analyzing and testing the structure of china’s imports for cotton – a bayesian system approach...
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Analyzing and Testing the Structure of
China’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, West Africa, Egypt and Sudan, Central Asia,
Indo-Subcontinent, Australia and USAIndo-Subcontinent, 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
p
p
p
p
p
pcpppcp 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
p
pBwBcwG
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
p
pb
p
pbA
S
S mm
iii
m
i
i
iij
m
lllji
j
i
jj
jiiij
SS
p
q
Spc
pq
c
q
1
log
log1
loglog
loglog
log
log
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
iforp
pb
p
pbTDMFATDWTOT
DMFADWTODS
S
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
Pr
Pr|Pr|Pr y
y
yy
16
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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”
27
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”
28
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”
29
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”
30
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”
31
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”
32
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”
33
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”