Optimal monetary policy mix at the zero lower bound

We study the optimal mix of forward guidance and quantitative easing at the ZLB. The welfare loss function depends on inflation, output, and consumption heterogeneity (which we label as inequality) between different households. When solely focusing on inflation and output, the central bank excessively expands its balance sheet, thereby increasing inequality. Forward guidance is more effective at stabilising inflation, and quantitative easing at stabilising output. The two tools are, therefore, complementary. Since neither instrument can fully neutralise adverse demand shocks, the optimal policy combines both, resulting in a shorter ZLB duration and milder balance-sheet expansion than if the central bank relied on one policy instrument alone.