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218 CHAPTER 7. THE REAL EXCHANGE RATEIf that is indeed the case, then in light of the statistical difficultiessurrounding unit-root tests, it can be argued that we should not evencare whether the real exchange rate has a unit root but we should insteadfocus on measuring the economic implications of the real exchangerate’s behavior. What market participants care about is the degree ofpersistence in the real exchange rate and one measure of persistence isthe half life.The annualized half-lives reported in Table 7.2 are based on estimatesadjusted for bias by Kendall’s formula [equation (2.81)]. 4 Theaverage half-life is 3.7 years when the US is the numeraire country. Thatis, on average, it takes 3.7 years–quite a long time since the businesscycle frequency ranges from 1.25 to 8 years–for half of a shock to thelog real exchange rate to disappear. The average half-life is 2.6 yearswhen Germany is the numeraire county.Univariate tests using data from the post Bretton-Woods ßoat typicallycannot reject the hypothesis that the real exchange rate is drivenby a unit-root process. Using the US as the home country, only two ofthetestscanrejecttheunitrootatthe10percentlevelofsigniÞcance.The results are somewhat sensitive to the choice of the home (numeraire)country. 5 Part of the persistence exhibited in the real valueof the dollar comes from the very large swings during the 1980s. Thereal appreciation in the early 1980s and the subsequent depreciationwas largely a dollar phenomenon not shared by cross-rates. To illustrate,the evidence for purchasing-power parity is a little stronger whenGermany is used as the home country since here, the unit root can berejected at the 10 percent level of signiÞcance for German real exchangerates with several European countries.Univariate Tests for PPP Over Long Time SpansOne reason that the evidence against a unit root in q t is weak may bethat the power of the test is low with only 100 quarterly observations. 64 Christiano and Eichenbaum [27] put forth this argument in the context of theunitrootinGNP.5 A point made by Papell and Theodoridis [119].6 The power of a test is the probability that the test correctly rejects the nullhypothesis when it is false.
7.4. LONG-RUN ANALYSES OF REAL EXCHANGE RATES 219Table 7.2: Augmented Dickey-Fuller Tests for a Unit Root in Post-1973Real Exchange RatesRelative to USRelative to GermanyCountry τ c (p-value) half-life τ c (p-value) half-lifeAustralia -1.895 (0.329) 4.582 -2.444 (0.124) 2.095Austria -2.434 (0.126) 3.208 -3.809 (0.004) 5.516Belgium -2.369 (0.138) 4.223 -2.580 (0.093) 2.914Canada -1.342 (0.621) – -2.423 (0.127) 2.914Denmark -2.319 (0.155) 3.733 -3.212 (0.017) 1.759Finland -2.919 (0.039) 2.421 -2.589 (0.089) 3.208France -2.526 (0.105) 2.761 -4.540 (0.001) 0.695Germany -2.470 (0.118) 3.025 – – –Greece -2.276 (0.169) 4.336 -2.360 (0.140) 1.278Italy -2.511 (0.107) 2.580 -1.855 (0.351) 5.709Japan -2.057 (0.252) 9.251 -1.930 (0.314) 11.919Korea -1.235 (0.677) 3.274 -2.125 (0.215) 1.165Netherlands -2.576 (0.094) 2.623 -2.676 (0.075) 2.969Norway -2.184 (0.193) 2.668 -2.573 (0.095) 2.539Spain -2.358 (0.140) 5.006 -2.488 (0.113) 2.861Sweden -2.042 (0.257) 5.516 -2.534 (0.103) 1.719Switzerland -2.670 (0.076) 2.215 -3.389 (0.011) 1.759UK -2.484 (0.113) 2.313 -2.272 (0.169) 3.274Notes: Half-lives are adjusted for bias and are measured in years. SigniÞcance atthe 10 percent level indicated in boldface.
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CONTENTSvii11 Balance of Payments C
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2 CHAPTER 1. SOME INSTITUTIONAL BAC
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80 CHAPTER 3. THE MONETARY MODEL3.1
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82 CHAPTER 3. THE MONETARY MODEL604
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84 CHAPTER 3. THE MONETARY MODEL0 <
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86 CHAPTER 3. THE MONETARY MODELexc
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92 CHAPTER 3. THE MONETARY MODEL=
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96 CHAPTER 3. THE MONETARY MODELTab
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102 CHAPTER 3. THE MONETARY MODELMo
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104 CHAPTER 3. THE MONETARY MODELwh
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106 CHAPTER 4. THE LUCAS MODEL(76)
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108 CHAPTER 4. THE LUCAS MODELsubje
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110 CHAPTER 4. THE LUCAS MODELeach
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112 CHAPTER 4. THE LUCAS MODELcompl
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116 CHAPTER 4. THE LUCAS MODELc yt
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118 CHAPTER 4. THE LUCAS MODELIn eq
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120 CHAPTER 4. THE LUCAS MODELn t =
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122 CHAPTER 4. THE LUCAS MODELRearr
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124 CHAPTER 4. THE LUCAS MODELTable
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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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130 CHAPTER 4. THE LUCAS MODELdisco
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132 CHAPTER 4. THE LUCAS MODEL1.02A
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134 CHAPTER 4. THE LUCAS MODELAppen
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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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268CHAPTER 9. THE NEW INTERNATIONAL
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308 CHAPTER 10. TARGET-ZONE MODELSa
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314 CHAPTER 10. TARGET-ZONE MODELSl
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318 CHAPTER 10. TARGET-ZONE MODELSa
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320 CHAPTER 10. TARGET-ZONE MODELSM
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322 CHAPTER 10. TARGET-ZONE MODELSt
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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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