provincial trade flow estimation for chinadwrh/slides/drc-drh-ii.pdf · • extending prior drc...

Provincial Trade Flow Estimation for China

David Roland-Holst and Muzhe YangUC Berkeley

Lecture II Presented to theDevelopment Research CentreState Council of the PRCBeijing, 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)


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


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


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


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


Procedure

• Definitional Framework– Define the provinces– Define sectoral classifications and

detail • Generate single-region and

national tables• Estimate interregional trade

distributions by commodity


Overview of the Estimation Problem

• Extending prior DRC work (He and Li: 2004) we propose a new gravity model specification of 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


Schematic Trade Matrix

Industry Commod Factor Institution Industry Commod Factor Institution Industry Commod Factor InstitutionDomestic

TradeForeign Trade

Industry

Commodity

Factor

Institution

Industry

Commodity

Factor

Institution

Industry

Commodity

Factor

Institution

Domestic Trade

Foreign Trade

Region 2

Region 3

Region 1

Region 1 Region 2 Region 3


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 of an international strategy proposed by Mátyás (1997).


Generic Gravity Model

• Consider the following specification ( ) ( ) ( )

1 2 3ln ln lni i imnt m n t mt nt mn mnty Y Y dα γ λ β β β ε= + + + + + +

where: ( )i

mnty is the volume of commodity i 's trade (exports) from region m to

region n at time t ; ( )i

mtY is the GDP for commodity i in region m at time t , and the same for ( )i

ntY for region n ;

dmn is the distance between the regions m and n ; mα is the home regional effect, nγ is the foreign regional effect, and tλ is the time effect; 1, ,m N= L , 1, , 1, 1, , 1n i i N= − + +L L , where the 1N + -th element is the rest of the world, 1, ,t T= L ; 1, ,i I= L , the number of tradable goods; mntε is a white noise disturbance term.


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 , 1β , 2β , 3β 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.


Estimating Bilateral Trade Flows

Consider commodity 1, 2, ,i I∈ L , the explained variable, ( )iy , in the model (1-1) is an N N T× × -vector of

observations, 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 Ty y y y y y y y′

+ +=y L L L L L L

The explanatory variables are arranged accordingly:

( ) ( ) ( ), , , , ,i i imt nt mnX D D D Y Y dα γ λ⎡ ⎤= ⎣ ⎦

where Dα , Dγ and Dλ are dummy variable matrices for

α , γ and λ .


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

, ,

0 0 00 0 0

0 0

I

N N T I

IN N T I I

Y

XX

X

X

′′ ′ ′

× × × ×

× × × × ×

=

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

y y yL

M M O M

L


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)


Ordinary Least Squares 1

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

Regressand: vector ( )iy consists of bilateral trade flows of

commodity 1, 2,i I∈ L between region m ( 1, ,m N= L )

and region ( 1, , 1, 1, , 1n 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 iT 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


OLS 2

Regressors: matrix ( )iX consists of dummy variables for home region m ,

foreign region n and time t :

1 for region 0 else

1 for region 0 else

1 for time 0 else

mD

nD

tD

α

γ

λ

⎧= ⎨⎩⎧

= ⎨⎩⎧

= ⎨⎩

( )

( ) ( )

( ) ( ) ( )

6

(1)

(2)

( )6

, , , , ,

0 0 00 0 0

0 0

i i imt nt mn N N T

IN N T I I

X D D D Y Y d

XX

X

X

α γ λ × × ×

× × × × ×

⎡ ⎤= ⎣ ⎦

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

M M O M

L


OLS 3

( )( )1 2 1, , , I N N T I

ε ε ε′′ ′ ′

× × × ×= Lε

( )( ) 2

| 0

| N N T I

E X

E X Iσ′× × ×

=

=

ε

εε

Disturbances are given by

with

Now formulate the model as

and estimate with

Y X= +β ε

( ) ( )1OLS X X X Y−′ ′=)β


Seemingly Unrelated Regressions 1

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

Regressand: vector ( )iy consists of bilateral trade flows

of commodity 1,2,i I∈ L between region m (

1, ,m N= L ) and region ( 1, , 1, 1, , 1n 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

N N T I

y y y y y y

Y i I

′

+ +

′′ ′ ′

× × × ×

=

= =

y

y y y

L L L L L

L L


SUR 2



1 for region 0 else

1 for region 0 else

1 for time 0 else

mD

nD

tD

α

γ

λ

⎧= ⎨⎩⎧

= ⎨⎩⎧

= ⎨⎩

( )

( ) ( )

( ) ( ) ( )

6

(1)

(2)

( )6

, , , , ,

0 0 00 0 0

0 0

i i imt nt mn N N T

IN N T I I

X D D D Y Y d

XX

X

X

α γ λ × × ×

× × × × ×

⎡ ⎤= ⎣ ⎦

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

M M O M

L


SUR 3

Disturbances in this case are given by

with

( )( ) ( ) ( )

( ) ( ) ( )

11 12 1

21 22 2

1 2

| 0

| 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 σσ σ σ

σ σ σ

′× × × × × × ×

× × × × × ×

=

= Ω

= Σ ⊗

⎡ ⎤⎢ ⎥⎢ ⎥Σ =⎢ ⎥⎢ ⎥⎣ ⎦

L

L

M M O M

L

ε

εε


SUR 4

Now formulate the model as in OLS, i.e.

but estimate with FGLS as

where

Y X= +β ε

( ) ( ))( ) )( )

11 1

11 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 OLSY X= −e)β can be used to

estimate consistently the elements of Σ with )

( ) , 1, ,i jij i j I

N N Tσ

′

= =× ×

e eL


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 int

m

N

ntm

INInt

m

IM i I

IM

IM

⋅=

⋅=

⋅=

= =

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

∑y

y

y

L

M M


GMM 2

Regressand: The vector ( )iy consists of bilateral trade flows of commodity 1,2,i I∈ L between region

1, ,m N= L , and region 1, , 1, 1, , 1n 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

N N T I

y y y y y y

Y i I

′

+ +

′′ ′ ′

× × × ×

=

= =

y

y y y

L L L L L

L L


GMM 3



1 for region 0 else

1 for region 0 else

1 for time 0 else

mD

nD

tD

α

γ

λ

⎧= ⎨⎩⎧

= ⎨⎩⎧

= ⎨⎩

( )

( ) ( )

( ) ( ) ( )

6

(1)

(2)

( )6

, , , , ,

0 0 00 0 0

0 0

i i imt nt mn N N T

IN N T I I

X D D D Y Y d

XX

X

X

α γ λ × × ×

× × × × ×

⎡ ⎤= ⎣ ⎦

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

M M O M

L


GMM 4

Disturbances in this case are given by

with

( )( ) ( ) ( )

( ) ( ) ( )

11 12 1

21 22 2

1 2

| 0

| 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 σσ σ σ

σ σ σ

′× × × × × × ×

× × × × × ×

=

= Ω

= Σ ⊗

⎡ ⎤⎢ ⎥⎢ ⎥Σ =⎢ ⎥⎢ ⎥⎣ ⎦

L

L

M M O M

L

ε

εε


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( , | ) ( , | )arg min

N N T I N N T Ii ii i

GMMX Y X YW

N N T I N N T Iβ

ψ β ψ β′

× × × × × ×= =⋅ ⋅

⎛ ⎞ ⎛ ⎞∑ ∑= ⎜ ⎟ ⎜ ⎟× × × × × ×⎝ ⎠ ⎝ ⎠

)β


GMM 6

)

( )

)( ))( )

11 1 1

11 1

( ) (1)1 111

( ) ( )1 1

1

( , | )

N N T Ii i i iN N T I

N N T Ii iK i iN N T I

Ni iK I ntN Nm

NI IntN N

m

x y x

x y xX Y

IM

IM

β

βψ β

′× × ×=× × ×

′× × ×=× × ×

⋅+ × ⋅

=

⋅=

⎡ ⎤−∑⎢ ⎥⎢ ⎥⎢ ⎥

−⎢ ⎥∑⎢ ⎥= ⎢ ⎥∑ −⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥

∑ −⎢ ⎥⎣ ⎦

y

y

M

M

)

) )( ))( ) )( )

1

1

Var ( , | )

( , | ) ( , | )

i

N N T Ii i i

W

X Y

X Y X Y

N N T I

ψ β

ψ β ψ β

−

⋅

′× × ×= ⋅ ⋅

= ∆

∆ =

⋅∑=

× × ×

where

and


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 .

2R


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.

provincial trade flow estimation for chinadwrh/slides/drc-drh-ii.pdf · • extending prior drc...

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