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8.3. A STOCHASTIC MUNDELL—FLEMING MODEL 243of any shock δ t is reversed in the next period. 7 To solve the model, theÞrst thing you need is to get the shadow ßexible-price solution.Flexible Price SolutionUnder fully-ßexible prices, θ = 1 and the goods market is continuouslyin equilibrium y t = yt d . Let q t = s t − p t be the real exchange rate.Substitute (8.19) into the IS curve (8.17), and re-arrange to get˜q t = y à !t − d t ση + σ + E t˜q t+1 . (8.24)η + σThis is a stochastic difference equation in ˜q. It follows that the solutionfor the ßexible-price equilibrium real exchange rate is given bythe present value formula which you can get by iterating forward on(8.24). But we won’t do that here. Instead, we will use the method ofundetermined coefficients. We begin by conjecturing a guess solutionin which ˜q depends linearly on the available date t information˜q t = a 1 y t + a 2 m t + a 3 d t + a 4 δ t . (8.25)We then deduce conditions on the a−coefficients such that (8.25) solvesthe model. Since m t does not appear explicitly in (8.24), it probably isthecasethata 2 = 0. To see if this is correct, take time t conditionalexpectations on both sides of (8.25) to getE t˜q t+1 = a 1 y t + a 2 m t + a 3 (d t − γδ t ). (8.26)Substitute (8.25) and (8.26) into (8.24) to get⇐(139)a 1 y t + a 2 m t + a 3 d t + a 4 δ t= y t − d tη + σ + ση + σ [a 1y t + a 2 m t + a 3 (d t − γδ t )]7 Recursive backward substitution in (8.23) gives, d t = δ t +(1 − γ)δ t−1 +(1 −γ)δ t−2 + ···. Thus the demand shock is a quasi-random walk without drift in thatashockδ t has a permanent effect on d t , but the effect on future values (1 − γ) issmaller than the current effect.