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
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 2
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 3
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 4
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 5
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 6
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 7
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 6 June 2005 Roland-Holst and Yang Slide 8
Schematic Trade Matrix Region 1 Region 2 Region 3 Domestic Foreign Industry Commod Factor Institution Industry Commod Factor Institution Industry Commod Factor Institution Trade Trade Industry R e g Commodity i o Factor n 1 Institution Industry R e g Commodity i o Factor n 2 Institution Industry R e g Commodity i o Factor n 3 Institution Domestic Trade Foreign Trade 6 June 2005 Roland-Holst and Yang Slide 9
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). 6 June 2005 Roland-Holst and Yang Slide 10
Generic Gravity Model • Consider the following specification = α + γ + λ + β + β + β + ε ( ) ( ) ( ) i i i ln ln ln y Y Y d 1 2 3 m nt m n t m t nt m n m nt where: ( ) i is the volume of commodity i 's trade (exports) from region m to y mnt region n at time t ; ( ) i is the GDP for commodity i in region m at time t , and the same for Y mt ( ) i for region n ; Y nt d mn is the distance between the regions m and n ; α is the home regional effect, γ is the foreign regional effect, and λ is m n t the time effect; = L = − + + N + -th element is the 1, , 1, L , 1, 1, L , 1 m N , n i i N , where the 1 = L rest of the world, 1, , ; t T = L 1, , , the number of tradable goods; i I ε is a white noise disturbance term. mnt 6 June 2005 Roland-Holst and Yang Slide 11
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 , β , β , β only bear the 1 2 3 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 12
Estimating Bilateral Trade Flows { } ∈ L 1,2, , Consider commodity , the explained variable, i I × × ( ) i , in the model (1-1) is an N -vector of N T y observations, arranged in the form: ( ) ′ = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i i i i i i L L L L L L , , , , , , , , , , , , , y y y y y y y y y ( ) ( ) + + 121 12 131 13 11 1 T T N N T 1 1 1 N N N N T The explanatory variables are arranged accordingly: ⎡ ⎤ = ⎣ ( ) ( ) ( ) i i i , , , , , ⎦ X D D D Y Y d α γ λ mt nt mn where D α , D γ and D λ are dummy variable matrices for α , γ and λ . 6 June 2005 Roland-Holst and Yang Slide 13
Trade Flow Estimation 2 = L Then we stack these I ( 1, , ) vectors to construct an i I I -good trade-flow (demand) system: ( ) ( ′ = ′ ′ ′ (1) (2) ( ) I L , , Y y y y ) × × × × 1 N N T I ⎡ ⎤ (1) 0 0 0 X ⎢ ⎥ (2) 0 0 0 ⎢ X ⎥ = ⎢ X ⎥ M M O M ⎢ ⎥ ⎢ ⎥ ( ) I L ⎣ ⎦ 0 0 X ( ) ( ) × × × × × 6 N N T I I 6 June 2005 Roland-Holst and Yang Slide 14
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 15
Ordinary Least Squares 1 OLS estimates for Y and X above can be obtained as follows: ( ) i Regressand: vector consists of bilateral trade flows of y { } ∈ = L L between region m ( 1,2, 1, , commodity m N ) i I = − + + L L 1, , 1, 1, , 1 ) sorted by t ( and region ( n i i N = L 1, , ). t T ( ) ′ = ( ) i ( ) i ( ) i ( ) i ( ) i ( ) i ( ) i L L L L L , , , , , , , , , , y y y y y y y ( ) ( ) + + 121 12 T N 11 N T 1 1 1 1 N N N N T ( ) ( ′ = ′ ′ ′ = (1) (2) ( ) I L L , , (where 1, , ) Y i I y y y ) × × × × 1 N N T I 6 June 2005 Roland-Holst and Yang Slide 16
OLS 2 ( ) i consists of dummy variables for home region m , Regressors: matrix X foreign region n and time t : ⎧ 1for region m ⎡ ⎤ = ⎣ ( ) ( ) ( ) i i i , , , , , = ⎨ X D D D Y Y d ⎦ D α γ λ ( ) mt nt mn × × × α N N T 6 ⎩ 0 else ⎡ ⎤ (1) 0 0 0 X ⎧ 1for region ⎢ ⎥ n = ⎨ (2) D 0 0 0 X ⎢ ⎥ γ = ⎢ ⎩ 0 else X ⎥ M M O M ⎢ ⎥ ⎧ 1for time t ⎢ ⎥ ( ) I = ⎨ L ⎣ 0 0 ⎦ X D ( ) ( ) × × × × × λ 6 N N T I I ⎩ 0 else 6 June 2005 Roland-Holst and Yang Slide 17
OLS 3 ( ) ( ′ ε = ε ε ′ ′ ε ′ L , , , Disturbances are given by 1 2 ) I × × × × 1 N N T I ( ) ε = | 0 E X with ( ) εε ′ = σ 2 | E X I × × × N N T I Now formulate the model as = β + ε Y X and estimate with ) ( ) ( ) − ′ 1 ′ β = X X X Y OLS 6 June 2005 Roland-Holst and Yang Slide 18
Seemingly Unrelated Regressions 1 In this case we use a technique called Feasible Generalized Least Squares (FGLS), with ( ) i Regressand: vector consists of bilateral trade flows y { } ∈ L between region m ( of commodity 1,2, i I = L = − + + L L 1, , ) and region ( 1, , 1, 1, , 1 ) m N n i i N = L sorted by t ( 1, , ). t T ( ) ′ = ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i L i L i L i L i L i , , , , , , , , , , y y y y y y y ( ) ( ) + + 121 12 11 1 T N N T 1 1 1 N N N N T ( ) ( ′ ′ ′ ′ = = (1) (2) ( ) I L L , , (where 1, , ) Y i I y y y ) × × × × 1 N N T I 6 June 2005 Roland-Holst and Yang Slide 19
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