Optimal Monetary Policy and Liquidity with Heterogeneous Households

This paper derives the optimal money injection at the Zero Lower Bound (ZLB), in a tractable model where households hold heterogeneous money holdings due to explicit financial fric- tions, such as limited participation or temporary binding credit constraints. This framework is moti- vated by recent empirical findings. A deleveraging shock generates deflationary pressure and a fall in the real interest rate, pushing the economy to the ZLB. The main result is that open-market opera- tions can stabilize the economy at the ZLB whereas lump-sum money transfers cannot. Moreover, an optimal money injection does not avoid the economy being at the ZLB