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

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.