Deviations from the law of one price across cities: testing for a border effect in persistence and volatility

In this paper, we test for border effects in deviations from the law of one price. With respect to the AR(p) representation of deviations from the law of one price, we test for a border effect in both the sum of the autoregressive coefficients (persistence) and the variance of the disturbance term (volatility). Using consumer price index data for a large number of categories of consumer goods and services for Canadian and U.S. cities from Engel and Rogers (1996), we first use the Hansen (1999) grid-bootstrap procedure to generate median-unbiased estimates of the persistence and volatility in deviations from the law of one price for every city pair and CPI category. We then estimate cross-section regression models across city pairs for the estimates of persistence and volatility for each CPI category, and we find that (after controlling for the distance between cities) crossing the Canadian-U.S. border leads to significant increases in both persistence and volatility for nearly all of the CPI categories. We also document a border effect in both persistence and volatility using the aggregate consumer price index data for European cities from Engel and Rogers (2001).