Probelm with parameter setting in welfare function

Dear Professor Pfeifer,

I read in this paper (page 16 in Monetary and macroprudential policies.pdf (823.3 KB)
) that the welfare loss function is written as L=\sigma _{\pi }^{2}+\sigma _{B/y}^{2}+\left( {{k}_{y,cb}}+{{k}_{y,mp}} \right)\sigma _{y}^{2}+{{k}_{r}}\sigma _{\Delta r}^{2}+{{k}_{v}}\sigma _{dv}^{2}.
Generally, how should we set these preference parameters like {k}_{y,cb} {k}_{r}? Their values seem quite important to the result of seeking optimal policy.

Thank you for your time reading this post.

Most often, these parameters are derived from household preferences as suggested in the cited paper. However, sometimes people just use values from the literature. That’s what they did in the referenced paper.

Dear Professor Pfeifer,

I have got another confusing question:
In that paper, the author considered the non-corporation case between monetary policy and macroprudential policy (as the description in page 17). In that case, policymakers minimizes their own objective function and treat the other policy rule as given. I have no idea how to realize this. For example, when I was minimizing the objective function of monetary policy, how should I set the parameter in macroprudential policy rule?

Thanks again for your kindness.

My guess is you have to iterate sequentially over the two problems until convergence is achieved.

Dear Professor Pfeifer,

Under what circumstances does it indicate that the “convergence is achieved”?

Thank you.

If the values of the objective function do not change by more than a specified tolerance.