PERSPECTIVES OF THE TRADE CHINABRAZIL-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
Outline
1.
2.
3.
4.
5.
Introduction: Brazilian-Chinese trade
perfomance
The Gravity Model
Empirical Model: The Bayesian
Inference
Results
Concluding remarks
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
Brazilian balance of trade (19842006)
140.0
120.0
Billion dollars
100.0
80.0
60.0
40.0
20.0
Years
Exports
Source: ONU/COMTRADE (2007)
Imports
Trade of balance
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
-20.0
1984
0.0
Chinese trade balance (US$ Billion
FOB)
1,000.0
800.0
Billion Dollars
600.0
400.0
200.0
-200.0
Years
Exports
Source: ONU/COMTRADE (2007)
Imports
Balance of trade
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
0.0
Brazil-China bilateral trade balance – US$
FOB
9,000.0
8,000.0
7,000.0
Million dollars
6,000.0
5,000.0
4,000.0
3,000.0
2,000.0
1,000.0
Years
Exports
Source: ONU/COMTRADE (2007)
Imports
Balance of trade
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
-1,000.0
1984
0.0
Composition of the Brazilian exports
to the world
Brazilian foreign exports composition (according to HS 2002)
Machinery and transportation equipment
Beverages, tobacco
Processed food
Minerals
Agricultural products
Wood, fur, silk, paper
Crude oil derivatives
Clothing
Fibers
Other personal products
Total
Source: UN/COMTRADE (2007).
27.21%
21.83%
11.85%
11.46%
9.94%
6.96%
4.56%
3.78%
1.23%
1.17%
100.00%
Most relevant categories of Brazilian
products exported to China. 2006
Brazilian exports to China
12.5%
0.8%
1.4%
2.1%
32.0%
3.3%
4.5%
4.5%
10.0%
Source: ONU/
COMTRADE (2007)
29.0%
Ores, slag and ash
Mineral fuels, mineral oils and products of their distillation
Pulp of wood or of other fibrous cellulose material
Iron and steel
Vehicles other than railway or tramway rolling stock
Oil seeds and oleaginous fruits
Raw hides and skins (other than fur skins) and leather
Machinery and mechanical appliances; parts thereof
Animal or vegetable fats and oils
others
Most relevant categories of Chinese
products imported by Brazil. 2006
Chinese exports to Brazil
32.9%
39.7%
2.9%
3.1%
15.8%
Source: ONU/
COMTRADE (2007)
5.7%
Electrical machinery and equipment and parts thereof; sound recorders and thereof
Machinery and mechanical appliances; parts thereof
Organic chemicals
Mineral fuels, mineral oils and products of their distillation
Man-made filaments
others
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.
2 – The Gravity Model
Structural form – based on Dixon &
Moon (1993)
Xijt = A Yβ1it Yβ2jt Gβ3ij Rβ4it exp(β5Djt + β6Fjt) εijt
(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.
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):
xijt = a + β1yit + β2yjt + β3gij + β4rit + β5djt + β6fjt + β7 xij(t–1) + ξt + ζi + uijt
(2)
In which xijt=lnXijt, a=lnA, yit=lnYit, yjt=lnYjt, gij=lnGij, rit=lnRit , djt=lnDjt,
fjt=lnFjt and uijt = lnεijt.
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)
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
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
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)
In which:
ν = 10-3
κ =10-3
(5)
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)
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.
Data set
1962 - 2003 (basic gravity model - traditional variables)
1995 - 2003 (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.
4 - Results
Comparison of different gravity models - Brazil bilateral
exports to China and US. Panel (cross-section/ time
series). 1962-2003
Variables
Constant
GDPi
GDPj
Distance
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
(1962-2003)
(1995-2003)
(1988-2003)
(1992-2003)
(1995-2003)
(1995-2003)
-98.31
(11.07)
1.93
(0.41)
1.72
(0.26)
2.12
(1.27)
-80.02
(45.76)
1.24
(3.30)
1.65
(1.10)
2.35
(3.69)
-73.98
(24.20)
1.95
(1.19)
1.23
(0.36)
0.93
(1.35)
-0.03
(0.02)
-8.24
(21.66)
2.47
(1.39)
-0.09
(0.69)
-3.79
(2.70)
-37.08
(37.27)
1.73
(2.84)
0.62
(1.08)
-0.38
(3.20)
-36.74
(24.79)
1.93
(2.51)
0.43
(1.03)
-0.54
(3.33)
-0.04
(0.13)
-0.38
(0.12)
-0.31
(1.17)
-0.38
(0.12)
Relative Prices
Weighted
Applied Tariffs
Freedom from
Corruption
Agreements
SPE
5.35
0.44
0.36
0.16
0.29
-0.01
(0.03)
0.29
Comparison of different gravity models - Brazil
bilateral exports to China and US. Panel (crosssection/ time series). 1995-2003
Variables
Constant
GDPi
GDPj
Distance
Model 7
Model 8
Model 9
(1995-2003)
(1995-2003)
(1995-2003)
-10.33
(27.30)
3.27
(3.03)
-1.18
(1.64)
-3.26
(3.82)
14.75
(26.55)
5.23
(4.22)
-0.27
(1.36)
-19.02
(9.63)
-0.31
(0.13)
1.83
(1.87)
-0.35
(0.12)
0.93
(1.49)
-100.40
(35.53)
3.83
(3.76)
-0.54
(3.58)
-1.36
(4.17)
-0.31
(6.48)
-0.23
(0.52)
2.05
(4.46)
Relative Prices
Weighted Applied
Tariffs
Freedom from
Corruption
Agreements
Linear trend
Latent variable for
the U.S.
Latent variable for
China
Latent economic
cycles (t)*
SPE
0.10
(0.06)
35.39
(2.20)
46.99
(4.86)
0.27
0.27
44.80
(2.11)
0.17
Comparison of different gravity models with a basic specification
for the United States bilateral exports to China and Brazil. Panel
(cross-section/time series). 1962-2003
Variables
Constant
Model 1
Model 2
Model 3
Model 4
Model 5
Model 6
(1962-2003)
(1995-2003)
(1992-2003)
(1995-2003)
(1995-2003)
(1995-2003)
-42.31
(8.30)
1.28 (0.45)
29.58
(12.28)
-0.91
(0.48)
1.22 (0.22)
-0.64
(0.53)
1.75 (0.33)
-3.05
(0.74)
-60.91
(17.99)
0.11
(0.72)
1.14
(0.39)
5.55
(2.24)
-0.10
(0.03)
-0.02
(0.14)
-78.23
(45.31)
0.97
(1.32)
0.54
(0.61)
6.40
(6.05)
-0.10
(0.06)
-0.01
(0.18)
-56.60
(18.46)
2.59
(0.59)
-0.85
(0.44)
2.77
(1.66)
-20.78
(17.95)
0.78
(1.83)
0.89
(0.47)
-0.91
(4.80)
-0.07
(0.04)
0.59
(0.41)
-1.53
(1.36)
GDPi
GDPj
Distance
Relative prices
Weighted
Applied Tariffs
Freedom from
Corruption
Corruption
Perception
AR(1)
SPE
-0.07
(0.16)
1.28
(0.35)
1.07
0.07
0.10
0.08
0.07
0.34
(0.24)
0.02
Comparison of different gravity models with a basic
specification for the United States bilateral exports to China
and Brazil. Panel (cross-section/ time series). 1995-2003
Independent variables
Constant
GDPi
GDPj
Distance
Relative prices
Weighted Applied Tariffs
Freedom from Corruption
Model 7
Model 8
Model 9
(1995-2003)
(1995-2003)
(1995-2003)
10.89
(39.06)
1.26
(1.35)
0.24
(0.64)
-10.76
(5.55)
-0.13
(0.06)
-0.22
(0.32)
0.45
(0.62)
20.12
(31.64)
1.89
(1.27)
0.06
(0.72)
-13.23
(3.91)
-0.10
(0.03)
-0.12
(0.28)
-98.40
(47.48)
2.19
(4.10)
-0.25
(1.48)
5.27
(9.09)
-0.07
(0.15)
-0.03
(0.43)
0.24
(0.38)
57.07
(1.33)
62.42
(1.27)
0.22
(1.25)
Trade Freedom
Latent variable for Brazil
Latent variable for China
57.53
(1.30)
62.85
(1.32)
Latent economic cycles (t)*
SPE
0.04
0.04
15.36
(1.05)
0.04
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)
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.
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
CEPEA – Center for Advanced Studies on
Applied Economics/ESALQ- University of
São Paulo -Brazil
Sílvia Miranda: smiranda@esalq.usp.br
Vitor Ozaki: vitorozaki@yahoo.com.br