Price levels in the European Monetary Union: Even tradables follow independent random walks

•Pairwise analysis of the time series behavior of the real exchange rates between the founding member states of the European Monetary Union.•Based on the Harmonized Index of Consumer Prices and eight sub-components for tradable and non-tradable goods and services.•The results of pairwise tests show that the real exchange rates are typically random walks and their components are generally not cointegrated.•Online graphical simulation tools, which demonstrate the relationship between the price levels and inflation differentials, for the case where price levels follow independent stationary processes around linear trends and for the case where price levels follow independent random walk processes. This study analyzes the time series behavior of real exchange rates between member states of the European Monetary Union. The analysis is based on the Harmonized Index of Consumer Prices and eight sub-components for tradable and non-tradable goods and services. Stationarity of the real exchange rates is a necessary condition for long-term convergence of price levels. The results of pairwise tests show that the real exchange rates, resulting from these price levels are typically random walks and their components are generally not cointegrated. There is no evidence of the existence of country-specific convergence clusters. A systematic difference in the results for tradable and non-tradable goods cannot be detected.