The large recession that followed the Global Financial Crisis of 2008-09 triggered unprecedented monetary policy easing around the world. Most central banks in advanced economies deployed new instruments to affect credit conditions and to provide liquidity on a large scale after short-term policy rates had reached their effective lower bound. In this paper, we study if this new set of tools, commonly labeled as unconventional monetary policies (UMP), should continue to be used once economic conditions and interest rates have normalized. In particular, we study the optimality of asset purchase programs by using an estimated non-linear DSGE model with a banking sector and long-term private and public debt for the United States. We find that the benefits of using such UMP in normal times are substantial, equivalent to 1.45 percent of consumption. However, the benefits of using UMP are shock-dependent and mostly arise when the economy is hit by financial shocks. By contrast, when more traditional business cycle shocks (such as supply and demand shocks) hit the economy, the benefits of using UMP are negligible or zero.