A central puzzle in international macroeconomics is that observed real exchange rates are highly volatile. Standard International Real Business Cycle (IRBC) models cannot reproduce this fact when calibrated using conventional parameterizations, and can only generate one fourth of the real exchange rate volatility observed in the data. Typically, IRBC models are solved assuming that total factor productivity (TFP) processes are stationary. In this paper, we …rst show that TFP processes for the U.S. and the "rest of the world" have a unit root, are cointegrated, and can be jointly characterized with a Vector Error Correction Model (VECM). Then, we explore the implications of extending an otherwise standard international real business cycle model that allows for cointegrated technology shocks. We show that the model can account for the high real exchange rate volatility observed in the data without having to rely on any particular nominal or real friction. Also, we show that the increase of relative volatility of the real exchange rate with respect to output in the last 20 years can be explained by changes in the parameter estimates of the VECM.