It is common in the literature on optimal policy to use conditional welfare starting from the deterministic steady state, the reason being to take into account the transition from the deterministic to the stochastic steady state, quoting Schmitt-Grohe and Uribe (2004): “Because different policy regimes will in general be associated with a different stochastic steady state, using unconditional expectations of welfare amounts to not taking into account the transitional dynamics leading to the stochastic steady state” as a reason for using conditional welfare.
However, the concept of stochastic steady state that SGU are referring to is not clear to me. Kim and Kim (2003) define the stochastic steady state as “a stochastic steady state which is defined as the expected value of a variable”. This means that in the SGU paper the stochastic steady state can be defined as the expected value of any variable conditional on the deterministic steady state? or in other words, is the stochastic steady state equal to the deterministic steady state plus the uncertainty correction?
Another related question. Is the risky steady state equal to the stochastic steady state?
I would really appreciate your comments, regards.