I mean to analyze the welfare loss under different policies and search for the opitmal policy. I set welfare loss function as in Monetary and macroprudential policies.pdf (823.3 KB)
by Angelini et. al.(2012). However, I donāt understand why the value of output gap and inflation in oo_.var is so small, and also these components in welfare loss function are not in the same order of magnitude. Is there anything I missed in the code? Would you please take a look?(The code is sent through message)

And also, the running of code for searching optimal parameters lasts very long time. Is there any way to shorten the time? e.g. loosen the accuracy of parameter or sth?

Iām less experienced in judging the value of variance of output gap, since our definitions or measures of output may be different. But in my project, variance of inflation is indeed small.

Perhaps we can think this phenomenon as follows:
For example, you have the Taylor rule: \displaystyle\frac{R_t}{R}=\left(\frac{\Pi_t}{\Pi}\right)^{\rho_p}\left(\frac{Y_t}{Y}\right)^{\rho_y}.
And you have the loss function: \mathbb{L}=\lambda_1Var (\Pi_t) +\lambda_2Var(Y_t).

Now think Var (\Pi_t) and Var(Y_t) as two distortions, externalities, or rigidities that you want to remove. Given predetermined \lambda_1 and \lambda_2 and given varying \rho_p and \rho_y, you could expect your policy tool R_t can correct / remove \mathbb{L}, with some hidden relations between \lambda_1 and \rho_p and between \lambda_2 and \rho_y. Because actually you have a weighted tool R_t of two instruments \Pi_t and Y_t in your hand. It is equivalently to say we have two instruments \Pi_t and Y_t to remove two distortions Var (\Pi_t) and Var(Y_t).

However, if maintaining the previous Taylor rule, we reset the loss function as: \mathbb{L}=\lambda_1Var (\Pi_t) +\lambda_2Var(GDP_t), by GDP_t\equiv p_{t}Y_t. Then I cannot guarantee Var(GDP_t) has a small value.

All above are my humble opinions. Please wait for Prof. Pfeiferās correction

Thank you very much for your reply. I actually used csminwel function as in Optimal policy parameters in a non-linear model. I wonder if I could change the options in csminwel to shorten the steps of searching parameters. Do you have any advice?

Sorry, @superj, yes, I viewed the linked topic before. I remember that csminwel is also a local method. For my situation, set_param_value(...) seems to be adequate. So Iām afraid that I fail to give you further suggestion.

Instead, CMAES is a global method. I attempted to apply CMAES in a Ramsey situation. See

In the result of my code, the var of output gap is like 5e-04, and var of inflation is like 5e-05. It seems so small that I have never seen such values in any papers. So I wonder if I miss any details?

And also, I get optimal value of the weight of inflation in Taylor Rule is like 38, which is so much larger than the prior or posterior value (around 1.5). Does this make any sense? And whatās the economic meaning if the weight of output gap in Taylor Rule is a negtive number?

Itās more intuitive to look at standard deviations. As I mentioned above, they are in the range of 0.02, i.e. 2 percent per time period in your model. That is normal.

Having the weight on inflation feedback going to infinity is not uncommon. This has been discussed in several posts here on the forum. The typical solution is to impose an upper bound.

With respect to negative output feedback, it is hard to interpret. Is the number meaningful in magnitude? Often times, the objective becomes very flat. If you have an inflation feedback of \approx 40, then having output feedback of -0.5 might not do anything.

To the 2nd one, I wonder if itās meaningful to display this big value of weight on inflation feedback in the paper? Is there any papers have done this before?

And also, if the optimal value of this weight on inflation feedback is actually so big, why prior and posterior value is around 1.5? Is it because itās difficult to achieve such big value in practice? What might be the appropriate upper bound of inflation feedbackļ¼

Looking forward to your advice, and thank you for your time on this.