Dealing with a liquidity trap when government debt matters: optimal time-consistent monetary and fiscal policy

How does the need to preserve government debt sustainability affect the optimal monetary and fiscal policy response to a liquidity trap? To provide an answer, we employ a small stochastic New Keynesian model with a zero bound on nominal interest rates and characterize optimal time-consistent stabilization policies. We focus on two policy tools, the short-term nominal interest rate and debt-financed government spending. The optimal policy response to a liquidity trap critically depends on the prevailing debt burden. While the optimal amount of government spending is decreasing in the level of outstanding government debt, future monetary policy is becoming more accommodative, triggering a change in private sector expectations that helps to dampen the fall in output and inflation at the outset of the liquidity trap