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80 CHAPTER 3. THE MONETARY MODEL3.1 Purchasing-Power ParityA key building block of the monetary model is purchasing-power parity(PPP), which can be motivated according to the Casellian approach orby the commodity-arbitrage view.Cassel’s ApproachThe intellectual origins of PPP began in the early 1800s with the writingsof Wheatly and Ricardo. These ideas were subsequently revivedby Cassel [22]. The Casselian approach begins with the observationthat the exchange rate S is the relative price of two currencies. Sincethe purchasing power of the home currency is 1/P and the purchasingpower of the foreign currency is 1/P ∗ , in equilibrium, the relative valueof the two currencies should reßect their relative purchasing powers,S = P/P ∗ .What is the appropriate deÞnition of the price level? The Casselianview suggests using the general price level. Whether the general pricelevel samples prices of non-traded goods or not is irrelevant. As aresult, the consumer price index (CPI) is typically used in empiricalimplementations of this theory. The following passage from Cassel isused by Frenkel [60] to motivate the use of the CPI in PPP research.“Some people believe that Purchasing Power Paritiesshould be calculated exclusively on price indices for suchcommodities as for the subject of trade between the twocountries. This is a misinterpretation of the theory . . . Thewhole theory of purchasing power parity essentially refersto the internal value of the currencies concerned, and variationsin this value can be measured only by general indexÞgures representing as far as possible the whole mass ofcommodities marketed in the country.”The theory implies that the log real exchange rate q ≡ s + p ∗ − pis constant over time. However, even casual observation rejects thisprediction. Figure 3.1 displays foreign currency values of the US dollarand PPPs relative to four industrialized countries formed from CPIs