Abstract This paper seeks to explain the high persistence in U.S. price differentials found in Cecchetti, S. G., N. C. Mark, and R. J. Sonora. 2002. “Price Index Convergence Among United States Cities.” International Economic Review 43: 1081–99, by means of the concept of change in persistence. To that end, have computed recently developed tests by Kejriwal, M., P. Perron, and J. Zhou. 2013. “Wald Tests for Detecting Multiple Structural Changes in Persistence.” Econometric Theory 29: 289–323, allowing for multiple changes in persistence under the alternative hypothesis. We conclude that change in persistence cannot be ruled out for some city price differentials.