Ramsey optimal unconventional monetary policy


I’m trying to find Ramsey optimal unconventional monetary policy (UMP). I also posted in another part of the forum (Optimal policy under Ramsey), but as I couldn’t find anything on unconventional policy it seemed worthwhile to open a new thread.

So, my code, which is an adaption of the code provided by the authors of Gertler&Karadi (2011), runs fine when I try to find Ramsey optimal conventional policy (I comment out the Taylor rule in this case and let i be the instrument). However, it doesn’t work for unconventional policy, in particular corporate sector credit policy (I comment out the UMP rule and use psi as the instrument). I get the message that the BK conditions are not fullfilled. Now I try to figure out what I’m doing wrong. Before, I implemented unconventional policy with an optimal simple rule. In the steady steady state I assumed credit provision to be equal to zero. Now, when I try to find Ramsey policy I leave the steady state as it is, hence, I assume that no UMP is provided in the steady state. This might be the problem. But I actually want to keep this feature, because I think it’s much more plausible that the CB resorts to these policies during “crisis” (shocks). And, when the CB provided it also in the steady state, this would be partly offsetting the financial friction. Has anyone elso tried to look at Ramsey optimal unconventioal monetary policy and ran across similar questions? Is there a trick where I can find Ramsey optimal unconventional monetary policy under the condition that it should only be provided out of the steady state? I know from one contribution where UMP is only provided in crisis, but it’s with occasionally binding constraints. (Jiang, 2018, https://onedrive.live.com/?authkey=!AJ_TaGjp-St9Nyc&cid=63E779C8DFC04282&id=63E779C8DFC04282!242152&parId=63E779C8DFC04282!216511&o=OneUp).
So here is my .mod file: FA_CP_new2.mod (9.9 KB)
parameters_FA.mat (2.2 KB)

1 Like

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.

Thank you very much for your explanations.