Using US micro price data at the city level, we provide evidence that both the volatility and the persistence of deviations from the law of one price (LOP) are rising in the distance between US cities. A standard, two-city, stochastic equilibrium model with trade costs can predict the relationship between volatility and distance but not between persistence and distance. To account for the latter fact, we augment the standard model with noisy signals about the state of nominal aggregate demand that are asymmetric across cities. We further show that the main predictions of the model continue to hold even if we allow for the interaction of imperfect information, sticky prices, and multiple cities.