Managing a Liquidity Trap: Monetary and Fiscal Policy

Working with a continuous-time version of the standard New Keynesian model, this paper studies optimal monetary and fiscal policy in a liquidity trap, where the zero lower bound on the nominal interest rate binds because the natural rate of interest is temporarily negative. Without commitment, a benevolent but discretionary central bank produces deflation and a depressed output gap that worsen, without bound, as the trap’s duration grows – and, perhaps counterintuitively, more flexible prices make both problems strictly worse rather than better, because faster deflation raises the real interest rate further and deepens the slump in a self-reinforcing spiral. Committing to future policy overturns this: the paper proves that optimal policy holds the nominal rate at zero for longer than current inflation alone would justify, which promotes future inflation and a future output boom that (via forward-looking expectations) raises consumption and narrows the output gap today; output must nonetheless start out below its efficient level even under the optimal commitment, and the exit from the trap features a discrete upward jump in the nominal rate even though the underlying natural-rate path is continuous. Adding government spending as a second instrument, the paper shows optimal spending is front-loaded – positive at the start of the trap and negative by its end – but that once spending is decomposed into a purely static, cost-benefit “opportunistic” component (spend more when the shadow cost of resources is low in a slump) and a residual “stimulus” component aimed at managing aggregate demand, stimulus spending is exactly zero at the start of every trap and, for a specific parameter configuration, can be identically zero throughout, so that observed front-loaded spending need not reflect deliberate demand management at all. When monetary policy instead lacks commitment while fiscal policy retains it, stimulus spending becomes unambiguously positive and rising through the trap, substituting for the missing monetary commitment.

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Managing a Liquidity Trap: Monetary and Fiscal Policy