Convergence to the law of one price without trade barriers or currency fluctuations

Using a panel of 51 prices from 48 cities in the United States, we provide an upper bound estimate of the rate of convergence to purchasing power parity. We find convergence rates substantially higher than typically found in cross-country data. We investigate some potentially serious biases induced by i.i.d. measurement errors in the data, and find our estimates to be robust to these potential biases. We also present evidence that convergence occurs faster for larger price differences. Finally, we find that rates of convergence are slower for cities farther apart. However, our estimates suggest that distance alone can only account for a small portion of the much slower convergence rates across national borders.