International Macroeconomics and Finance: Theory and Empirical Methods Phần 9 pdf

9.2. PRICING TO MARKET 297 From the money demand functions it follows that the steady state change in the nominal exchange rate is ˆ S = ˆ M − ˆ M ∗ − 1 ² h ˆ C − ˆ C ∗ i . (9.171) Adjustment to Monetary Shoc ks under Stic ky Prices Consider an unanticipated and permanent monetary shock at time t, where ˆ M t = ˆ M,and ˆ M ∗ t = ˆ M ∗ . As in Redux, the n ew steady state is attained at t +1,sothat ˆ S t+1 = ˆ S, ˆ P t+1 = ˆ P, and ˆ P ∗ t+1 = ˆ P ∗ . Date t nominal goods prices are set and Þxedone-periodinadvance. By (9.10) and (9.11), it follows that the general price levels are also predetermined, ˆ P t = ˆ P ∗ t =0. The short-run versions of (9.141) and (9.142) are ˆ M = 1 ² ˆ C t + β ²(1 − β) ˆ δ t , (9.172) ˆ M ∗ = 1 ² ˆ C ∗ t + β ²(1 − β) [ ˆ δ t + ˆ S − ˆ S t ]. (9.173) Subtracting (9.173) from (9.172) gives ˆ M t − ˆ M ∗ t = 1 ² ( ˆ C t − ˆ C ∗ t ) − β ²(1 − β) ( ˆ S − ˆ S t ). (9.174) From (9.153) and (9.154) you get ˆ C t = ˆ δ t + ˆ C + ˆ P, (9.175) ˆ C ∗ t = ˆ δ t + ˆ C ∗ + ˆ P ∗ + ˆ S − ˆ S t . (9.176) At t +1PPPisrestored, ˆ P = ˆ P ∗ + ˆ S. Subtract (9.176) from (9.175) to get ˆ C − ˆ C ∗ = ˆ C t − ˆ C ∗ t − ˆ S t . (9.177) The monetary shock generates a short-run violation of purchasing power parity and therefore a short-run international divergence of real interest rates. The incompleteness in the international asset market results in imperfect international risk sharing. Domestic and foreign consumption movements are therefore not perfectly correlated. 298CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS To solve for the exchange rate take ˆ S from (9.171) and plug into (9.174) to get " 1+ β ²(1 − β) # ³ ˆ M t − ˆ M ∗ t ´ = 1 ² ³ ˆ C t − ˆ C ∗ t ´ + β ² 2 (1 − β) ³ ˆ C − ˆ C ∗ ´ + β ²(1 − β) ˆ S t . Using (9.177) to eliminate ˆ C − ˆ C ∗ ,youget ˆ S t = β + ²(1 − β) β(² − 1) h ²( ˆ M t − ˆ M ∗ t ) − ( ˆ C t − ˆ C ∗ t ) i . (9.178) This is not the solution because ˆ C t − ˆ C ∗ t is endogenous. To get the solution, you have from the consolidated budget constraints (9.143) and (9.144) ˆ C t = nˆx t (z)+(1− n)[ ˆ S t +ˆv t (z)] − β ˆ b t , (9.179) ˆ C ∗ t =(1− n)ˆx ∗ t (z ∗ )+n[ˆv ∗ t (z ∗ ) − ˆ S t ]+β n 1 − n ˆ b t , (9.180) and you have from (9.147)—(9.150)(201-202)⇒ ˆx t (z)= ˆ C t ;ˆx ∗ t (z ∗ )= ˆ C ∗ t ;ˆv t (z)= ˆ C ∗ t ;ˆv ∗ t (z ∗ )= ˆ C t . (9.181) Subtract (9.180) from (9.179) and using the relations in (9.181), you have ˆ S t =( ˆ C t − ˆ C ∗ t )+ β 2(1 − n) 2 ˆ b t . (9.182) Substitute the steady state change in relative consumption (9.170) into (9.177) to get ˆ b = − 2θ(1 − n) β(1 + θ) [ ˆ C t − ˆ C ∗ t − ˆ S t ], (9.183) and plug (9.183) into (9.182) to get ˆ C t − ˆ C ∗ t − ˆ S t = 2θ (1 + θ) [ ˆ C t − ˆ C ∗ t − ˆ S t ]. It follows that ˆ C t − ˆ C ∗ t − ˆ S t =0. Looking back at (9.183), it must be the case that ˆ b = 0 so there are no current account effects from monetary shocks. By (9.164) and (9.165), you see that ˆ C = ˆ C ∗ =0,andby 9.2. PRICING TO MARKET 299 (9.155) and (9.156) it follows that ˆ P = ˆ M,and ˆ P ∗ = ˆ M ∗ .Moneyis therefore neutral in the long run. Now substitute ˆ S t = ˆ C t − ˆ C ∗ t back into (9.178) to get the solution for the exchange rate ˆ S t =[²(1 − β)+β]( ˆ M t − ˆ M ∗ t ). (9.184) The exchange rate overshoots its long-run value and exhibits more volatility than the monetary fundamentals if the consumption elastic- ity of money demand 1/² < 1. 14 Relative prices are unaffected by the change in the exchange rate, ˆp t (z) − ˆq t (z ∗ ) = 0. A domestic monetary shock raises domestic spending, part of which is spent on foreign goods. Thehomecurrencydepreciates ˆ S t > 0 in response to foreign Þrms repa- triating their increased export ear nings. Because goods prices are Þxed there is no expen diture switching effect. However, the exchange rate adjustment does have an effect on relative income. The depreciation raises current period dollar (and real) earnings of US Þrms and reduces current p eriod euro (and real) earnings of European Þrms. This redis- tribution of income causes home consumption to increase relative to foreign consumption. Real and nominal exchange rates. The short-run change in the real exchange rate is ⇐(205) ˆ P t − ˆ P ∗ t − ˆ S t = − ˆ S t , which is perfectly correlated with t he short-run adjustment in the nom- inal exchange rate. Liquidity effect. If r t is the real interest rate at home, then (1 + r t )= (P t )/(P t+1 δ t ). Since ˆ P t =0,itfollowsthatˆr t = −( ˆ P + ˆ δ t )=−( ˆ δ t + ˆ M) and (9.175)—(9.172) can be solved to get ˆ δ t =(1− β)(² − 1) ˆ M, (9.185) which is positive under the presumption that ²>0. It follows that ⇐(206) 14 Obstfeld and Rogoff show that a sectoral version of the Redux model with traded and non-traded goods produces many of the same predictions as the pricing- to-market model. 300CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS ˆr t =[²(β −1) −β] ˆ M, (9.186) is negative if ²>1. Now let r ∗ t be the real interest rate in the foreign coun try. Then, (1 + r ∗ t )=(P ∗ t S t )/(P ∗ t+1 S t+1 δ t ), and ˆr ∗ t = ˆ S t − [ ˆ P ∗ + ˆ S + ˆ δ t ]. But you know that ˆ P ∗ = ˆ M ∗ =0, ˆ S = ˆ M,soˆr ∗ t =ˆr t + ˆ S t . It follows from (9.184) and (9.186) that ˆr ∗ t = 0. The expansion of the domestic money supply has no effect on the foreign real interest rate. International transmission and co-movements. Since ˆ δ t + ˆ S − ˆ S t =0, it follows from (9.172) th at ˆ C t =[²(1 −β)+β] ˆ M>0 a nd from (9.173) that ˆ C ∗ t = 0. Under pricing-to-market, there is no international trans- mission of money shocks to consumption. Consumption exhibits a low degree of co-movement. From (9.181), output exhibits a high-degree of co-movement, ˆy t =ˆx t = ˆ C t =ˆy ∗ t =ˆv ∗ t . The monetary shock raises con- sumption and output at home. The foreign country experiences higher output, less leisure but no change in consumption. As a result, for- eign welfare must decline. Monetary shocks are positively transmitted internationally with respect to output but are negatively transmitted with respect to welfare. Expansionary monetary policy under pricing to market retains the ‘beggar-thy-neighbor’ prop erty of depreciation from the Mundell—Fleming model. The terms of trade.LetP xt be the home country export price index and P ∗ xt be the foreign country expo rt price index(207-208)⇒ P xt = µ Z n 0 [S t q ∗ t (z)] 1−θ dz ¶ 1/(1−θ) = n 1 1−θ S t q ∗ t , P ∗ xt = µ Z 1 n [q t (z ∗ )/S t ] 1−θ dz ∗ ¶ 1/(1−θ) =[(1− n) 1 1−θ q t ]/S t . Thehometermsoftradeare, τ t = P xt S t P ∗ xt = µ n 1 − n ¶ 1 1−θ S t q ∗ t q t , and in the short run are determined by changes in the nominal exchange rate, ˆτ t = ˆ S t . Since money is neutral in the long run, there are no steady state effects on τ . Recall that in the Redux model, the monetary shock 9.2. PRICING TO MARKET 301 caused a nominal depreciation and a deterioration of the terms of trade. Under pricing to market, the monetare shock results in a short-run improvement in the terms of trade. 302CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS Summary of pricing-to-market and comparison to Redux. Many of the Mundell—Fleming results are restored under pricing to market. Money is neutral in the long run, exchange rate overshooting is restored, real and nominal exchange rates are perfectly correlated in the short run and under reasonable parameter values expansionary monetary policy is a ‘beggar thy neighbor’ policy that raises domestic welfare and lowers foreign welfare. Short-run PPP is violated which means that real interest rates can differ across countries. Deviations from real interest parity allow im- perfect correlation between home and foreign consumption. While con- sumption co-movements are low, outp ut co-movements are high and that is consistent with the empirical evidence found in Chapter 5. There is no exchange-rate pass-through and there is no expenditure switching effect. Exchange rate ßuctuations do not affect relative prices but do affect relative income. For a given level of output, the depreciation generates a redistribution of income by raising the d ollar earnings of domestic Þrms and reduces the ‘euro’ earnings of foreign Þrms. In the Redux model, the exchange rate response to a monetary shock is inversely related to the elasticity of demand, θ. The substitutability between domestic and foreign goods is increasing in θ. Higher values of θ require a smaller depreciation to generate an expenditure switch of a given magnitude. Substitutability is irrelevant under full pricing- to-market. Part of a monetary transfer to domestic residents is spent on foreign goods which causes the home currency to depreciate. The depreciation raises domestic Þrm income which reinforces the increased home consumption. What is relevant here is the consumption elasticity of money demand 1/². In both Redux and pricing to market, one-period nominal rigidities are introduced as an exogenous feature of the environment. This is mathematically convenient b e cause the economy goes to new steady state in just one period. The nominal rigidities can perhaps be moti- vated by Þxed menu costs, and the analysis is relevant for reasonably small shoc ks. If the monetary shock is sufficiently large however, the beneÞts to immediate adjustment will outweigh the menu costs that generate the stickiness. 9.2. PRICING TO MARKET 303 New International Macroeconomics Summary 1. Like Mundell-Fleming models, the new international macroeco- nomics features nominal rigidities and demand-determined out- put. Unlike Mundell-Fleming, however, these are dynamic gen- eral equilibrium models with optimizing agents where tastes and technology are clearly spelled out. These are macroeconomic models with solid micro-foundations. 2. Combining market imperfections and nominal price stickiness allow the new international m acroeconomics to address features of the data, such as international correlations of consumption and output, and real and nominal exchange rate dynamics, that cannot be explained by pure real business cycle models in the Arrow-Debreu framework. It makes sense to analyze the welfare effects of policy choices here, but not in real business cycle mod- els, since all real business cycle dynamics are Pareto efficient. 3. The monopoly distortion in the new international macroeco- nomics means that equilibrium welfare lies below the social op- timum which potentially can be eliminated by macroeconomic policy interventions. 4. Predictions regarding the international transmission of mone- tary sho cks are sensitive to the speciÞcation of Þnancial struc- ture and price setting behavior. 304CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS Problems 1.Solveforeffect on the money comp onent of foreign welfare following a permanent home money shock in the Redux model. (a) Begin by showing that ∆U ∗3 t = −γ µ M ∗ P ∗ 0 ¶ 1−² · ˆ P ∗ t + β 1 − β ˆ P ∗ ¸ Next, sho w that ˆ P ∗ t = −n ˆ S t and ˆ P ∗ = rn(θ 2 − 1) ²[r(1 + θ)+2θ] ˆ S t . Finally, show that ∆U ∗3 t = " −(θ 2 − 1) ²[r(1 + θ)+2θ] − 1 # µ M ∗ P ∗ 0 ¶ 1−² nγ ˆ S t This component of foreign w elfare evidently declines following the permanent M t shoc k. Is it reasonable to think that it will offset the increase in foreign utility from the consumption and leisure components? 2. Consider the Redux model. Fix M t = M ∗ t = M 0 for all t. Begin in the ‘0’ equilibrium. (a) Consider a permanent increase in home governmen t spending, G t = G>G 0 =0. at time t. Sho w that the shock leads to a home depreciation of ˆ S t = (1 + θ)(1 + r) r(θ 2 − 1)+²[r(1 + θ)+2θ] ˆg, andaneffect on the current account of, ˆ b = (1 − n)[²(1 − θ)+θ 2 − 1] ²[r(1 + θ)+2θ + r(θ 2 − 1)] ˆg. What is the likely effect on ˆ b? 9.2. PRICING TO MARKET 305 (b) Consider a temporary home government spending shock in which G s = G 0 =0fors ≥ t + 1,andG t > 0. Show that the effect on the depreciation and current account are, ˆ S t = (1 + θ)r ²[r(1 + θ)+2θ + r(θ 2 − 1)] ˆg t , ˆ b = −²(1 −n)2θ (1 + r) r²[r(1 + θ)+2θ + r(θ 2 − 1)] ˆg t . 3. Consider the pricing-to-market model. Show that a permanent in- crease in home government spending leads to a short-run depreciation of the home currency and a balance of trade deÞcit for the home coun- try. 306CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS [...]... System in 199 2, Mexico in 199 4, and the Asian Crisis of 199 7 Evidently, no Þxed exchange rate regime has ever truly been Þxed This chapter covers models of the causes and the timing of currency crises We begin with what Flood and Marion [57] call Þrst generation models This class of models, developed to explain balance of payments crises experienced by developing countries during the 197 0s and 198 0s These... f = −f , the time unit is one day (∆t = 1), and ut ∼ N (0, 1) λ1 and λ2 are given in (10.34)-(10.35), and A and B are given in (10.38) 318 CHAPTER 10 TARGET-ZONE MODELS and (10. 39) The observations are daily DM prices of the Belgian franc, French franc, and Dutch guilder from 2/01/87 to 10/31 /90 Log exchange rates are normalized by their central parities and multiplied by ¯ 100 The parameters to be... data supports Britain and the U.S were forced off of the gold standard during WWI and the Great Depression More recent collapses occurred in the face of crushing speculative attacks on central bank reserves Some well-known foreign exchange crises include the breakdown of the 194 6— 197 1 IMF system of Þxed but adjustable exchange rates, Mexico and Argentina during the 197 0s and early 198 0s, the European Monetary... interventions Estimating and Testing the Krugman Model DeJong [36] estimates the Krugman model by maximum likelihood and by simulated method of moments (SMM) using weekly data from January 198 7 to September 199 0 He ends his sample in 199 0 so that exchange rates affected by news or expectations about German reuniÞcation, which culminated in the European Monetary System crisis of September 199 2, are not included... DISCRETE INTERVENTION 3 19 Table 10.1: SMM Estimates of Krugman Target-Zone Model (units in percent) with deutschemark as base currency ¯ η σ α f χ2 1 Currency (s.e.) (s.e.) (s.e.) (s.e.) (p-value) Belgian 0. 697 0.865 1.737 2.641 11.672 franc ( 69. 01) (83 .98 ) (327.1) (334.3) (0.001) French 0.007 0.117 6.045 2.44 12. 395 franc (0.318) (1.7 59) (1 590 ) (67.88) (0.000) Dutch 2.484 2.240 4.152 5. 393 11.35 guilder... instant that s touches the lower band s, ds = 0 and G0 (f ) = 1 + λ1 Aeλ1 f + λ2 Beλ2 f = 0 (10.37) (10.36) and (10.37) are 2 equations in the 2 unknowns A and B, which you can solve to get ¯ eλ2 f − eλ2 f A = ¯ ¯ < 0, λ1 [e(λ1 f +λ2 f ) − e(λ1 f +λ2 f ) ] ¯ eλ1 f − eλ1 f B = ¯ ¯ > 0 λ2 [e(λ1 f +λ2 f ) − e(λ1 f +λ2 f ) ] 4 (10.38) (10. 39) In the case of a pure ßoat and in the absence of bubbles, you... (67.88) (0.000) Dutch 2.484 2.240 4.152 5. 393 11.35 guilder (1.317) (0.374) (146. 19) (5.235) (0.001) 10.4 Discrete Intervention Flood and Garber [56] study a target-zone model where the authorities intervene by placing the fundamentals back in the middle of the band ¯ after one of the bands are hit If the band width is β = f − f and ¯ either f or f is hit, the central bank intervenes in the foreign exchange... foreign exchange reserves ¯ when f is hit and gains reserves when f is hit ¯ ˜ ˜ Letting A ≡ Aeλ1 f and B ≡ Beλ2 f , rewrite the solution (10.33) ¯ explicitly as a function of the bands f and f ¯ ¯ ˜ ˜ G(f |f, f ) = f + αη + Aeλ1 (f −f ) + Beλ2 (f −f ) (10.43) ¯ Impose the symmetry conditions, η = 0 and f = f It follows that q ˜ ˜ λ1 = −λ2 = λ = 2/(ασ 2 ) > 0, and B = −A > 0 (10.43) can be ⇐(215) written... (10.48) 8 9 10.6 IMPERFECT TARGET-ZONE CREDIBILITY 323 there will come a time in any target-zone arrangement when it is no longer worthwhile for the authorities to continue to defend the zone This means that the target-zone bands cannot always be completely credible In fact, during the twelve years or so that the Exchange Rate Mechanism of the European Monetary System operated reasonably well ( 197 9— 199 2),... realignments of the bands It would be strange to think that a zone would be completely credible given that there is already a history of realignments We now modify the target-zone analysis to allow for imperfect credibility along the lines of Bertola and Caballero [8] Let the bands for the ¯ ¯ fundamentals be [f , f] and let β = f − f be the width of the band If the fundamentals reach the lower band, there is . (9. 183), it must be the case that ˆ b = 0 so there are no current account effects from monetary shocks. By (9. 164) and (9. 165), you see that ˆ C = ˆ C ∗ =0,andby 9. 2. PRICING TO MARKET 299 (9. 155). (9. 174) From (9. 153) and (9. 154) you get ˆ C t = ˆ δ t + ˆ C + ˆ P, (9. 175) ˆ C ∗ t = ˆ δ t + ˆ C ∗ + ˆ P ∗ + ˆ S − ˆ S t . (9. 176) At t +1PPPisrestored, ˆ P = ˆ P ∗ + ˆ S. Subtract (9. 176) from (9. 175) to. (9. 147)— (9. 150)(201-202)⇒ ˆx t (z)= ˆ C t ;ˆx ∗ t (z ∗ )= ˆ C ∗ t ;ˆv t (z)= ˆ C ∗ t ;ˆv ∗ t (z ∗ )= ˆ C t . (9. 181) Subtract (9. 180) from (9. 1 79) and using the relations in (9. 181), you have ˆ S t =( ˆ C t − ˆ C ∗ t )+ β 2(1 − n) 2 ˆ b t . (9. 182) Substitute the steady state