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Appendix 1 - Reduced form equations of the model in section 4

In this appendix we derive the reduced form equations for l_t and ln(C / P)_t
corresponding to model discussed in section 4, i.e., the model composed of equations
(3.1), (3.2), (3.3) and (4.1) with γ₂ =0.

For ease of presentation we start by repeating the equations of the model:

ln(D/P)t^d =β0+β1lnyt+β2πt+β3it

(+)      (-)    (-)

(A1.1)

^ln( D / P ) S = γ о+Yιlⁿ(R / P)⁺γ з it⁺γ 4 r
(+)          (+) (-)

ln(C/P)_t^d =λ₀+λ₁lny_t+λ₂π_t+λ₃l_t+λ₄i_t
(+)     (-)    (-) (+)

(A1.2)

(A1.3)

ln(C / P)S = α0 + α₁ln(D / P)_t + α2ln(D / P)_t z_t + α3l_t + α4i_t + α₅π_t
(+)            (-)               (+) (-)   (-)

From (A1.1) and (A1.2) we get the equilibrium solution for the money market:

it = μ0⁺μι lⁿ( R / P ) t⁺ μ2 lⁿ y_t ⁺ μ3^πt⁺μ4 r

(-)             (+)       (-) (+)

(A1.5)

where

ln( D / P ) t = δ0 + δι ln( R / P ) t + δ2 ln y_t + δ3∏t + δ4 r_t
(+)            (+)        (-) (-)

(A1.6)

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