Time-varying policy rule under learning

•Literature showed that expectations based rule induces E-stability of equilibrium.•We derive a fundamentals based rule equivalent to the expectations based one.•Such rule is time-varying as agents learn, and induces E-stability.•This rule is learnable by Central Bank while private sector learns.

Previous literature has shown that, in a New Keynesian model, an expectations based policy rule induces E-stability of the fundamental equilibrium, while a fundamentals based one does not. We derive an alternative rule, based only on fundamentals, which can also achieve stability of equilibrium under learning. This policy has parameters that evolve over time and is adaptively learnable by the policymaker.