The possible long-run relationships between the Consumer Price Index and the Wholesale Price Index are analyzed for three inflation targeting countries - Canada, Sweden and the UK - using three different statistical techniques. The Engle-Granger test finds cointegration only for Sweden. The Johansen's test and the model-free and seasonality robust periodogram based test conclusively show that the two price indexes are not cointegrated in the three countries included in the sample. Hence, the values of these indexes may consistently diverge over time. However, the two price indexes move together in the short run. These findings have some implications for the success of inflation targeting monetary policies. © 2006 - IOS Press and the authors. All rights reserved.