Managing a Liquidity Trap: Monetary and Fiscal Policy

I study monetary and fiscal policy in liquidity trap scenario, where the zero bound on the nominal interest rate is initially binding. I adopt a continuous-time formulation of the standard New Keynesian model, which allows for an intuitive, graphical analysis and produces some novel results. Without commitment the economy suffers from deflation and depressed output. Perhaps counterintuitively, both are exacerbated with greater price flexibility. Turning to optimal monetary policy, I find that the interest rate should be kept at zero past the liquidity trap. I also show that inflation may be positive throughout. Thus, the absence of deflation is not evidence against a liquidity trap, but may actually be an optimal response to it. Output, on the other hand, always starts below its efficient level and rises above it. Finally, I study fiscal policy and show that, regardless of parameters that underlie estimated "multipliers", at the start of a liquidity trap spending be above its natural level. However, I also show that spending should declines and go below its natural level before returning to zero. I then decompose spending into its "opportunistic" and "stimulus" motives. The former is the optimal level of government purchases from a static, cost-benefit standpoint; the latter measures deviations from the former. I show that, at the start of a liquidity trap, optimal stimulus spending may be positive or negative.