(Optimal) monetary policy with and without debt

We propose a framework of optimal monetary policy where debt sustainability may, or may not, be a relevant constraint for the central bank. We show analytically that in each environment the optimal interest rate path consists of a Taylor rule augmented with forward guidance terms. These terms arise either i) from "twisting interest rates" when the central bank ensures debt sustainability, or ii) under no debt concerns, from committing to keep interest rates low at the exit of the liquidity trap. The optimal policy is isomorphic to Leeper's (1991) "passive monetary/active fiscal policy" regime in the first instance, or "active monetary/passive fiscal policy" regime in the second. We insert our framework into a standard medium scale DSGE model calibrated to the US. Optimal passive monetary policy with debt concerns is ineffective in stabilizing inflation, whereas under no debt concerns, monetary policy is very effective in stabilizing the macroeconomy.