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7.4. LONG-RUN ANALYSES OF REAL EXCHANGE RATES 217that services are relatively labor intensive. While this may be true ofsome services, such as haircuts, it is not true that all services are nontradedor that they are labor intensive. Financial services are sold athome and abroad by international banks which make them traded, andtransportation and housing services are evidently capital intensive.7.4 Long-Run Analyses of Real ExchangeRatesEmpirical research into the long-run behavior of real exchange rateshas employed econometric analyses of nonstationary time series andis aimed at testing the hypothesis that the real exchange rate has aunit root. This research can potentially provide evidence to distinguishbetween the Casselian and the Balassa—Samuelson views of the world.Univariate Tests of PPP Over the FloatTo test whether PPP holds in the long run, you can use the augmentedDickey-Fullertest(chapter2.4)totestthehypothesisthattherealexchange rate contains a unit root. Using quarterly observations of theCPI-deÞned real exchange rate from 1973.1 to 1997.4 for 19 high-incomecountries, Table 7.2 shows the results of univariate unit-root tests forUS and German real exchange rates. Four lags of ∆q t and a constantwere included in the test equation. The p-values are the proportion ofthe Dickey—Fuller distribution that lies to the left (below) τ c . Includinga trend in the test regressions yields qualitatively similar results andare not reported.Statistical versus Economic SigniÞcance. Classical hypothesis testingis designed to establish statistical signiÞcance. Given a sufficiently longtime series, it may be possible to establish statistical signiÞcance of thestudentized coefficients to reject the unit root, but if the true value ofthe dominant root is 0.98, the half-life of a shock is still over 34 yearsand this stationary process may not be signiÞcantly different from atrue unit-root process in the economic sense.