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240 CHAPTER 8. THE MUNDELL-FLEMING MODEL2.32.22.12.01.91 9 17 25 33 41 49 57Figure 8.7: Exchange Rate Overshooting in the Dornbusch model withπ =0.15, δ =0.15, σ =0.02, λ =5.the monetary expansion produces a liquidity effectdi = − 1 dm < 0. (8.15)λDifferentiate (8.9) while holding i ∗ constant and use d¯s = dm to getdi = θ(dm − ds). Use this expression to eliminate di in (8.15). Solvingfor the instantaneous depreciation yieldsµds = 1+ 1 dm > d¯s. (8.16)λθThis is the famous overshooting result. Upon impact, the instantaneousdepreciation exceeds the long-run depreciation so the exchangerate overshoots its long-run value. During the transition to the longrun, i
8.3. A STOCHASTIC MUNDELL—FLEMING MODEL 241tals even when agents have perfect foresight. The implied dynamics areillustrated in Figure 8.7.If there were instantaneous adjustment (π = ∞), we would immediatelygo to the long run and would continuously be in equilibrium. Solong as π < ∞, the goods market spends some time in disequilibriumand the economy-wide adjustment to the long-run equilibrium occursgradually. The transition paths, which we did not solve for explicitlybut is treated in the chapter appendix, describe the disequilibrium dynamics.It is in comparison to the ßexible-price (long-run) equilibriumthat the transitional values are viewed to be in disequilibrium.There is no overshooting nor associated excess volatility in responseto Þscal policy shocks. You are invited to explore this further in theend-of-chapter problems.8.3 A Stochastic Mundell—Fleming ModelLet’s extend the Mundell-Fleming model to a stochastic environmentfollowing Obstfeld [111]. Let ytd be aggregate demand, s t be the nominalexchange rate, p t be the domestic price level, i t be the domesticnominal interest rate, m t be the nominal money stock, and E t (X t )bethe mathematical expectation of the random variable X t conditionedon date—t information. All variables except interest rates are in naturallogarithms. Foreign variables are taken as given so without loss ofgenerality we set p ∗ =0andi ∗ =0.The IS curve in the stochastic Mundell-Fleming model isy d t = η(s t − p t ) − σ[i t − E t (p t+1 − p t )] + d t , (8.17)where d t is an aggregate demand shock and i t − E t (p t+1 − p t )istheexante real interest rate. The LM curve ism t − p t = y d t − λi t, (8.18)where the income elasticity of money demand is assumed to be 1. Capitalmarket equilibrium is given by uncovered interest parityi t − i ∗ = E t (s t+1 − s t ). (8.19)
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CONTENTSvii11 Balance of Payments C
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2 CHAPTER 1. SOME INSTITUTIONAL BAC
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106 CHAPTER 4. THE LUCAS MODEL(76)
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126 CHAPTER 4. THE LUCAS MODEL4.5 C
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128 CHAPTER 4. THE LUCAS MODELTable
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132 CHAPTER 4. THE LUCAS MODEL1.02A
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136 CHAPTER 4. THE LUCAS MODELProbl
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138 CHAPTER 5. INTERNATIONAL REAL B
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162CHAPTER 6. FOREIGN EXCHANGE MARK
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290CHAPTER 9. THE NEW INTERNATIONAL
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308 CHAPTER 10. TARGET-ZONE MODELSa
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320 CHAPTER 10. TARGET-ZONE MODELSM
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324 CHAPTER 10. TARGET-ZONE MODELS
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326 CHAPTER 10. TARGET-ZONE MODELS
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328 CHAPTER 11. BALANCE OF PAYMENTS
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358 AUTHOR INDEXFama, E.F., 161, 16
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Subject IndexAAbsorption, 16, 230AI
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362 SUBJECT INDEXEfficient capital
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364 SUBJECT INDEXMethod of undeterm
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366 SUBJECT INDEXRisk neutrality, 9
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368 SUBJECT INDEXImpulse response a
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