Optimal constrained interest-rate rules under heterogeneous expectations

This paper examines optimal monetary policy under heterogeneous expectations. To this end, we develop a stochastic New Keynesian model with a cost-push shock and coexistence of one-step-ahead rational and adaptive expectations in decentralized markets. On the one side, heterogeneous expectations imply an amplification mechanism that has many adverse consequences missing under the rational expectations paradigm. On the other side, even discretionary optimal monetary policy can manipulate expectations via a novel channel. We argue that the incorporation of heterogeneous expectations in both the design and implementation of discretionary optimal monetary policy to exploit this channel lowers macroeconomic volatility. We find that: (1.) surprisingly, a more hawkish policy can reduce losses due to volatility, but an overly hawkish policy does not; (2.) overestimating the share of rational expectations in the design and implementation of policy creates additional losses, while the underestimation does not; (3.) credible commitment eliminates or mitigates many of the ramifications of heterogeneous expectations.