The objective of this paper is to analyze the effects of alternative monetary rules on real exchange rate persistence. Using a two country stochastic dynamic general equilibrium with nominal price stickiness and local currency pricing, we will show how the persistence of PPP deviations can be related to a monetary theory of these deviations. There is no relationship of proportionality between the time during which prices remain sticky and the persistence of the response of the real exchange rate: high nominal price rigidity is not sufficient, per se, in generating any persistence following a monetary shock. Moreover, we emphasize the role of interest rates smoothing policies and relative price stickiness within countries in understanding the relationship between the real exchange rate and monetary shocks. With reasonable parameters values, a wide range of monetary policy rules can generate real exchange rate autocorrelations around .8, close to the one observed in the data.