We modify the Gali and Monacelli small open economy dynamic stochastic general equilibrium (DSGE) model, calibrate to Mexican data and simulate the impact of the financial crisis on Mexico, under floating and counter factual fixed exchange rates. The floating exchange rate ameliorates welfare losses for Mexico. They are greater under fixed exchange rates because the return paths to equilibrium are more volatile (higher variance) and output, consumption and employment impulse response functions (IRFs) overshoot. Monetary policy, inflation targeting with floating exchange rates, clearly reduced the welfare costs vis‐à‐vis other counter factual policies including consumer price index‐based Taylor rule, domestic inflation Taylor rule and fixed exchange rates.