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208 CHAPTER 7. THE REAL EXCHANGE RATEexpenditures to switch from home goods toward foreign goods. Domesticoutput might then be expected to fall in response. Although thedomestic traded-goods sector is hurt, consumers evidently beneÞt. Onthe other hand, a real depreciation may be beneÞcial to the tradedgoodssector and harmful to consumers. The foreign debt of manydeveloping countries, is denominated in US dollars, however, so a realdepreciation reßects a real increase in debt servicing costs. These expenditureswitching effects are absent in the ßexible price theories thatwe have covered thus far.So what leads you to conclude that PPP does not hold in the longrun. Would this make any sense? What theory predicts that PPPdoes not hold? The Balassa [6]—Samuelson [124] model, which is developedin this chapter provides one such theory. The Balassa—Samuelsonmodel predicts that the long-run real exchange rate depends on relativeproductivity trends between the home and foreign countries. If relativeproductivity is governed by a stochastic trend, the real exchangerate will similarly be driven and will not exhibit any mean-revertingbehavior.Theresearchonrealexchangeratebehaviorraisesmanyquestions,but as we will see, offers few concrete answers.7.1 Some Preliminary IssuesThe Þrst issue that you confront in real exchange rate research is thatdata on price levels are generally not available. Instead, you typicallyhave access to a price index Pt I , which is the ratio of the price level P tin the measurement year to the price level in a base year P 0 . Lettingstars denote foreign country variables and lower case letters to denotevariables in logarithms, the empirical log real exchange rate uses priceindices and amounts toq t =(p 0 − p ∗ 0 )+s t + p ∗ t − p t. (7.2)s t +p ∗ t −p t is the relative price of the foreign commodity basket in termsof the domestic basket. This term is 0 if PPP holds instantaneously,and is mean-reverting about 0 if PPP is violated in the short run butholds in the long run. Tests of whether PPP holds in the long run