Adaptive Importance Sampling for DSGE Models

This paper introduces a new adaptive methodology for the estimation of Dynamic Stochastic General Equilibrium (DSGE) models based on the Mixture of Students t by Importance Sampling weighted Expectation-Maximization (MitISEM). The use of Importance Sampling and of an adaptive scheme based on Expectation-Maximization allows us to eficiently estimate any sort of DSGE model. We apply the MitISEM in simulation examples with two workhorse DSGE models. Our results indicate how the MitISEM achieves identification of the model parameters even in the presence of bimodality. We also use the MitISEM to estimate an open economy model encompassing international trade between two countries, namely Canada and the US. For both countries, we consider a rich fiscal policy sector that includes two di erent types of public expenditure: productive and unproductive government spending. Our findings show that, in the presence of nominal rigidities, an increase in productive spending generates a crowding-in on domestic private consumption, whereas unproductive spending induces a fall in domestic private consumption. We also find that irrespective of the type of government expenditure, an increase in public spending for the domestic economy induces an exchange rate appreciation and an improvement in the trade balance. Finally, our results show that the degree of trade openness matters in terms of propagation of government spending shocks.