When governments are over-indebted, it is mainly the role of monetary policy to focus on reflating the economy in order to release it from the liquidity trap. We show that the following problems may arise in this context: linking inflation expectations to base money developments; increased uncertainty on the possible reversal of quantitative easing by central banks in close correlation with banks' lower liquidity preference after escaping the liquidity trap; higher inflation when central banks fail to reverse the quantitative easing at an adequate pace for a long period; losses reported by central banks once economies exit the liquidity trap and yields go up. Given the recurrence of the instability cycle and the higher probability of the economy to avoid falling into the liquidity trap if inflation is relatively high when a bubble bursts, then such inflation is preferable to a relatively low one. This paper proposes an enhancement of the monetary policy objective by shifting from explicit or implicit targeting of low and stable inflation to targeting moderate and stable inflation.