Evidence of Markov regime switching in the process governing monetary base growth and in the bilateral exchange rate between the two countries is presented. Given this evidence, a two-country general equilibrium monetary model is constructed to account for observed properties of the U.S.-Canadian dollar exchange rate and for measured effects of monetary policy on key variables. Agents in the model face a monetary policy process with regime switching and form beliefs about regimes and money growth using observations and Bayesian learning. With the driving process for money growth rates parameterized using estimates from U.S. and Canadian data, quantitative implications of the model for behaviors of exchange rates and other key variables are examined. The findings are that inclusion of learning by agents contributes somewhat to the model's ability to account for persistence in effects of money shocks on variables, provided that the shocks themselves are persistent; inclusion of learning contributes little in accounting for business cycle fluctuations and exchange rate variability; inclusion of a nonlinear driving process for money growth rates is important for the model to account for long swings in exchange rates; inclusion of learning adds only slightly to the ability of the model to account for long swings. The importance of nonlinearities in the driving process and the relative lack of importance of learning are consistent with other findings in the literature of learning effects in the face of regime switches.