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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].