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This paper investigates the sources of exchange rate fluctuations when monetary policy follows a Taylor rule interest rate reaction function. We first present a simple dynamic exchange rate model with Taylor rule fundamentals which is triangular in the long-run impacts of shocks to the output market, the interest rate differential, and the Taylor rule. We then proceed to assess the relative importance of various shocks in exchange rate determination by estimating a structural VAR with long-run identification restrictions based on the triangular structure of the model. We find demand shocks to be less important than in earlier VAR studies, with both supply shocks and nominal shocks explaining a substantial part of real exchange rate fluctuations.