Optimal monetary policy mix at the zero lower bound

Long-term asset purchases carried out by central banks increase the consumption volatility of households holding long-term debt. For this reason, monetary authorities should not just aim at stabilising inflation and the output gap but also mitigate the volatility of their balance sheet. In response to negative demand shocks at the zero lower bound (ZLB), the optimal monetary policy consists of a mix of forward guidance and mild adjustments in the balance sheet. The presence of balance-sheet policies reduces the optimal ZLB duration and significantly improves social welfare. Mitigating the effectiveness of forward guidance calls for a more substantial balance-sheet expansion and a shorter ZLB duration. If a central bank only aims to stabilise inflation and the output gap, welfare losses are significantly larger than under the optimal policy and balance-sheet policies only improve welfare if the weight on output-gap stabilisation is relatively large. Last, simple implementable policy rules can achieve welfare outcomes close to those under the optimal policy.