1. IATRC Beijing Conference
PERSPECTIVES OF THE TRADE CHINA-BRAZIL-USA: EVALUATION THROUGH A GRAVITY MODEL APPROACH
Sílvia H. G. de Miranda
Vitor A. Ozaki
Ricardo Fonseca
Caio Mortatti
ESALQ – University of Sao Paulo - Brazil
8- 9th July 2007
IATRC Beijing Conference
I AM A PROFESSOR OF THE ECONOMICS DEPARTMENT OF THE UNIVERSITY OF SÃO PAULO - BRAZIL
A PAPER WE ARE WORKING ON ....TITLE
STATISTICIAN

2. Outline Introduction: Brazilian-Chinese trade perfomance
The Gravity Model
Empirical Model: The Bayesian Inference
Results
Concluding remarks
I HAVE DIVIDED MY PRESENTATION INTO FIVE ASPECTS
FIRST –
This study was developed by myself and by Vitor Ozaki who is a statistician and two other colaborators
Please if you have any questions, feel free to ask me after my presentation.

3. 1 - Introduction Brazilian foreign trade: highly concentrated
2004: 43% (EU and US)
2005: 42.2%
China and Brazil informal trade since the creation of the Republic of China, in 1949.
In the 50’s: inexpressive flows (US$ 8 million)
Since 2002: the 3rd major importer from Brazil
1999 to 2003: 15.4% of Brazilian exports
End of 2000: a bilateral agreement
CHECAR NUMEROS DE 2006
Accounted for 43% of the exportations and importations
Some reasons to explain this performance
In turn

4. Brazilian balance of trade (1984-2006)
Source: ONU/COMTRADE (2007)

5. Chinese trade balance (US$ Billion FOB)
Source: ONU/COMTRADE (2007)

6. Brazil-China bilateral trade balance – US$ FOB
Source: ONU/COMTRADE (2007)

7. Composition of the Brazilian exports to the world
Source: UN/COMTRADE (2007).

8. Most relevant categories of Brazilian products exported to China. 2006
Check all the names
Source: ONU/ COMTRADE (2007)

9. Most relevant categories of Chinese products imported by Brazil. 2006
Source: ONU/ COMTRADE (2007)

10. Objectives
To identify the relevant variables for the trade flow among Brazil and China
And the US
In the gravity model framework we consider the size, distance, cultural and political aspects and economical importance of these countries.
Bayesian Inference (Hierarchical model): Limited number of observations.
The gravity model was the most appropriated to be applied to reach this goal

11. 2 – The Gravity Model Structural form – based on Dixon & Moon (1993)
(1)
Xijt = Exports from nation i to importer j at time t;
Y = Economic size of exporter i and importer j;
G = Geographical distance between two nations;
R = Relative price index;
D = Factors that stimulate or restrict trade between pairs of countries; and
F = Political variable.

12. Functional Form
Taking logarithmic of equation (1) and including the autoregressive term, the deterministic trend and the latent variables (country-effect ζi and the Business Cycle effect ξt):
(2)
In which xijt=lnXijt, a=lnA, yit=lnYit, yjt=lnYjt, gij=lnGij, rit=lnRit , djt=lnDjt, fjt=lnFjt and uijt = lnεijt.

13. 3 - Empirical Model: Bayesian Inference Approach
Ranjan and Tobias (2007) - modeling data through non-parametric Bayesian inference and specific country effects
Choice of the econometric method:
Limitations on the data set available - Short period of analysis
Only three countries
Panel data framework - a more detailed analysis (countries or regions)

14. The multivariate regression model
yi = XiBi + εi (i = 1, 2, ... , m) (3)
y observations allocated in a t x m matrix where
m variables
t observations.
Matrix Xi is composed of covariates t x k,
Bi = (β1, β2 , ... , βm) is a k x m matrix of the regression parameters, and
εi is a t x m matrix of non-observed random errors.
The dependence structure - Hierarchical models
Uai
M means variables
The matrix X involves all the explanatory variables

15. Two important modelling features adopted
An univariate formulation for each i.
yi ~ N(μi, τ)
In which τ is the precision parameter.
The prior distributions of B were modeled in a multivariate framework
we are modeling the mean structure, leaving precision constant throughout the analysis.
μi ≡ E(yi)
The dependence structure - Hierarchical models

16. The prior distributions
B ~ Nm(μ0, Λ0), p(B)  | Λ0 |m/2 exp [–1/2 (B – μ0)´ Λ01 (B – μ0)] (4)
τ ~ G (ν, κ), p(τ) = (e-κ τ κ ν τ ν-1)/Γ(ν) (5)
In which:
ν = 10-3
κ =10-3
Iérarquí or ierarquicãl

17. To the hiper-parameters of the prior distribution B were associated the following hiper-prioris:
μ0 ~ Nm(μ1, Λ1), p(μ0)  | Λ1 |m/2 exp [–1/2 (B – μ1)´ Λ1 (B – μ1)] (6)
Λ0 ~ Wm(Θ, ψ), p(Λ0) = | Θ |ψ/2 | Λ0|( ψ –p–1)/2 exp [–1/2(tr(Θ Λ0))] (7)

18. Criteria for the models selection
Criteria for the models selection: Gelfand and Ghosh (1998): the “squared predictive error criteria” (SPE)
Objective: to minimize the posterior predictive loss.
The lower the SPE the better the model results

19. Data set 1962 - 2003 (basic gravity model - traditional variables)
(relative price index, tariffs and political variables)
Sources:
World Development Indicators 2005
United Nations Commodity Trade Statistics Database – COMTRADE (2007).
Maritime distances - Dataloy, 2007
Tariffs (bound and applied rates): World Integrated Trade Solution (WITS); Comtrade, IDB/WTO
Political indicators: Transparency International (2007) - The corruption perception index (CPI); Heritage Foundation (2007) - Index of trade freedom and Freedom from corruption; number of trade agreements (U.S. Department of Commerce – USA and the Brazilian Ministry of External Relations.
WINBUGS – the program to run the model

20. 4 - Results

21. Comparison of different gravity models - Brazil bilateral exports to China and US. Panel (cross-section/ time series)

22. Comparison of different gravity models - Brazil bilateral exports to China and US. Panel (cross-section/ time series)
If we break down the data into segments we can have better results on relative prices

23. Comparison of different gravity models with a basic specification for the United States bilateral exports to China and Brazil. Panel (cross-section/time series)

24. Comparison of different gravity models with a basic specification for the United States bilateral exports to China and Brazil. Panel (cross-section/ time series)

25. 5 - Concluding Remarks
Even using the Bayesian Inference approach, the small amount of data seems to hinder the results;
Distance and the political effects had a poor performance (Cross-section variables).
Consistent results for the temporal variables: GDP; the Applied Weighted Average Tariffs (particularly significant for Brazilian exports)

26. Concluding remarks
Relative Prices: interesting results for the US but not for Brazil
Latent Variables – Business Cycle: better effects in the US case;
but if we include business cycle it seems to cause unexpected changes in other variables.
Cross-sectional Latent Variables: large and significant coefficients, systematically higher for China.

27. Next steps Other Relative Prices data set – Index for export prices
Transportation costs
Increase number of countries considered (the cross-section analysis) – for Economic Blocks and integration effects
Analyze the differentiated and homogeneous products

28. CEPEA – Center for Advanced Studies on
Applied Economics/ESALQ- University of São Paulo -Brazil
Sílvia Miranda:
Vitor Ozaki:
Well, that was my presentation for you today. Feel free to ask me any questions you may have, after the comments from the moderator.