia, the U.S.A. and the ROW”

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First separable structure (2)Own-price AES Posterior Mean Posterior S.D. Min Max

σ 11 -8.56949 1.52519 -11.03462 -4.11650

σ 22 -33.24628 6.43713 -43.45481 -15.26419

σ 33 -3.98569 1.79418 -7.71165 -0.73031

σ 44 -3.89582 1.74530 -7.52283 -0.72859

σ 55 -5.27118 2.27470 -9.32428 -0.29843

σ 66 -0.65289 0.16529 -0.95668 -0.21627

σ 77 -3.63215 1.52545 -6.35287 -0.28848

Table 6.5 Own-price AES with separability between “Africa”, “Asia” and “Australia, the U.S.A. and the ROW”

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First separable structure (3)Cross AES Posterior Mean Posterior S.D. Min Max

σ 12 0.96546 0.38774 0.035253 1.71509

σ 13 0.67747 0.41924 -0.24943 1.64659

σ 15 0.75248 0.14306 0.20779 1.01028

σ 34 0.38949 0.59734 -0.64639 1.63474

σ 35 0.46449 0.14718 0.14402 0.85260

σ 56 0.53950 0.38284 -0.26878 1.22312

Table 6.6 Cross AES with separability between “Africa”, “Asia” and “Australia, the U.S.A. and the ROW”

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Second separable structure (1)

Parameter Posterior Mean Posterior S.D. Min Max

b1 0.29476 0.17688 0.00016773 0.85024

b3 0.74349 0.13224 0.16912 0.99614

b7 0.29781 0.16870 0.0044466 0.93932

Success Rate 39.4%

Table 6.10 BBMR results for the separability between “Africa”, “Asia and the U.S.A.” and “Australia and the ROW”

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Second separable structure (2)Own-price AES Posterior Mean Posterior S.D. Min Max

σ 11 -7.86476 1.86576 -11.03292 -1.90113

σ 22 -30.82870 7.62410 -43.58931 -6.77768

σ 33 -2.27765 1.04378 -6.76458 -0.28019

σ 44 -2.22859 1.01849 -6.60565 -0.27945

σ 55 -6.48624 1.45176 -9.04898 -0.99892

σ 66 -0.45045 0.10337 -0.88257 -0.21304

σ 77 -4.37393 0.94541 -6.08577 -0.81640

Table 6.11 Own-price AES with the separability between “Africa”, “Asia and the U.S.A.” and “Australia and ROW”

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Second separable structure (3)Cross AES Posterior Mean Posterior S.D. Min Max

σ 12 1.00836 0.36982 -0.18128 1.78818

σ 13 0.55963 0.20518 -0.033744 1.04522

σ 15 1.00531 0.13555 0.28349 1.26980

σ 34 0.11090 0.18876 -0.25817 0.97235

σ 35 0.55658 0.13853 0.12082 0.88492

σ 57 1.00227 0.35807 -0.35184 1.65707

Table 6.12 Cross AES with the separability between “Africa”, “Asia and the U.S.A.” and “Australia and the ROW”

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Third separable structure (1)

Parameter Posterior Mean Posterior S.D. Min Max

b1 0.52855 0.23922 0.0068842 0.99885

b3 0.49099 0.24856 0.0047872 0.99441

b7 0.23340 0.19133 0.00062770 0.95420

Success Rate 41.4%

Table 6.16 BBMR results with separability between “Africa and the U.S.A.”, “Asia” and “Australia and the ROW”

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Third separable structure (2)Own-price AES Posterior Mean Posterior S.D. Min Max

σ 11 -5.53458 2.61693 -11.23669 -0.39045

σ 22 -20.88591 10.40643 -43.57438 -0.42778

σ 33 -4.26759 1.81406 -7.89002 -0.59855

σ 44 -4.17023 1.76658 -7.70072 -0.59748

σ 55 -7.18799 1.58631 -9.15679 -1.08003

σ 66 -0.63466 0.13318 -0.94817 -0.26430

σ 77 -4.88194 1.01126 -6.15053 -0.94226

Table 6.17 Own-price AES with the separability between “Africa and the U.S.A.”, “Asia” and “Australia and ROW”

34

Third separable structure (3)Cross AES Posterior Mean Posterior S.D. Min Max

σ 12 0.39707 0.39396 -0.39255 1.30183

σ 13 0.43464 0.22381 -0.14231 1.07775

σ 15 0.69222 0.15286 0.27742 1.08631

σ 34 0.47220 0.51055 -0.64299 1.55849

σ 35 0.72978 0.31886 -0.13160 1.43864

σ 57 0.98737 0.45801 -0.59162 1.71293

Table 6.18 Cross AES with the separability between “Africa and the U.S.A.”, “Asia” and “Australia and ROW”