The first cge model. Johansen for Cops Norway Leif johansen 1930-1982 16
16 The first CGE model: Johansen for CoPS Norway Leif Johansen 1930-1982
Johansen put equations in linear Cops percentage change form K x:=y; *I; +B. *k ∑L1 L*1=∑ Johansens equation system: Qmm*vmn =0 m=no of equations (46), n=no of variables(132 0 mxm mxl mr(n-m)(n-mlrl T*V2 where T=-Ql*Q j is the elasticity of the itn endogenous variable with respect to the jt exogenous variable For Johansen t is 46x86 3956 elasticities Johansen, L(1960), A Multisectoral Study of Economic Growth, Contributions to 17 Economic Analysis 21, North-Holland Publishing Company, Amsterdam, pp x+177
17 CoPS Johansen put equations in linear percentage change form j j X L *K j j j = l j j j j j x * *k = + j j L L = l l j j j L* L * = Johansen’s equation system: 0 Q * v m n m n x x = m= no. of equations (46), n = no. of variables (132) 1 1 2 2 Q * v Q * v + = 0 m mx m 1x m n-m x( ) ( ) n-m x1 1 2 v T* v = where 1 T Q *Q 1 2 − = − Tij is the elasticity of the ith endogenous variable with respect to the jth exogenous variable For Johansen, T is 46x86 3956 elasticities Johansen, L. (1960), A Multisectoral Study of Economic Growth, Contributions to Economic Analysis 21, North-Holland Publishing Company, Amsterdam, pp. x+177
Johansen's t matrix CoP 46by86 18
18 CoPS Johansen’s T matrix 46 by 86
Johansen's CGE model versus Leontief's I-O model: CoPS Effects of demand stimulation Leontief: X(1-A)y Johansen v,=T*v all≥0 mainly >0 (I-A) complementary l≥0 mainly >0 mainly <0 competition T(x, Z) mainly<0 T(x, z) is the 22 by 22 sub-matrix ofT showing 19 elasticities of outputs with respect to exogenous demands
19 CoPS Leontief: X=(I-A)-1*y Johansen: v1 = T*v2 1 (I A)− − = T(x,z) = mainly < 0 all 0 mainly > 0 all 0 mainly > 0 mainly < 0 complementary competition Johansen’s CGE model versus Leontief’s I-O model: Effects of demand stimulation T(x,z) is the 22 by 22 sub-matrix of T showing elasticities of outputs with respect to exogenous demands