PERSPECTIVES OF THE TRADE CHINA-BRAZIL-USA: EVALUATION THROUGH A

GRAVITY MODEL APPROACH

Sílvia H. G. de Miranda

Vitor A. Ozaki

Ricardo Fonseca

Caio MortattiESALQ – University of Sao Paulo - Brazil

8- 9th July 2007

IATRC Beijing Conference

Outline1. Introduction: Brazilian-Chinese trade

perfomance

2. The Gravity Model

3. Empirical Model: The Bayesian Inference

4. Results

5. Concluding remarks

1 - IntroductionBrazilian 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 (1984-2006)

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

Years

Bil

lio

n d

oll

ars

Exports Imports Trade of balance

Source: ONU/COMTRADE (2007)

Chinese trade balance (US$ Billion FOB)

-200.0

0.0

200.0

400.0

600.0

800.0

1,000.0

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

Years

Bil

lio

n D

oll

ars

Exports Imports Balance of trade Source: ONU/COMTRADE (2007)

Brazil-China bilateral trade balance – US$ FOB

Source: ONU/COMTRADE (2007)

-1,000.0

0.0

1,000.0

2,000.0

3,000.0

4,000.0

5,000.0

6,000.0

7,000.0

8,000.0

9,000.0

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

Years

Mil

lio

n d

oll

ars

Exports Imports Balance of trade

Composition of the Brazilian exports

to the world

Source: UN/COMTRADE (2007).

Brazilian foreign exports composition (according to HS 2002) Machinery and transportation equipment 27.21% Beverages, tobacco 21.83% Processed food 11.85% Minerals 11.46% Agricultural products 9.94% Wood, fur, silk, paper 6.96% Crude oil derivatives 4.56% Clothing 3.78% Fibers 1.23% Other personal products 1.17% Total 100.00%

Most relevant categories of Brazilian products exported to China. 2006

Brazilian exports to China

32.0%

29.0%

10.0%

4.5%

4.5%

3.3%

2.1%1.4%

0.8%

12.5%

Ores, slag and ash Oil seeds and oleaginous fruitsMineral fuels, mineral oils and products of their distillation Raw hides and skins (other than fur skins) and leatherPulp of wood or of other fibrous cellulose material Machinery and mechanical appliances; parts thereofIron and steel Animal or vegetable fats and oilsVehicles other than railway or tramway rolling stock others

Source: ONU/ COMTRADE (2007)

Most relevant categories of Chinese products imported by Brazil. 2006

Chinese exports to Brazil

32.9%

15.8%

5.7%3.1%

2.9%

39.7%

Electrical machinery and equipment and parts thereof; sound recorders and thereofMachinery and mechanical appliances; parts thereofOrganic chemicalsMineral fuels, mineral oils and products of their distillationMan-made filamentsothers

Source: ONU/ COMTRADE (2007)

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 = 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; andF = Political variable.

(1)

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) (5)

In which: ν = 10-3 κ =10-3

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 set1962 - 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). 1962-2003Variables Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

(1962-2003) (1995-2003) (1988-2003) (1992-2003) (1995-2003) (1995-2003)

Constant

-98.31 (11.07)

-80.02 (45.76)

-73.98 (24.20)

-8.24 (21.66)

-37.08 (37.27)

-36.74 (24.79)

GDPi 1.93

(0.41) 1.24

(3.30) 1.95

(1.19) 2.47

(1.39) 1.73

(2.84) 1.93

(2.51)

GDPj 1.72

(0.26) 1.65

(1.10) 1.23

(0.36) -0.09 (0.69)

0.62 (1.08)

0.43 (1.03)

Distance 2.12

(1.27) 2.35

(3.69) 0.93

(1.35) -3.79 (2.70)

-0.38 (3.20)

-0.54 (3.33)

Relative Prices -0.03 (0.02)

Weighted Applied Tariffs

-0.04 (0.13)

-0.38 (0.12)

-0.38 (0.12)

Freedom from Corruption

-0.31 (1.17)

Agreements -0.01 (0.03)

SPE 5.35 0.44 0.36 0.16 0.29 0.29

Comparison of different gravity models - Brazil bilateral exports to China and US. Panel (cross-section/ time series). 1995-2003

Variables Model 7 Model 8 Model 9 (1995-2003) (1995-2003) (1995-2003)

Constant -10.33 (27.30)

14.75 (26.55)

-100.40 (35.53)

GDPi 3.27 (3.03)

5.23 (4.22)

3.83 (3.76)

GDPj -1.18 (1.64)

-0.27 (1.36)

-0.54 (3.58)

Distance -3.26 (3.82)

-19.02 (9.63)

-1.36 (4.17)

Relative Prices

-0.31 (6.48)

Weighted Applied Tariffs

-0.31 (0.13)

-0.35 (0.12)

-0.23 (0.52)

Freedom from Corruption

1.83 (1.87)

0.93 (1.49)

2.05 (4.46)

Agreements Linear trend 0.10

(0.06)

Latent variable for the U.S.

35.39 (2.20)

Latent variable for China

46.99 (4.86)

Latent economic cycles (t)*

44.80 (2.11)

SPE 0.27 0.27 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 Model 1 Model 2

Model 3

Model 4

Model 5

Model 6

(1962-2003) (1995-2003) (1992-2003) (1995-2003) (1995-2003) (1995-2003)

Constant -42.31 (8.30)

29.58 (12.28)

-60.91 (17.99)

-78.23 (45.31)

-56.60 (18.46)

-20.78 (17.95)

GDPi 1.28 (0.45)

-0.91 (0.48)

0.11 (0.72)

0.97 (1.32)

2.59 (0.59)

0.78 (1.83)

GDPj 1.22 (0.22) 1.75 (0.33)

1.14 (0.39)

0.54 (0.61)

-0.85 (0.44)

0.89 (0.47)

Distance -0.64 (0.53)

-3.05 (0.74)

5.55 (2.24)

6.40 (6.05)

2.77 (1.66)

-0.91 (4.80)

Relative prices

-0.10 (0.03)

-0.10 (0.06)

-0.07 (0.04)

Weighted Applied Tariffs

-0.02 (0.14)

-0.01 (0.18)

-0.07 (0.16)

0.59 (0.41)

Freedom from Corruption

-1.53 (1.36)

Corruption Perception

1.28 (0.35)

AR(1)

0.34 (0.24)

SPE 1.07 0.07 0.10 0.08 0.07 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 Model 7 Model 8 Model 9 (1995-2003) (1995-2003) (1995-2003)

Constant 10.89 (39.06)

20.12 (31.64)

-98.40 (47.48)

GDPi 1.26 (1.35)

1.89 (1.27)

2.19 (4.10)

GDPj 0.24 (0.64)

0.06 (0.72)

-0.25 (1.48)

Distance -10.76 (5.55)

-13.23 (3.91)

5.27 (9.09)

Relative prices -0.13 (0.06)

-0.10 (0.03)

-0.07 (0.15)

Weighted Applied Tariffs -0.22 (0.32)

-0.12 (0.28)

-0.03 (0.43)

Freedom from Corruption 0.45 (0.62)

Trade Freedom

0.24 (0.38)

0.22 (1.25)

Latent variable for Brazil 57.53 (1.30)

57.07 (1.33)

Latent variable for China 62.85 (1.32)

62.42 (1.27)

Latent economic cycles (t)*

15.36 (1.05)

SPE 0.04 0.04 0.04

5 - Concluding RemarksEven 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 remarksRelative 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 stepsOther 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

Sílvia Miranda: smiranda@esalq.usp.br

Vitor Ozaki: vitorozaki@yahoo.com.br

CEPEA – Center for Advanced Studies on Applied Economics/ESALQ- University of São Paulo -Brazil