Analyzing and Testing the Structure of
China’s Imports for Cotton – A Bayesian
System Approach
Ruochen Wu
Master Thesis Prepared for the Erasmus Mundus
AFEPA Programme
Thesis Defense
Corvinus University of Budapest
Budapest, Hungary
09/08/2013
Organization







Background
Statement of problems
Objectives
Research hypotheses
Former studies
Theoretical model
CDE cost function







Weak separability
Model specification
Methodology
Data
Results
Conclusion
Further research
2
Background


Largest producer and importer of cotton
 43%
of total import in 2005
 TRQ
and STE
Six major sources:
 West Africa,
Egypt and Sudan, Central Asia,
Indo-Subcontinent, Australia and USA
 ROW
3
Statement of problems

What are the distributions of Allen
elasticities of substitution: sample mean and
standard deviation?

Which separable structures are more
plausible?
4
Objectives

To estimate the Chinese import demand for
cotton with Bayesian bootstrap

To estimate the posterior distribution of the
Allen elasticities of substitution

To test the separable structures among
different sources of import (success rate)
5
Research hypotheses

Cotton is an intermediate product as input in
textile industry

The Chinese Government has the power to
determine the cotton import quantity

The cotton imports are used to close the gap
between domestic production and total
demand
6
Former studies

Armington and its problem

Homotheticity

constant elasticity, no separability allowed

Constant Difference of Elasticity (CDE)

The cotton trade is still heavily influenced by trade barriers,
including that of China

Different results deeming agricultural products as
intermediate ones
7
Theoretical model

An Armington – type model: differentiation
by origins

Two stage cost minimization
 The
textile industry
 The
cotton imports
8
Theoretical model – stage 1

Textile industry produces under the
production function as:
Y  f K , L, TD, TI   f K , L, TD, TI q1 , q2 ,, qm 1

Cost minimization:
C wK , wL , wD , wI  p1 , p2 , pm , Y 
 min{ wK K  wL L  wDTD  wI TI } s.t. Y  f K , L, TD, TI 2
9
Theoretical model – stage 2

Cost minimization on imported cotton
CI  p1 , p2 ,, pm , TI   min{ p1q1  p2q2 ,, pm qm }
s.t. TI  TI q1 , q2 ,, qm 3

Unit cost function on imported cotton:
CI  p1 , p2 ,, pm , TI   c p1 , p2 ,, pm  TI 4

Price
 p1 p2
pm 
  15
p  c p1 , p2 ,, pm   c , ,,
 p
p
p 
10
CDE cost function (1)

Indirectly implicit additive CDE functional
form:
 pi 
Gi wi , c    Bi w   Bi  

i 1
i 1
i 1
 p
m
m
m
bi
i

1 i 
 16
According to characters of cost functions
Bi  0 and bi  0 for all i  1,2,, m
or Bi  0 and 0  bi  1 for all i  1,2,, m7
11
CDE cost function (2)

With Roy’s Identity
 Si 
 pi 
 pm 
8
log    Ai  bi log    bm log 
 p
 p 
 Sm 

Allen elasticities of substitution
 log qi  log qi  log p j
1  log qi
 ij 


 log c
 log c  log p j
S j  log p j
m
i
l 1
Si
  i   j    l S l   ij
 ij  1 if i  j;  ij  0 if i  j 9
12
Weak separability

Definition:
 



c  c c1 p11, , p1n1 , , ck pk1 , , pknk 10

If the m products x1, x2 ,, xm are separated
into k subsets S1, S2 ,, Sk (Moschini et al., 2004)
 lm ,  sn xl , xs  Si , xm , xn  S j ,
i  j , for all l , s, m, n 11

In CDE, xi and x j in the same subset means
bi  b j
13
Model specification

To capture affairs in the world cotton market, the
model is specified as:
 Si 
log     i  1i  D93   2i  DWTO   3i  DMFA
 S7 
 pi 
  4i  DWTOT   5i  DMFAT   6i  T  bi log  
 p
 p7 
 b7 log  
 p

for i  1,2, ,6  12 
Reduced form: p on all exogenous variables
14
Methodology (1)
Bayesian Bootstrap Multivariate Regression
 Bayesian methods

 Bayesian
Theorem
Pr  y |   Pr  
Pr  | y  
 Pr  y |   Pr  13
Pr  y 
 Parameters
as random variables
 Allows to study the distribution of parameters
 Prior information
15
Methodology (2)

Algorithm to bootstrap
Ynm  n11m  X nl lm  Z nk  km  U nm 14
Z nk  Tn p pk  Vnk 15
1. OLS on reduced form
  T ' T  T ' Z , V  Z  T  , S  V 'V 16
^
1
^
^
^
^
2. Generate N bootstraps of the rows in
the estimated residuals matrix to obtain
N matrices Vi* , i  1,2,, N
16
Methodology (3)
Vi  Vi S
**
*
1 2
SS S 
*1
i
12
, i  1,2,, N
With Si*  Vi* ' MVi* and M  I  T T 'T  T '17
1
*

samples i , i  1,2,, N
3. Obtain N bootstrap
^
*
 i    T ' T 1T 'Vi** , i  1,2, , N 18
4. Obtain N bootstrap samples Zi* ,
Z i*  T i* , i  1,2, , N 19
i  1,2,, N
5. Insert the Z*s and 3SLS the structural
equations, combining the prior restrictions
17
Methodology (4)

In the context, testing for separability is
equivalent to testing bi  b j

Frequentist econometrics: Quasi Likelihood
Ratio (Gallant and Jorgenson, 1979)

Bayesian econometrics: HPDI or HPD
Pr   | y    Pr | y d   20

18
Data

FAO dataset 1992 – 2011, relatively short

Quantity and total expenditure on cotton
from different sources

Both prices and expenditure shares were
volatile

The U.S. cotton always had a large share
19
Results (1)
“Africa”, “Asia” and “Australia, the U.S.A. and the ROW”
b1  b2 , b3  b4 and b5  b6  b7 (success rate 22.4%)

“Africa”, “Asia and the U.S.A.” and “Australia and the
ROW”
b1  b2 , b3  b4  b6 and b5  b7 (success rate 39.4%)

“Africa and the U.S.A.”, “Asia” and “Australia and the
ROW”
b1  b2  b6 , b3  b4 and b5  b7
(success rate 41.4%)
20
Results (2)

Own-price AES



Cross-price AES



U.S. has minimum mean in all three separable structures, Egypt
and Sudan maximum
For the S.D., more dependent on separable structures
The mean is between 0 and 1 for the 1st and 3rd structures;
clustered into 3 groups in the 2nd: slightly more than 1, around 0.55
and around 0.1
The S.D. in the 1st and 3rd structures are relatively large to the
mean, and smaller in the 2nd; Central Asia and Indo Subcontinent is
rather variable
Should not be over interpreted
21
Results (3)

Testing for separable structures
Shared Hypothesis
95% HPDI
Smallest HPD Probability
b1  b2  0
[-0.10854, 7.41145]
0.940
b3  b4  0
[-6.03060, 0.053560]
0.948
b5  b7  0
[-6.48984, -0.94374]
0.976
b6  b7  0
[-2.55294, 4.20667]
0.536
b3  b6  0
[-7.09208, 1.54325]
0.878
b1  b6  0
[-2.80300, 2.58693]
0.082
22
Conclusion

Generalized Armington model on China’s cotton
import demand

Sensitive Allen elasticities of substitution to
separable structures

“Africa and the U.S.A.”, “Asia” and “Australia and
the ROW” is the most plausible separable structure
23
Further research

Success rate relatively low

The generalized Armington model may still
be too restrictive, may improve with a more
flexible model if data permit that
24
Thank you for your attention
Ruochen Wu
Master Thesis Prepared for the Erasmus Mundus
AFEPA Programme
Thesis Defense
Corvinus University of Budapest
Budapest, Hungary
09/08/2013
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”
26
First separable structure (2)
Own-price AES
Posterior Mean
Posterior S.D.
Min
Max
σ11
-8.56949
1.52519
-11.03462
-4.11650
σ22
-33.24628
6.43713
-43.45481
-15.26419
σ33
-3.98569
1.79418
-7.71165
-0.73031
σ44
-3.89582
1.74530
-7.52283
-0.72859
σ55
-5.27118
2.27470
-9.32428
-0.29843
σ66
-0.65289
0.16529
-0.95668
-0.21627
σ77
-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”
27
First separable structure (3)
Cross AES
Posterior Mean
Posterior S.D.
Min
Max
σ12
0.96546
0.38774
0.035253
1.71509
σ13
0.67747
0.41924
-0.24943
1.64659
σ15
0.75248
0.14306
0.20779
1.01028
σ34
0.38949
0.59734
-0.64639
1.63474
σ35
0.46449
0.14718
0.14402
0.85260
σ56
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”
28
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”
29
Second separable structure (2)
Own-price AES
Posterior Mean
Posterior S.D.
Min
Max
σ11
-7.86476
1.86576
-11.03292
-1.90113
σ22
-30.82870
7.62410
-43.58931
-6.77768
σ33
-2.27765
1.04378
-6.76458
-0.28019
σ44
-2.22859
1.01849
-6.60565
-0.27945
σ55
-6.48624
1.45176
-9.04898
-0.99892
σ66
-0.45045
0.10337
-0.88257
-0.21304
σ77
-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”
30
Second separable structure (3)
Cross AES
Posterior Mean
Posterior S.D.
Min
Max
σ12
1.00836
0.36982
-0.18128
1.78818
σ13
0.55963
0.20518
-0.033744
1.04522
σ15
1.00531
0.13555
0.28349
1.26980
σ34
0.11090
0.18876
-0.25817
0.97235
σ35
0.55658
0.13853
0.12082
0.88492
σ57
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”
31
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”
32
Third separable structure (2)
Own-price AES
Posterior Mean
Posterior S.D.
Min
Max
σ11
-5.53458
2.61693
-11.23669
-0.39045
σ22
-20.88591
10.40643
-43.57438
-0.42778
σ33
-4.26759
1.81406
-7.89002
-0.59855
σ44
-4.17023
1.76658
-7.70072
-0.59748
σ55
-7.18799
1.58631
-9.15679
-1.08003
σ66
-0.63466
0.13318
-0.94817
-0.26430
σ77
-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”
33
Third separable structure (3)
Cross AES
Posterior Mean
Posterior S.D.
Min
Max
σ12
0.39707
0.39396
-0.39255
1.30183
σ13
0.43464
0.22381
-0.14231
1.07775
σ15
0.69222
0.15286
0.27742
1.08631
σ34
0.47220
0.51055
-0.64299
1.55849
σ35
0.72978
0.31886
-0.13160
1.43864
σ57
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”
34