This paper examines the dynamic relationship between the price of crude oil and the CPI energy price sub-index in Canada and the U.S. using a Markov-regime switching model and the Bai-Perron sequential method. Since these two series are cointegrated during the sample period (January 1961-June 2013), a short-run dynamic model is thus estimated for each country in which all coefficients and the error-variance terms can freely switch over time between two values prevailing in Regimes 0 and 1. Previous studies indicate that the price of crude oil does not currently affect the aggregate CPI as much as it did in the 1970s. This finding is not disputed in this paper. However, the sequentially-determined break date as well as the time-varying regim...