Analytics of the government expenditure multiplier with QE

This paper analyses the government expenditure multiplier at the zero lower bound (ZLB) in the presence of quantitative easing (QE), using a tractable New Keynesian model with financial frictions. We show that sufficiently large exogenous QE can lift the economy off the ZLB, thus yielding multipliers below one even for a small fiscal stimulus. Pre-commitment to a gradual QE unwinding further reduces the fiscal stimulus needed to keep multipliers below unity. When QE instead follows an instrument rule that responds to conventional monetary shortfalls, the multiplier can remain below one even at the ZLB. This result also holds under an optimally designed, welfare-based QE policy. Our analysis provides theoretical support for the growing empirical evidence that government spending multipliers can remain below unity at the ZLB.