For the steadystate-operator question, see [An infinity of steady states with Taylor rules)
- Yes, you can use any objective function you want as long as you find a recursive representation, but you need to go to second order. That allows you implement the conditional variance as e.g.
(pi(+1)-pi_ss)^2. If you are interested in the unconditional variance, you can loop over the required parameters to minimize some linear combination in oo_.var. That is what the osr-command does. - Schmitt-Grohé/Uribe (2007): “Optimal simple and implementable monetary and fiscal rules - Expanded Version” is similar. Note that for the osr-command, it is the unconditional variance that is minimized.