This study examines how money and monetary policy have influenced output and inflation during the past decade in Israel by comparing two New Keynesian DSGE models. One is a baseline separable model (Gali, 2008) and the other assumes non-separable household preferences between consumption and money (Benchimol & Fourçans, 2012). We test both models by using rolling window Bayesian estimations over the last decade (2001–2013). The results of the presented dynamic analysis show that the sensitivity of output with respect to money shocks increased during the Dot-com, Intifada, and Subprime crises. The role of monetary policy increased during these crises, especially with regard to inflation, even though the effectiveness of conventional monetary policy decreased during the Subprime crisis. In addition, the non-separable model including money provides lower forecast errors than the baseline separable model without money, while the influence of money on output fluctuations can be seen as a good predictive indicator of bank and debt risks. By impacting and monitoring households’ money holdings, policy makers could improve their forecasts and crisis management through models considering monetary aggregates.