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 bankâ€™s objective is obtained by taking a second-order approximation to the representative agentâ€™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: https://archives.dynare.org/phpBB3/viewtopic.php%3Fp=25515.html
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-GrohĂ© 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 agentâ€™s welfare or the HHâ€™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 professorâ€¦

Kind regards
Chashika

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