Gross outputs X can be split into intermediate and final products AX+Y=Ⅹ X=BI B=(-A is the( global) Leontief inverse matrix VBp i GNXGN Value added from a source country-sector i used in the production of final goods and services in country-sector
Gross outputs X can be split into intermediate and final products： 𝐴𝑋 + 𝑌 = 𝑋 𝑋 = 𝐵𝑌 𝐵 = (𝐼 − 𝐴) −1 is the (Global) Leontief inverse matrix 𝑽𝑩𝒀 ➢ Value added from a source country-sector i used in the production of final goods and services in country-sector j i GN×GN j
Decomposition of value-added and final goods production based on Leontief insights When n=g=2 buu b,2 bu bi SS b20y200 丿BY b,3 b,3 b, 1 6 bnb2b1b2⊥000y 1v2 6i2 2 v2bi1 1 26232 Decompose GDP by blyr v1612 sector: forward nkage based b,1y 1, y Decompose final goods production by Va source; backward Linkage based
Decomposition of value-added and final goods production based on Leontief insights Decompose GDP by sector; forward linkage based Decompose final goods production by VA source; backward Linkage based When N=G=2 = = r rs s r rs s r rr r r rr r r rs s r rs s r rr r r rr r s ss s s ss s s sr r s sr r s ss s s ss s s sr r s sr r r r s s rs rs rr rr rs rs rr rr ss ss sr sr ss ss sr sr r r s s v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y v b y y y y y b b b b b b b b b b b b b b b b v v v v VBY 2 21 1 2 22 2 2 21 1 2 22 2 1 11 1 1 12 2 1 11 1 1 12 2 2 21 1 2 22 2 2 21 1 2 22 2 1 11 1 1 12 2 1 11 1 1 12 2 2 1 2 1 21 22 21 22 11 12 11 12 21 22 21 22 11 12 11 12 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ˆ
VBY =VLYD VLYF+ VLAF LY+VLAF(BY-LYD (1 )Pure Domestic: VLy, Value added that is domestically produced and consumed (2)Traditional Final Goods Trade: VLYF, Value-added that is embodied in exports/imports of intermediate goods and services (3)Simple GVC: VLA Lr Simple cross country production sharing activities, with only I border crossing. (4) Complex GVC: VLA (BY-LYD ), Complex cross country production sharing activities with at least 2 border crossings
𝑽𝑩𝒀 = 𝑉𝐿𝑌𝐷 + 𝑉𝐿𝑌𝐹 + 𝑉𝐿𝐴 𝐹𝐿𝑌𝐷 + 𝑉𝐿𝐴 𝐹 (𝐵𝑌 − 𝐿𝑌𝐷) (1) Pure Domestic: 𝑉 𝐿𝑌𝐷 , Value added that is domestically produced and consumed. (2) Traditional Final Goods Trade: 𝑉 𝐿𝑌𝐹 , Value-added that is embodied in exports/imports of intermediate goods and services. (3) Simple GVC: 𝑉 𝐿𝐴 𝐹𝐿𝑌𝐷 , Simple cross country production sharing activities, with only 1 border crossing. (4) Complex GVC: 𝑉 𝐿𝐴 𝐹 (𝐵𝑌 − 𝐿𝑌𝐷), Complex cross country production sharing activities, with at least 2 border crossings
vBY=VLYd+VLyF +Vla LYD+VLA (BY-LYDy a Summing up along the row direction Decompose value-added generated from each country-sector pair in terms of where it goes igure la Decomposition of GDP Which types of production and trade are global value chain activities? A country/sector's total Value-added (V) GDP bv industry Forward linkage GVC Participation Ratio: In production of final V GVC In production of final In production of products to domestic market directly(V D) exports directly intermediate exports M-RT) V_GVC sorbed by direct Re-export/re-import importer Complex GVCs Simple GVCs N GVC C)
𝑽𝑩𝒀 = 𝑉𝐿𝑌𝐷 + 𝑉𝐿𝑌𝐹 + 𝑉𝐿𝐴 𝐹𝐿𝑌𝐷 + 𝑉𝐿𝐴 𝐹 (𝐵𝑌 − 𝐿𝑌𝐷) Figure 1a Decomposition of GDP — Which types of production and trade are Global Value Chain activities? Summing up along the row direction: Decompose value-added generated from each country-sector pair in terms of where it goes. Forward Linkage GVC Participation Ratio: 𝑉_𝐺𝑉𝐶 𝑉
vBY=VLYd+VLyF +Vla LYD+VLA (BY-LYDy a Summing up along the column direction Decompose country-sector final goods production in terms of where the value added comes from igure 1b Decomposition final goods production Which part of final goods production and trade belong to gvcs? Production of final goods and services by country/sector(Y) Backward linkage GVC Participation Ratio: Domestic VA in Domestic VA in final Domestic and foreign VA Y GVC domestically used final exports in intermediate imports products(Y D) MY RT) M_ GVC Partner VA in production In production of exported of domestic used products (Y GVC C) Y GVC S
𝑽𝑩𝒀 = 𝑉𝐿𝑌𝐷 + 𝑉𝐿𝑌𝐹 + 𝑉𝐿𝐴 𝐹𝐿𝑌𝐷 + 𝑉𝐿𝐴 𝐹 (𝐵𝑌 − 𝐿𝑌𝐷) Figure 1b Decomposition final goods production — Which part of final goods production and trade belong to GVCs? Summing up along the column direction: Decompose country-sector final goods production in terms of where the value added comes from. Backward Linkage GVC Participation Ratio: 𝑌_𝐺𝑉𝐶 𝑌