Monetary Policy in Times of Structural Reallocation

We characterize optimal monetary policy in response to asymmetric shocks that shift demand from one sector to another, a condition arguably faced by many economies emerging from the Covid-19 crisis. We show that the asymmetry manifests itself as an endogenous cost-push shock, breaking divine coincidence, and resulting in inflation optimally exceeding its target despite elevated unemployment. In fact, there is no simple, possibly re-weighted, inflation index that can be used as the optimal target. When labor is mobile between sectors, monetary easing can have the additional benefit of inducing faster reallocation, by producing wage increases in the expanding sector.