Noisy information, distance and law of one price dynamics across US cities

US micro price data at the city level suggests that both the volatility and the persistence of law of one price deviations are rising in the distance between US cities. A standard two-city equilibrium model with trade costs can predict the relationship between volatility and distance but not between persistence and distance. We show that if there is imperfect information about the state of nominal aggregate demand, with noisy signals that are asymmetric across cities, then distance and persistence will be positively correlated. Our main results are shown to be robust to the introduction of sticky prices and multiple cities.