A new method called MitISEM was developed to estimate DSGE models efficiently. It uses Importance Sampling and an adaptive scheme based on Expectation-Maximization. The method was tested on two DSGE models and an open economy model involving Canada and the US. Results showed that increasing productive government spending boosts domestic private consumption, while unproductive spending decreases it. Regardless of the spending type, more public spending leads to an exchange rate appreciation and an improved trade balance. The level of trade openness affects how government spending shocks spread.