1 A Recursive Dynamic Computable General Equilibrium Model For ...

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1 − ρ ⎡ −ρ ⎤ , = , ⎢∑δ , , , , ⎥ ⎣ = 1 ⎦ n X j k Aj k i j kVi j k (B9) i Substituting (B9) into (B8) simplifies the latter: i, j, k − ρ j, k ( 1+ ρ ) j, k i, j, k −( 1+ ρ ) i, j, R = ΛA X δ V k (B10) where (B9) and (B10) are the levels first order conditions. Linearisation of (B9) gives: where n x j, k ∑ Si, j, kvi , j, k i= 1 S = (B11) δ V − ρ l, j, k l, j, k l, j, k = n −ρ ∑δ i, j, kVi, j, k i= 1 (B12) Substituting (B10) into the input expenditure share formula (B13) in the intermediate nest: R V 1, j, k 1, j, k n ∑ Ri, j, kVi, j, k i= 1 58 (B13) and cancelling terms shows the equivalence of expressions (B12) and (B13). This alternative form of the share Si,j,k avoids the process of calibration since it eliminates distribution parameter δ i,j,k where the shares are merely updated by the percentage changes in prices and quantities. Linearisation of (B10) gives: = λ ( 1 ρ) ( 1+ ρ) (B14) r i, j, k + + x j, k − vi, j, k Thus, equations (B11) and (B14) are linearised first order conditions, where r, x, v and λ are percentage changes in R, X, V and Λ.
Rearrange (B14) in terms of v i,j,k gives: = σ σλ (B15) v i, j, k − ri , j, k + + x j, k where σ is the elasticity of substitution between all pairwise types of primary factors (i.e. labour, capital) in the value added nest: 1 σ = (B16) 1+ ρ substituting (B15) into (B11) and rearranging in terms of σλ yields: n ∑ i= 1 σλ = σ S r (B17) i, j, k i, j, k Substituting (B17) into (B15) eliminates the percentage change Lagrangian variable λ. Factorising the resulting expression gives linearised CES Hicksian primary factor demands: v n ⎡ = x j, k − ⎢ri , j, k −∑ S ⎣ i= r i, j, k σ i, j, k i, j, k (B18) 1 <strong>For</strong> consistent aggregation expression (B19) must hold: n U j, k X j, k ∑ Ri, j, kVi, j, k i= 1 ⎤ ⎥ ⎦ = (B19) By linearising (B19), substituting (B11) and rearranging, it is possible to derive the percentage change in the composite price in the value added nest as: n u j, k ∑ Si, j, k ri , j, k i= 1 = (B20) Further substitution of (B20) into (B18) gives a simplified version of the linearised Hicksian demand function: 59
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A Recursive Dynamic Computable Gene
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Figure 5: The Private consumption n
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which the commodity is purchased. I
Page 7 and 8: 1.1.2 Private Final Demand In ORANI
Page 9 and 10: capital goods in industry ‘i’ i
Page 11 and 12: nesting to incorporate energy deman
Page 13 and 14: Note, that the values of the capita
Page 15 and 16: disposable income grouping. 11 Once
Page 17 and 18: equal for each using industry ‘i
Page 19 and 20: modelled as sector-wide output cons
Page 21 and 22: Spain on (i) the biophysical charac
Page 23 and 24: the crops for which data on ‘gros
Page 25 and 26: ⎡ B ⎤ AREA = 1 − ⎢ ρ ⎣C
Page 27 and 28: qo(i,r) q1lnd(FCP) q1lnd(other agri
Page 29 and 30: Given that set-aside is mainly comp
Page 31 and 32: Price Pm Pfob Expenditure E1 E0 Q m
Page 33 and 34: household income is simply the addi
Page 35 and 36: G t = I/K (22) Relating changes in
Page 37 and 38: An additional extension of this dyn
Page 39 and 40: pick up) rather than a long term st
Page 41 and 42: A proportional link between househo
Page 43 and 44: (TRANSFER(“spend”)), less socia
Page 45 and 46: downward (negative) shock in the ex
Page 47 and 48: the data base and model structure a
Page 49 and 50: Harrison, W. J., and K. R. Pearson
Page 51 and 52: Appendix A: Nesting The choice of f
Page 53 and 54: The second condition is that the ag
Page 55 and 56: Appendix B: A Linearised representa
Page 57: Note that the absence of any price
Page 61 and 62: t n ⎡ = y j, k − ⎢ f n, j, k
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