ρ0 =
α0λ3 - α3λ0
λ3- α3
α1λ3
ρ1 = 13
λ3- α3
α2λ3
ρ2 = 23
λ3- α3
(+) (-)
(A1.12)
α3λ1 α5λ3 - α3λ2 α4λ3 - α3λ4
31 53 32 43 34
45
λ3- α3 λ3- α3 λ3- α3
(+) (-) (?)
Finally substituting (A1.5) and (A1.6) into (A1.9) and (A1.10) we get the reduced
form equations for lt and ln(C / P)t . The reduced form for ln(C / P)t , which is
equation (4.2) in the main text, reads as:
ln(C / P) = θ0 + θι ln yt + θ2 ln ytzt + θ3rt + θ4rtzu
(?) (-) (?) (+)
+ θ5πt + θ6πtzit + θ7 ln(R / P) + θ8 ln(R / P)zt + θ9zt
(?) (+) (?) (-) (?)
where
θ1 = Ρ1δ2 + P 3 + P 5μ2 =
αiλ3βiγ 3 λια 3(β3 γ 3) βι(α 4 λ3 α 3λ4)
(λ3- α 3)(β3- γ 3)
(A.14)
θ2=P2δ2=
α 2λ3β1Y 3
(λ3 - α3 )(β3 - γ3 )
θ3 = P1δ4 + P5μ4 =
α1λ3β3γ4 + (α4λ3 - α3λ4)γ4
(λ3 - α3)(β3 - Y3)
θ4=P2δ4=
α 2λ3βY 4
λ - α3 )(β3 - γ3)
(A1.15)
(A1.16)
(A1.17)
θ5 = P1δ3 + P 4 + P5μ3 =
-α1λ3β2γ3-(β3-γ3)(α5λ3-α3λ2)-β2(α4λ3-α3λ4)
(λ3-α3)(β3-γ3)
(A1.18)
θ6 = ρ2δ3 =-----α 2λ3β2γ 3---
6 3 (λ3 -α3)(β3 - γ3)
(A1.19)
θ7 p1δ1 + ρ5μi
αiλ3β3γi + Y1(a 4λ3 α 3λ4)
(λ3- α 3)(β3- γ 3)
(A1.20)
41
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