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7.4. LONG-RUN ANALYSES OF REAL EXCHANGE RATES 225Table 7.7: Canzoneri et. al.’s IPS tests of Balassa—SamuelsonAllEuropeanVariable countries G-7 Countries(p N − p T ) − (x T − x N ) -3.762 -2.422 –s t − (p T − p ∗ T )(dollar) -2.382 -5.319 –s t − (p T − p ∗ T )(DM) -1.775 – -1.565Notes: Bold face indicates asymptotically signiÞcant at the 10 percent level.retail trade,” “restaurants and hotels,” “transport, storage and communications,”“Þnance, insurance, real estate and business,” “communitysocial and personal services,” and the “non-market services” sectors.Their analysis begins with the Þrst-order conditions for proÞt maximizingÞrms. Equating (7.12) to (7.13), the relative price of nontrad- ⇐(133)ables in terms of tradables can be expressed asP NP T= 1 − α T A T k α TT1 − α N A N k α (7.19)NNwhere k = K/L is the capital labor ratio. By virtue of the Cobb-Douglas form of the production function, Ak α = Y/L is the averageproduct of labor. Let x T ≡ ln(Y T /L T )andx N ≡ ln(Y N /L N )denotethe log average product of labor. We rewrite (7.19) in logarithmic formasµ 1 − αTp N − p T =ln + x T − x N . (7.20)1 − α NTable 7.7 shows the standardized ¯t calculated by Canzoneri, Cumbyand Diba. All calculations control for common time effects. Theirresults support the Balassa—Samuelson model. They Þnd evidence thatthere is a unit root in p N − p T and in x T − x N , and that they arecointegrated, and there is reasonably strong evidence that PPP holdsfor traded goods.