Time Consistency and the Duration of Government Debt: A Signalling Theory of Quantitative Easing

We present a signalling theory of quantitative easing in which open market operations that change the duration of outstanding nominal government debt affect the incentives of the central bank in determining the real interest rate. In a time consistent (Markov-perfect) equilibrium of a sticky-price model with coordinated monetary and fiscal policy, we show that shortening the duration of outstanding government debt provides an incentive to the central bank to keep short-term real interest rates low in future in order to avoid capital losses. In a liquidity trap situation then, where the current short-term nominal interest rate is up against the zero lower bound, quantitative easing can be effective to fight deflation and a negative output gap as it leads to lower real long-term interest rates by lowering future expected real short-term interest rates. We show illustrative numerical examples that suggest that the benefits of quantitative easing in a liquidity trap can be large in a way that is not fully captured by some recent empirical studies