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8.3. A STOCHASTIC MUNDELL—FLEMING MODEL 247getm t −˜p t +(1−θ)[v t −z t +αδ t ]=d t +ηq t −(σ+λ)(E t q t+1 −q t )−λE t (p t+1 −p t ).(8.37)By (8.36) and (8.34) you know thatE t (p t+1 − p t )=−αδ t +(1− θ)[v t − z t + αδ t ]. (8.38)Substitute (8.38) and ˜p tequation in q tinto (8.37) to get the stochastic difference(η+σ+λ)q t = y t −d t +(1−θ)(1+λ)(v t −z t )−θ(1+λ)αδ t +(σ+λ)E t q t+1 .(8.39)Let the conjectured solution beq t = c 1 y t + c 2 d t + c 3 δ t + c 4 v t + c 5 z t . (8.40)It follows thatE t q t+1 = c 1 y t + c 2 (d t − γδ t ). (8.41)Substitute (8.40) and (8.41) into (8.39) to get⇐(140)(η + σ + λ)[c 1 y t + c 2 d t + c 3 δ t + c 4 v t + c 5 z t ]= y t − d t +(1− θ)(1 + λ)(v t − z t )−θ(1 + λ)αδ t +(σ + λ)[c 1 y t + c 2 (d t − γδ t )].Equating coefficients givesc 1 = 1 η = −c 2,c 3 =c 4 =γ(σ + λ) − ηαθ(1 + λ),η(η + σ + λ)(1 − θ)(1 + λ)= −c 5 ,η + σ + λand the solution isq t = y t − d tη+γ(σ + λ) − αηθ(1 + λ) (1 − θ)(1 + λ)d t +η(η + σ + λ)η + σ + λ (v t − z t ).⇐(141)