When does the cost channel pose a challenge to inflation targeting central banks?

In a sticky-price model where firms finance their production inputs, there is both a lower and an upper bound on the central bank's inflation response necessary to rule out the possibility of self-fulfilling inflation expectations. This paper shows that real wage rigidities decrease this upper bound, but coefficients in the range of those on the Taylor rule place the economy well within the determinacy region. However, when there is time-variation in the share of firms who finance their inputs (i.e. Markov-Switching) then inflation targeting interest rate rules are often found to result in indeterminacy, even if the central bank also targets output. In this case, adding money growth as an intermediate target in the Taylor rule can alleviate this indeterminacy and anchor inflation expectations. Whether the money growth target should be a constant feature of the central bank's policy rule or Markov-Switch depends on the weight the central bank places on output stability relative to inflation stability and the size of money demand shocks.