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

2 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

3 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

4 Statement of problems  What are the distributions of Allen elasticities of substitution: sample mean and standard deviation?  Which separable structures are more plausible?

5 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)

6 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

7 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

8 Theoretical model  An Armington – type model: differentiation by origins  Two stage cost minimization  The textile industry  The cotton imports

9 Theoretical model – stage 1  Textile industry produces under the production function as:  Cost minimization:

10 Theoretical model – stage 2  Cost minimization on imported cotton  Unit cost function on imported cotton:  Price

11 CDE cost function (1)  Indirectly implicit additive CDE functional form:  According to characters of cost functions

12 CDE cost function (2)  With Roy ’ s Identity  Allen elasticities of substitution

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

14 Model specification  To capture affairs in the world cotton market, the model is specified as:  Reduced form: p on all exogenous variables

15 Methodology (1)  Bayesian Bootstrap Multivariate Regression  Bayesian methods  Bayesian Theorem  Parameters as random variables  Allows to study the distribution of parameters  Prior information

16 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

17 Methodology (3) 3. Obtain N bootstrap samples 4. Obtain N bootstrap samples 5. Insert the Z*s and 3SLS the structural equations, combining the prior restrictions

18 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

19 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

20 Results (1) “ 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 ROW ”, and (success rate 39.4%), and (success rate 39.4%)  “ Africa and the U.S.A. ”, “ Asia ” and “ Australia and the ROW ”, and (success rate 41.4%), and (success rate 41.4%)

21 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 1 st and 3 rd structures; clustered into 3 groups in the 2 nd : slightly more than 1, around 0.55 and around 0.1  The S.D. in the 1 st and 3 rd structures are relatively large to the mean, and smaller in the 2 nd ; Central Asia and Indo Subcontinent is rather variable  Should not be over interpreted

22 Results (3) Shared Hypothesis95% HPDISmallest HPD Probability [ , ]0.940 [ , ]0.948 [ , ]0.976 [ , ]0.536 [ , ]0.878 [ , ]0.082  Testing for separable structures

23 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

24 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

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

26 First separable structure (1)

27 First separable structure (2)

28 First separable structure (3)

29 Second separable structure (1)

30 Second separable structure (2)

31 Second separable structure (3)

32 Third separable structure (1)

33 Third separable structure (2)

34 Third separable structure (3)