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334 CHAPTER 11. BALANCE OF PAYMENTS CRISESThus there will be a peso problem as long as the Þx isineffect. By(11.17), we know how p t behaves. Now let’s characterize E t (˜s t+1 )andthe forecast errors. First note thatE t (˜s t+1 ) = αγµ + γE t (d t+1 )= αγµE t·µ − 1 λ + d t + v t+1¸= αγµ + µ − 1 λ + d t +E t (v t+1 ). (11.19)(222)⇒E t (v t+1 ) is computed conditional on a collapse next period which willoccur if v t+1 > θ t . To Þnd the probability density function of v conditionalon a collapse, normalize the density of v such that the probabilitythat v t+1 > θ t is 1 by solving for the normalizing constant φ in1=φ R ∞θ tλe −λu du. This yields φ = e λθt . It follows that the probabilitydensity conditional on a collapse next period isf(u|collapse) =(λeλ(θ t −u)u ≥ θ t ≥ 0λe −λu θ t < 0,andE t (v t+1 )=( R ∞θ tuλe λ(θt−u) du = θ t + 1 λθ t ≥ 0R ∞0 uλe −λu du = 1 λθ t < 0 . (11.20)Now substitute (11.20) into (11.19) and simplify to obtainE t (˜s t+1 )=(¯s +γλθ t ≥ 0(1 + α)γµ + γd t θ t < 0 . (11.21)Substituting (11.21) into (11.18) you get the systematic but rationalforecast errors predicted by the modelE t (s t+1 ) − ¯s =( ptγλθ t ≥ 0(1 + α)γµ + γd t − ¯s θ t < 0 . (11.22)