The Law of One Price Without the Border: The Role of Distance Versus Sticky Prices

We examine the role of nominal price rigidities in explaining the deviations from the Law of One Price (LOP) across cities in Japan. Focusing on intra-national relative prices isolates the border effect and thus enables us to extract the pure effect of sticky prices. A two-city model with nominal rigidities and transportation costs predicts that the variation of LOP deviations is lower for goods with less frequent price adjustment after controlling for the distance separating the cities. Using retail price data for individual goods and services collected in Japanese cities, we find strong evidence supporting this prediction. Adapting the Engel and Rogers (1996) regression framework to our theoretical setting, we quantify the separate roles of nominal rigidities and trade costs (proxied by distance) in generating LOP variability. Our estimates suggest that the distance equivalent of nominal rigidities can be as large as the `width' of the border typically found in the literature on international LOP deviations. The findings point to both the utility of the regression framework in identifying qualitative effects (i.e., sign of a coefficient) and the challenges interpreting their quantitative implications.