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I show that the empirical impulse response of the real exchange rate is hump-shaped. This fact can explain why a number of recent authors have been unable to match the persistence of the real exchange rate using sticky-price business cycle models driven by monetary shocks. The key failure of the models used in the recent literature is that they yield monotonic impulse responses for the real exchange rate. While it is extremely difficult for models that have this feature to match the empirical persistence of the real exchange rate, models that yield hump-shaped impulse responses for the real exchange rate can easily match the empirical persistence of the real exchange rate. I present a two-country sticky-price business cycle model that yields humpshaped responses for the real exchange rate in response to a number of different disturbances. This model can match the half-life of the real exchange rate as well as and the humped shape of its impulse response.

The Dynamic Behavior of the Real Exchange Rate in Sticky Price Models