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3.5. TESTING MONETARY MODEL PREDICTIONS 91wherewehaveusedthefactthatγ =1− ψ. Some additional algebrarevealsVar(∆s t )= (1 − ρψ)2 +2ρψ(1 − ρ)Var(∆f(1 − ρψ) 2 t ) > Var(∆f t ).This is not very encouraging since the levels of the fundamentals areexplosive. The end-of-chapter problems show that neither an AR(1) nora permanent—transitory components representation (chapter 2.4) forthe fundamentals allows the monetary model to explain why exchangerate returns are more volatile than the growth rate of the fundamentals.3.5 Testing Monetary Model PredictionsThis section looks at two empirical strategies for evaluating the monetarymodel of exchange rates.MacDonald and Taylor’s TestThe Þrst strategy that we look at is based on MacDonald and Taylor’s[96] adaptation of Campbell and Shiller’s [20] tests of the presentvalue model. 3 This section draws on material on cointegration presentedin chapter 2.6.Let I t be the time t information set available to market participants.Subtracting f t from both sides of (3.8) givess t − f t = λE(s t+1 − s t |I t )=λ(i t − i ∗ t ). (3.17)s t is by all indications a unit-root process, whereas ∆s t and E(∆s t+1 |I t )are clearly stationary. It follows from the Þrst equality in (3.17) thats t and f t must be cointegrated. Using (3.12) and noting that ψ = λγgives⎛λE t (∆s t+1 ) = λ ⎝γ∞Xj=0ψ j E t f t+1+j − γ∞Xj=0ψ j E t f t+j⎞⎠3 The seminal contributions to this literature are Leroy and Porter [90] andShiller [127].