Optimal monetary policy under learning in a new Keynesian model with cost channel and inflation inertia

We show that a so-called expectations-based optimal monetary policy rule has desirable properties in a standard New Keynesian model augmented with a cost channel and inflation rate expectations that are partly backward-looking. In particular, optimal monetary policy under commitment is associated with a determinate rational expectations equilibrium that is stable under least squares learning for all parameter constellations considered, whereas, under discretion in policy-making, the central bank has to be sufficiently inflation rate averse for the rational expectations equilibrium to have the same properties.