The Central Bank's Dilemma: Look Through Supply Shocks or Control Inflation Expectations?

When countries are hit by supply shocks, central banks often face the dilemma of either looking through such shocks or reacting to them to ensure that inflation expectations remain anchored. In this paper, we propose a tractable framework to capture this dilemma and explore optimal policy under a range of assumptions on how expectations are formed, including a form of bounded rationality involving level-k thinking (LKT). Despite modelling LKT in a way that nests both adaptive and rational expectations as special cases, we show that the optimal policy under LKT is qualitatively different and involves abrupt pivots in the policy stance. In particular, it is optimal for the central bank to initially look through supply shocks until a threshold is reached, then pivot discontinuously to a more hawkish anti-inflationary stance. We find that such pivots can, if optimally executed, be compatible with soft landings in the sense that most (or even all) of the reduction in inflation occurs through re-anchoring of expectations rather than economic slack. We also discuss risks and why policy errors in terms of tightening too late or too slowly can be especially costly in such an environment.