Active and passive monetary policy in an overlapping generations model

We consider an overlapping generations model in which the growth rate of money is determined either by inflation forecast targeting or by inflation targeting. New money is distributed via lump-sum transfers to old agents. We study how the responsiveness of the policy rule with respect to (expected) inflation affects determinacy and stability of the monetary steady state. A policy rule is called active (passive) if it responds strongly (weakly). Active inflation forecast targeting reinforces mechanisms that lead to indeterminacy. Active inflation targeting, on the other hand, makes indeterminacy less likely but can create instability of the monetary steady state.