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226 CHAPTER 7. THE REAL EXCHANGE RATESize Distortion in Unit-Root TestsEmpirical researchers are typically worried that unit-root tests mayhave low statistical power in applications due to the relatively smallnumber of time series observations available. Low power means thatthe null hypothesis that the real exchange rate has a unit root will bedifficult to reject even if it is false. Low power is a fact of life becausefor any Þnite sample size, a stationary process can be arbitrarily wellapproximated by a unit-root process, and vice versa. 10 The conßictingevidence from post 1973 data and the long time-span data are consistentwith the hypothesis that the real exchange rate is stationary but thetests suffer from low statistical power.The ßip side to the power problem is that the tests suffer size distortionin small samples. Engel [45] suggests that the observational equivalenceproblem lies behind the inability to reject the unit root duringthe post Bretton Woods ßoat and the rejections of the unit root in theLothian—Taylor data and argues that these empirical results are plausiblygenerated by a permanent—transitory components process with aslow—moving permanent component. Engel’s point is that the unit-roottests have more power as T grows and are more likely to reject withthe historical data than over the ßoat. But if the truth is that the realexchange rate contains a small unit root process, the size of the testwhich is approximately equal to the power of the test, is also higherwhen T is large. That is, the probability of committing a type I erroralso increases with sample size and that the unit-root tests suffer fromsize distortion with the sample sizes available.10 Think of the permanent—transitory components decomposition. T < ∞ observationsfrom a stationary AR(1) process will be observationally equivalent to Tobservations of a permanent—transitory components model with judicious choice ofthe size of the innovation variance to the permanent and the transitory parts. Thisis the argument laid forth in papers by Blough [16], Cochrane [30], and Faust [50].
7.4. LONG-RUN ANALYSES OF REAL EXCHANGE RATES 227Real Exchange Rate Summary1. Purchasing-power parity is a simple theory that links domesticand foreign prices. It is not valid as a short-run proposition butmost international economists believe that some variant of PPPholds in the long run.2. There are several explanations for why PPP does not hold. TheBalassa—Samuelson view focuses on the role of nontraded goods.Another view, that we will exploit in the next chapter, is thatthe persistence exhibited in the real exchange rate is due tonominal rigidities in the <strong>macroe</strong>conomy where Þrms are reluctantto change nominal prices immediately following shocks ofreasonably small magnitude.
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CONTENTSvii11 Balance of Payments C
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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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112 CHAPTER 4. THE LUCAS MODELcompl
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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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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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276CHAPTER 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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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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