Those who advocate the use of traded good prices [in bringing about purchasing power parity] emphasize the role of commodity arbitrage as the mechanism which governs the relationship between prices and the exchange rate, while those who advocate the broader price index emphasize the role of equilibrium in asset markets as a major factor governing the relationship between prices and the exchange rate.
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This pattern of ‘causality’ [that exchange rates granger-cause prices, rather than vice versa] is consistent with the hypothesis that speeds of adjustment in asset markets exceed those in the commodity markets. Thus, to the extent that exchange rates and commodity prices are influenced by common factors, the differential speed of adjustment may yield the observed pattern of ‘causality’.#
The relationship embodied in the traditional formulations of [purchasing power parity] should not be viewed as a theory of the determination of exchange rates. Rather, it describes an equilibrium relationship between two endogenous variables. As such, the PPP relationship should be viewed as a short-cut rather than a substitute for a complete model of the determination of prices and exchange rates. #