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ch9ans - Foundations of International Macroeconomics1...

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Foundations of International Macroeconomics 1 Workbook 2 Maurice Obstfeld, Kenneth Rogo ff , and Gita Gopinath Chapter 9 Solutions 1. (a) In the problem, the government unexpectedly freezes the money supply, which had previously been growing predictably at the proportional rate ° , at the previous period°s level m , say. Since the economy was initially in a steady state, we have that p 0 = m + (1 + η ) ° , which, together with eq. (12) in Chapter 9, implies that q 0 = e 0 m (1 + η ) °. (1) (Recall that y , i , p 0 . This problem di ff ers from the one in section 9.2.5 in that here, there is a forecast error in the level of the date 0 money supply, whereas in the chapter, there is no surprise concerning the date 0 money supply.) Let us reproduce eq. (18) from Chapter 9 (which assumes a constant long-run real exchange rate): e t e flex t = 1 φδ 1 + ψδη ( q t q ) . For t = 0 , we may use eq. (1) to eliminate q 0 from the preceding equation: e 0 e flex 0 = 1 φδ 1 + ψδη [ e 0 m (1 + η ) ° q ] . 1 By Maurice Obstfeld (University of California, Berkeley) and Kenneth Rogo ff (Prince- ton University). c ° MIT Press, 1996. 2 c ° MIT Press, 1998. Version 1.1, February 27, 1998. For online updates and correc- tions, see http://www.princeton.edu/ObstfeldRogo ff Book.html 96
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Observe that e flex 0 , the post-disturbance ° exible-price exchange rate, simply equals q + m (because the money supply has been frozen at its date t = 1 level). The preceding equation therefore becomes e 0 = q + m ° 1 φδ ψδη + φδ (1 + η ) ° = e flex 0 ° 1 φδ ψδη + φδ (1 + η ) °. The e ff ect on the real exchange rate (relative to the economy°s initial path) is the di ff erence e 0 p 0 q = e 0 [ m + (1 + η ) ° ] q , which, from the last displayed equation equals ° 1 φδ ψδη + φδ (1 + η ) ° (1 + η ) ° = ° 1 + ψδη ψδη + φδ (1 + η ) °. Thus, there is an initial real appreciation on date 0, after which the real exchange rate converges back to its long-run level q according to eq. (13) in Chapter 9. [The real appreciation is proportional to the total monetary shock, equal to the money-supply level shock, ° , plus the money-supply growth rate e ff ect, η ° , with the same proportionality factor as in eq. (17), Chapter 9.] From the aggregate demand equation in the chapter, eq. (3), we see that output falls initially by a percentage equal to δ times the percentage real appreciation, and then gradually rises back to its full-employment level. Footnote 17 in the chapter implies that the initial Home-less-Foreign real interest di ff erential is the expected change in q after the shock hits. Equation (13) in the chapter shows that q 1 q 0 = q 1 q ( q 0 q ) = ψδ ( q 0 q ) = ψδ ° 1 + ψδη ψδη + φδ (1 + η ) °. Thus Home°s relative real interest rate rises, a result that also can be derived from eq. (24) in Chapter 9.
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