Model variables x observable variables

Dear all,
I have a question about how I present the results of my estimates.
I read published papers and this is not clear to me.
I would like to present the IRFs and make a comparative table with the second simulated moment, based on the estimates of the model’s posteriors.
Should I present the IRF of the model variables, for example the y_hat, pi_hat or R_hat (my model variables) or my y_obs, pi_obs and R_obs?
The second moment that I want to compare with the data, should I simulate the y_hat, pi_hat or R_hat or my observables y_obs, pi_obs and R_obs?
Thank you in advance,

For judging model fit, you compare the moments of the data with the ones corresponding objects in the model, i.e. y_obs etc. Otherwise, you would be comparing apples and oranges.

Things are different for IRFs. Here, you can plot the IRFs of the objects that are of interest to you, which is typically y_hat etc.

Dear professor Johannes,
Thanks for the answer.
Now all my doubts are cleared.