We estimate a multivariate unobserved components-stochastic volatility model to explain the dynamics of a panel of six exchange rates against the US Dollar. The empirical model is based on the assumption that both countries' monetary policy strategies may be well described by Taylor rules with a time-varying inflation target, a time-varying natural rate of unemployment, and interest rate smoothing. The estimates closely track major movements along with important time-series properties of the real and nominal exchange rates across all currencies considered. The model generally outperforms a simple benchmark model that does not account for changes in trend inflation and trend unemployment.