Welfare comparison with Ramsey optimal policy

[bvajda]

Hi All,

I'm trying to compare the welfare properties of different policy rules in a version of the Gertler and Karadi (2011). In all of my model specifications I'm able to include a Welfare variable such that Welf = U(c,l) + beta*Welf(+1) , so I can directly see the welfare response for given exogenous shocks. As for a policy comparison, I also have the Ramsey optimal policy, however I encounter two problems:

1) For any general policy objevtive function (excluding the contemporaneous utility function), dynare runs into a 'maxit' problem. The code runs however, but there's clearly something wrong.

2) If the policy objective function is given by the utility function (which would be preferable to me instead of ad hoc quadratic loss functions), I'm not even able to include Welfare into the model equations as it coincides with the policy funtion. As a consequence, I tried to replicate the loss function (in the welfare sense) but the IRF of the Welfare (or loss) for different shocks of the ramsey model is not appropriate (performs worse sometimes for specific shocks than the others).

I could greatly appreciate if anyone could point me to the source of the problem and how could it be remediated.
I attached the simplified versions of the above mentioned codes.

Best,

Balazs

[jpfeifer]

1. Please use the unstable version. I don't get a maxit problem there
2. By design, it is not possible with Ramsey to have the welfare definition in the model and as the objective as in that case, you have the objective function again as a constraint. That will introduce a singularity. You have to drop the welfare definition from the model-block and only use it for the policy objective.
3. How do you judge that Ramsey performs worse?

[bvajda]

Thanks for recommending to use the unstable version, now I don't run into a maxit problem.
Regarding performance, when I set the policy objective function in the ramsey model to maximize welfare, then I assess the model performance on the Welfare IRF for some shocks. As we cannot include a Welfare variable in the ramsey model block, I replicated it outside the code in the "MP_Comparison.m" file under 'loss3' variable. Since the steady state of the ramsey and the benchmark (IT) model is the same, I can assess the performance of the two models in a welfare sense by looking at the Welfare losses due to exogenous shocks. And my problem is, as I mentioned, that Ramsey suffers bigger losses than some other monetary policy framework (e.g. nGDP targeting).

I attached the additional relevant codes as well as an updated MP_Comparison .m file, which replicates the above mentioned

[jpfeifer]

Welfare analysis is not my strong suit, thus the late reply. Is it necessary that the Ramsey policy yields higher welfare as a response to every single shock? Alternatively, could it be that Ramsey is computed around a wrong steady state? There may be multiple ones.