Failures of the law of one price explain much of the variation in real C.P.!. exchange rates. We use C.P.I. data for U.S. cities and Canadian cities for 14 categories of consumer prices to examine the nature of the deviations from the law of one price. The distance between cities explains a significant amount of the variation in the prices of similar goods in different cities. But, the variation of the price is much higher for two cities located in different countries than for two equidistant cities in the same country. By our most conservative measure, crossing the border adds as much to the volatility of prices as adding 2500 miles between cities.

The value of the dollar appears to move in one direction for long periods of time. We develop a new statistical model of exchange rate dynamics as a sequence of stochastic, segmented time trends. The paper implements new techniques for parameter estimation and hypothesis testing for this framework. We reject the null hypothesis that exchange rates follow a random walk in favor of our model of long swings. Our model also generates better forecasts than a random walk. We conclude that persistent movement in the value of the dollar is a fact that calls for greater attention in the theory of exchange rate behavior. The model is a natural framework for assessing the importance of the "peso problem" for the dollar. It allows for the expectation of future exchange rates to be influenced by the probability of a change in regime. We nonetheless reject uncovered interest parity. The forward premium appears frequently to put too high a probability on a change in regime.

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