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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.