Analyzing and Testing the Structure of China

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Analyzing and Testing the Structure ofChinas
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

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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

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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

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Statement of problems

• What are the distributions of Allen elasticities
  of substitution sample mean and standard
  deviation?
• Which separable structures are more plausible?

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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)

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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

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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

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Theoretical model

• An Armington type model differentiation by
  origins
• Two stage cost minimization
• The textile industry
• The cotton imports

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Theoretical model stage 1

• Textile industry produces under the production
  function as
• Cost minimization

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Theoretical model stage 2

• Cost minimization on imported cotton
• Unit cost function on imported cotton
• Price

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CDE cost function (1)

• Indirectly implicit additive CDE functional form
• According to characters of cost functions

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CDE cost function (2)

• With Roys Identity
• Allen elasticities of substitution

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Weak separability

• Definition
• If the m products are separated
  into k subsets (Moschini et al.,
  2004)
• In CDE, and in the same subset means

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Model specification

• To capture affairs in the world cotton market,
  the model is specified as
• Reduced form p on all exogenous variables

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Methodology (1)

• Bayesian Bootstrap Multivariate Regression
• Bayesian methods
• Bayesian Theorem
• Parameters as random variables
• Allows to study the distribution of parameters
• Prior information

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Methodology (2)

• Algorithm to bootstrap
• 1. OLS on reduced form
• 2. Generate N bootstraps of the rows in the
  estimated residuals matrix to obtain N matrices

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Methodology (3)

• 3. Obtain N bootstrap samples
• 4. Obtain N bootstrap samples
• 5. Insert the Zs and 3SLS the structural
  equations, combining the prior restrictions

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Methodology (4)

• In the context, testing for separability is
  equivalent to testing
• Frequentist econometrics Quasi Likelihood Ratio
  (Gallant and Jorgenson, 1979)
• Bayesian econometrics HPDI or HPD

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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

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Results (1)

• Africa, Asia and Australia, the U.S.A. and
  the ROW
• , and
  (success rate 22.4)
• Africa, Asia and the U.S.A. and Australia
  and the ROW
• , and
  (success rate 39.4)
• Africa and the U.S.A., Asia and Australia
  and the ROW
• , and
  (success rate 41.4)

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Results (2)

• Own-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
• Cross-price AES
• 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

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Results (3)

• Testing for separable structures

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
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Conclusion

• Generalized Armington model on Chinas 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

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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

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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

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First separable structure (1)
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First separable structure (2)
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First separable structure (3)
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Second separable structure (1)
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Second separable structure (2)
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Second separable structure (3)
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Third separable structure (1)
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Third separable structure (2)
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Third separable structure (3)