Ramsey optimal unconventional monetary policy

A couple of notes:

  1. Ramsey looks for the unconstrained efficient policy. It will be nature also try to alleviate frictions present in steady state, because they create first order welfare losses. So when you want to put in a restriction that the instrument is not used in steady state, you are actually leaving the Ramsey framework and move to a rule-based setup. For that reason, I have no idea on how to do this. Essentially, you are trying to put an additional constraint on the static model.
  2. As outlined in my reply at Optimal policy under Ramsey, numerical steady state finding in the Ramsey case is often problematic. The problem is nonlinear, so there might be different steady states. I have seen cases where depending on the initial values chosen, the BK conditions were satisfied for some steady states found and not satisfied for others.