Provincial Trade Flow Estimation for China David Roland-Holst and - - PowerPoint PPT Presentation

Provincial Trade Flow Estimation for China

David Roland-Holst and Muzhe Yang

UC Berkeley Lecture II Presented to the Development Research Centre State Council of the PRC Beijing, 6 June 2005

6 June 2005 Roland-Holst and Yang Slide 2

Objectives

• Implement an efficient procedure for

estimating a multi-regional trade flows across China

• Integrate this with a complete set of

consistent provincial SAMs to form a national Multi-regional Social Accounting Matrix (MrSAM)

6 June 2005 Roland-Holst and Yang Slide 3

Motivation

• Single-region IO tables are already accessible, but

neither mutually consistent not integrable

• MRSAM is of interest for its own sake, but can also

support more integrated policy analysis

– CGE – Economic integration studies

• Generate a prototype data set as a template for

more standardized regional data reporting and management

6 June 2005 Roland-Holst and Yang Slide 4

Foundation – PRC Provincial IO Tables

• Already available
• Nationally comprehensive and

consistent in terms of account definitions

• Builds on DRC capacity for SAM and

CGE research at the national level

6 June 2005 Roland-Holst and Yang Slide 5

Consistency Issues

• Provincial trade statistics are

maintained independently

• Domestic imports and exports are not

consistently distributed across other sub-national regions

• There is very little accounting of

margins arising from distribution costs and administrative measures

6 June 2005 Roland-Holst and Yang Slide 6

Proposed Approach

• Uses a new gravity specification to

estimate bilateral trade econometrically

• Integrates the steps necessary to

– Generate the interregional trade flow portions of the China MrSAM, while – insuring the consistency of the province accounts, regional aggregations, and the national system as a whole

6 June 2005 Roland-Holst and Yang Slide 7

Procedure

• Definitional Framework

– Define the provinces – Define sectoral classifications and detail

• Generate single-region and

national tables

• Estimate interregional trade

distributions by commodity

6 June 2005 Roland-Holst and Yang Slide 8

Overview of the Estimation Problem

• Extending prior DRC work (He and Li: 2004)

we propose a new gravity model specification

• f bilateral trade.
• We then propose three alternative estimators.
• Each of these can be implemented with

standard statistical software, and the most attractive estimates used for multi-regional analysis

6 June 2005 Roland-Holst and Yang Slide 9

Schematic Trade Matrix

Industry Commod Factor Institution Industry Commod Factor Institution Industry Commod Factor Institution Domestic Trade Foreign Trade Industry Commodity Factor Institution Industry Commodity Factor Institution Industry Commodity Factor Institution Domestic Trade Foreign Trade R e g i

• n

2 R e g i

• n

3 R e g i

• n

1

Region 1 Region 2 Region 3

6 June 2005 Roland-Holst and Yang Slide 10

Estimation Technique

• The gravity type model has been commonly

used in estimating trade flows in international economics.

• We apply this approach to modeling and

predicting regional trade flows with a variation

• f an international strategy proposed by

Mátyás (1997).

6 June 2005 Roland-Holst and Yang Slide 11

Generic Gravity Model

• Consider the following specification

( ) ( ) ( ) 1 2 3

ln ln ln

i i i m nt m n t m t nt m n m nt

y Y Y d α γ λ β β β ε = + + + + + +

where:

( ) i mnt

y is the volume of commodity i 's trade (exports) from region m to region n at time t ;

( ) i mt

Y is the GDP for commodity i in region m at time t , and the same for

( ) i nt

Y for region n ; dmn is the distance between the regions m and n ;

m

α is the home regional effect,

n

γ is the foreign regional effect, and

t

λ is the time effect; 1, , m N = L , 1, , 1, 1, , 1 n i i N = − + + L L , where the 1 N + -th element is the rest of the world, 1, , t T = L ; 1, , i I = L , the number of tradable goods;

mnt

ε is a white noise disturbance term.

6 June 2005 Roland-Holst and Yang Slide 12

Comments

From an econometric point of view, the α , γ and λ specific

effects can be treated as either random effects or fixed effects. In this analysis, we assume those specific effects associated with regions are time-invariant, and adopt the fixed effects approach.

Also note that our main goal is prediction, so the parameter

estimates for α , γ , λ ,

1

β ,

2

β ,

3

β only bear the

meaning of best linear predictor, not estimates for latent structural parameters.

In addition, we could also add other terms to the right hand

side, such as ln POP mt , and ln POP mt , the population for region m and region n at time t respectively.

6 June 2005 Roland-Holst and Yang Slide 13

Estimating Bilateral Trade Flows

Consider commodity

{ }

1,2, , i I ∈ L

, the explained variable,

( ) i

y

, in the model (1-1) is an N N T × ×

• vector of
• bservations, arranged in the form:

( ) ( )

( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 121 12 131 13 11 1 1 1 1

, , , , , , , , , , , , ,

i i i i i i i i i T T N N T N N N N T

y y y y y y y y

′ + +

= y L L L L L L

The explanatory variables are arranged accordingly:

( ) ( ) ( )

, , , , ,

i i i mt nt mn

X D D D Y Y d

α γ λ

⎡ ⎤ = ⎣ ⎦

where Dα , Dγ and Dλ are dummy variable matrices for

α , γ and λ .

6 June 2005 Roland-Holst and Yang Slide 14

Trade Flow Estimation 2

Then we stack these I (

1, , i I = L

) vectors to construct an

I -good trade-flow (demand) system:

( )(

) ( ) ( )

(1) (2) ( ) 1 (1) (2) ( ) 6

, ,

I N N T I I N N T I I

Y X X X X

′ ′ ′ ′ × × × × × × × × ×

= ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ y y y L M M O M L

6 June 2005 Roland-Holst and Yang Slide 15

Three Alternative Estimators

Modern econometrics has developed a large set of alternative estimation strategies, each performing differently under different data conditions. For the present application, we recommend three alternative estimators, to be evaluated ex post in terms of statistical performance: 1. Ordinary Least Squares (OLS)– the most traditional approach 2. Seemingly Unrelated Regressors (SUR) – an generalization of OLS that imposes less prior assumptions on the data structure 3. Generalized method of moments (GMM)

6 June 2005 Roland-Holst and Yang Slide 16

Ordinary Least Squares 1

OLS estimates for Y and X above can be obtained as follows:

Regressand: vector

( ) i

y

consists of bilateral trade flows of commodity

{ }

1,2, i I ∈ L

between region m (

1, , m N = L

) and region (

1, , 1, 1, , 1 n i i N = − + + L L

) sorted by t (

1, , t T = L

).

( ) ( )

( )

( )(

)

( ) ( ) ( ) ( ) ( ) ( ) ( ) 121 12 11 1 1 1 1 (1) (2) ( ) 1

, , , , , , , , , , , , (where 1, , )

i i i i i i i T N N T N N N N T I N N T I

y y y y y y Y i I

′ + + ′ ′ ′ ′ × × × ×

= = = y y y y L L L L L L L

6 June 2005 Roland-Holst and Yang Slide 17

OLS 2

Regressors: matrix

( ) i

X

consists of dummy variables for home region m , foreign region n and time t :

1for region else 1for region else 1for time else m D n D t D

α γ λ

⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩

( ) ( ) ( )

( ) ( ) ( ) 6 (1) (2) ( ) 6

, , , , ,

i i i mt nt mn N N T I N N T I I

X D D D Y Y d X X X X

α γ λ × × × × × × × ×

⎡ ⎤ = ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ M M O M L

6 June 2005 Roland-Holst and Yang Slide 18

OLS 3

( )(

)

1 2 1

, , ,

I N N T I

ε ε ε

′ ′ ′ ′ × × × ×

= L ε

( )

( )

2

| |

N N T I

E X E X I σ

′ × × ×

= = ε εε

Disturbances are given by with Now formulate the model as and estimate with

Y X = + β ε

( ) ( )

1 OLS

X X X Y

−

′ ′ = ) β

6 June 2005 Roland-Holst and Yang Slide 19

Seemingly Unrelated Regressions 1

In this case we use a technique called Feasible Generalized Least Squares (FGLS), with

Regressand: vector

( ) i

y

consists of bilateral trade flows

• f commodity

{ }

1,2, i I ∈ L

between region m (

1, , m N = L

) and region (

1, , 1, 1, , 1 n i i N = − + + L L

) sorted by t (

1, , t T = L

).

( ) ( )

( )

( )(

)

( ) ( ) ( ) ( ) ( ) ( ) ( ) 121 12 11 1 1 1 1 (1) (2) ( ) 1

, , , , , , , , , , , , (where 1, , )

i i i i i i i T N N T N N N N T I N N T I

y y y y y y Y i I

′ + + ′ ′ ′ ′ × × × ×

= = = y y y y L L L L L L L

6 June 2005 Roland-Holst and Yang Slide 20

SUR 2

Regressors: matrix

( ) i

X

consists of dummy variables for home region m , foreign region n and time t :

1for region else 1for region else 1for time else m D n D t D

α γ λ

⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩

( ) ( ) ( )

( ) ( ) ( ) 6 (1) (2) ( ) 6

, , , , ,

i i i mt nt mn N N T I N N T I I

X D D D Y Y d X X X X

α γ λ × × × × × × × ×

⎡ ⎤ = ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ M M O M L

6 June 2005 Roland-Holst and Yang Slide 21

SUR 3

Disturbances in this case are given by with

( )

( )

( ) ( ) ( ) ( ) ( )

11 12 1 21 22 2 1 2

| |

N N T I N N T I I I N N T N N T I I I I II

E X E X I σ σ σ σ σ σ σ σ σ

′ × × × × × × × × × × × × ×

= = Ω = Σ ⊗ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ Σ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L M M O M L ε εε

6 June 2005 Roland-Holst and Yang Slide 22

SUR 4

Now formulate the model as in OLS, i.e. but estimate with FGLS as where

Y X = + β ε

฀

( )

฀

( )

)

( )

)

( )

1 1 1 1 1 1 FGLS

X X X Y X I X X I Y

− − − − − −

′ ′ = Ω Ω ⎡ ⎤ ⎡ ⎤ ′ ′ = Σ ⊗ Σ ⊗ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ) β

)

) ) ) ) ) ) ) ) )

11 12 1 21 22 2 1 2 I I I I II

σ σ σ σ σ σ σ σ σ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ Σ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L M M O M L

The least squares residuals

OLS

Y X = − e ) β

can be used to estimate consistently the elements of Σ with

)

( )

, 1, ,

i j ij

i j I N N T σ

′

= = × × e e L

6 June 2005 Roland-Holst and Yang Slide 23

Generalized Method of Moments 1

Using information of aggregate provincial/regional trade flows by commodity, we can add additional moment restrictions: where IM denotes provincial/regional domestic import demand.

( ) ( ) 1 (1) (1) 1 ( ) ( ) 1

( 1 , )

N i i nt m N nt m I N I nt m

IM i I IM IM

⋅ = ⋅ = ⋅ =

= = ⎡ ⎤ ∑ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ∑ ⎢ ⎥ ⎣ ⎦

∑y

y y L M M

6 June 2005 Roland-Holst and Yang Slide 24

GMM 2

Regressand: The vector

( ) i

y

consists of bilateral trade flows of commodity

{ }

1,2, i I ∈ L

between region

1, , m N = L

, and region

1, , 1, 1, , 1 n i i N = − + + L L

, sorted by t (

1, , t T = L

).

( ) ( )

( )

( )(

)

( ) ( ) ( ) ( ) ( ) ( ) ( ) 121 12 11 1 1 1 1 (1) (2) ( ) 1

, , , , , , , , , , , , (where 1, , )

i i i i i i i T N N T N N N N T I N N T I

y y y y y y Y i I

′ + + ′ ′ ′ ′ × × × ×

= = = y y y y L L L L L L L

6 June 2005 Roland-Holst and Yang Slide 25

GMM 3

Regressors: matrix

( ) i

X

consists of dummy variables for home region m , foreign region n and time t :

1for region else 1for region else 1for time else m D n D t D

α γ λ

⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩

( ) ( ) ( )

( ) ( ) ( ) 6 (1) (2) ( ) 6

, , , , ,

i i i mt nt mn N N T I N N T I I

X D D D Y Y d X X X X

α γ λ × × × × × × × ×

⎡ ⎤ = ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ M M O M L

6 June 2005 Roland-Holst and Yang Slide 26

GMM 4

Disturbances in this case are given by with

( )

( )

( ) ( ) ( ) ( ) ( )

11 12 1 21 22 2 1 2

| |

N N T I N N T I I I N N T N N T I I I I II

E X E X I σ σ σ σ σ σ σ σ σ

′ × × × × × × × × × × × × ×

= = Ω = Σ ⊗ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ Σ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L M M O M L ε εε

6 June 2005 Roland-Holst and Yang Slide 27

GMM 5

Again we formulate the model as in OLS, i.e. but use the GMM estimator given by

Y X = + β ε

)

)

฀

)

1 1

( , | ) ( , | ) argmin

N N T I N N T I i i i i GMM

X Y X Y W N N T I N N T I

β

ψ β ψ β

′ × × × × × × = = ⋅ ⋅

⎛ ⎞ ⎛ ⎞ ∑ ∑ = ⎜ ⎟ ⎜ ⎟ × × × × × × ⎝ ⎠ ⎝ ⎠ ) β

6 June 2005 Roland-Holst and Yang Slide 28

GMM 6

)

( )

)

( )

)

( )

1 1 1 1 1 1 1 ( ) (1) 1 1 1 1 ( ) ( ) 1 1 1

( , | )

N N T I i i i i N N T I N N T I i iK i i N N T I N i i K I nt N N m N I I nt N N m

x y x x y x X Y IM IM β β ψ β

′ × × × = × × × ′ × × × = × × × ⋅ + × ⋅ = ⋅ =

⎡ ⎤ − ∑ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ − ⎢ ⎥ ∑ ⎢ ⎥ = ⎢ ⎥ ∑ − ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ∑ − ⎢ ⎥ ⎣ ⎦ y y M M

฀

) )

฀

)

( )

)

( )

)

( )

1 1

Var ( , | ) ( , | ) ( , | )

i N N T I i i i

W X Y X Y X Y N N T I ψ β ψ β ψ β

− ⋅ ′ × × × = ⋅ ⋅

= ∆ ∆ = ⋅ ∑ = × × ×

where and

6 June 2005 Roland-Holst and Yang Slide 29

Estimator Selection

• After generating estimates by all three

methods, we can use a variety of criteria to choose between them.

• In traditional econometric analysis, one

would use the goodness of fit measure, adjusted R2 as the selection criterion.

• For our primary objective is imputing

missing bilateral trade flows, we would choose the estimator with the largest .

2

R

6 June 2005 Roland-Holst and Yang Slide 30

References

• He, Jianwu, and Shantong Li (2004), “A

Three-regional CGE Model for China,” presentation to the DRC, Beijing, November.

• He, Jianwu (2004), “A Social Accounting

Matrix for China: 2000,” processed, DRC, Beijing, November.

• Mátyás, L. (1997), “Proper Econometric

Specification of the Gravity Model,” The World Economy 20(3): 363--368.