International real business cycle (IRBC) models predict a real exchange rate volatility that is much lower than the levels observed in the data. In this paper, we build a two-country IRBC model with both a traded and a non-traded goods sector, and calibrate it to UK-euro area (EA) data. We provide evidence on the existence of a cointegrating relationship between UK and EA traded sector total factor productivity (TFP) by estimating a vector error correction model (VECM). To account for this relationship, we incorporate non-stationary technology shocks in the traded sectors in our model, and show that then the model is able to match the observed volatility of the UK-EA real exchange rate. Our analysis points out that both the presence of non-traded sectors and non-stationary technology shocks are necessary to account for the observed volatility in the real exchange rate.