Stabilising Taylor rules when the supply shock has a unit root

• This paper studies the implication of persistent cost-push shocks for the Taylor rule.
• When cost push shocks have a unit root, simple guidance for the Taylor rule is derived.
• For stationarity of inflation, the nominal interest rate should not react to output gaps.
• In this case, response to output gaps is more important than response to inflation.

This paper studies the implication of unit root supply shocks for the Taylor rule. I find that, when supply shocks have a unit root, if a central bank wishes to guarantee the stationarity of inflation, then their interest rate reaction function should not respond to the output gap. Once the stationarity of inflation is guaranteed by the output-gap-response parameter, the “Taylor principle” can be applied for warranting determinacy of the dynamics.