The law of two prices: trade costs and relative price variability

The paper investigates whether deviations from the law of one price can attributed to real factors, such as transportation and distribution costs. Even if trade is costly, the prices of a good at di.erent locations will be linked as long as the good is traded. Instead of the usual iceberg assumption, I model costly trade as a transportation sector that uses real resources with potentially different factor intensities than the production of the good. First I use a latent factor model to see if distance specific ("transportation") and location specific ("retailing") factors can explain deviations from the law of one price across U.S. cities. For many products, these two factors explain 10-20% of all the variation in prices. The estimated transportation factor tends to move together with oil prices. Next I derive the variance of relative prices at di.erent locations when the price of transportation is determined in general equilibrium. This variance is high if (i) the good is costly to transport and (ii) it is produced with different factor intensities than transportation. Preliminary empirical results suggest that goods similar to transportation in terms of factor intensity have indeed lower relative price variability. As these goods tend to be costly to ship, this helps resolve the puzzling finding of Engel and Rogers (2001) that less tradable goods have less volatile relative prices.