Comparing the Welfare under Ramsey Policy and OSR

Dear Prof. Pfeifer,

I have been trying all the resources here to find a solution to my problem but I could not.

I developed a DSGE model similar to Airaudo and Olivero (2019). They use Ramsey Policy. I developped the model and code.

Now I want to compare the Ramsey Policy (RP) vs Simple Optimal Rule (OSR). i.e. instead of adopting a more complex RP I want to know if we can find the optimal parameter values for the Taylor rule that might deliver a closer welfare gains to RP.

I use the ramsey_policy command to run the RP and osr command to run the optimal simple rule. The entire model is same in both cases and the initial values in RP has been adjusted as you have advised (i.e. conditional on R_ss).

Following (Airaudo and Olivero, 2019), the central bank’s objective is obtained by taking a second-order approximation to the representative agent’s welfare. Which will give me the following Loss function;

Loss = (1/2)*(coeff_pi * (pi^2) + coeff_y_gap * (Y_g^2))

I specify this loss function under planner_objective in the ramsey_policy command and I use coeff_pi and coeff_y_gap as optim_weights in osr command. If my understanding is correct this implies: loss = coeff_pi*var(pi) + coeff_y_gap*var(Y_g).

Next, I want to compare the welfare under these TWO policies. i.e. Adopting a Ramsey Policy vs OSR to see which policy I should recommend. In doing that I want to make a welfare comparison.

From this post:
I understand that I cannot simply use the value of the objective function in ramsey_policy and osr to compare these two policies.

But Schmitt-Grohé and Uribe (2007) Table 2, they do a Welfare comparison between Ramsey Policy and OSR. Please kindly advice how can I do a similar comparison using ramsey_policy and 'osr` commands in Dynare. Unfortunately I cannot follow the method they have done, because they do not use Dynare as you may know.

Question: 1
I am really grateful to you if you could kindly advice me how I should carryout the welfare comparison between these two policies (welfare under RP vs OSR).

Question: 2
Should I use,
Loss = (1/2)*(coeff_pi * (pi^2) + coeff_y_gap * (Y_g^2))
function which I obtained by taking a second-order approximation to the representative agent’s welfare or the HH’s Utility function as the planner_objective in the ramsey_policy?

I am extremely sorry for asking such a long questions, I was trying to figure it out myself but I am completely lost.

Thank you very much for your time professor…

Kind regards

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