I am interested in calculating the stochastic steady state of my model. If I choose a second order approximation in stoch_simul, are the values contained in the vector ys_ (dynare 3) or oo_.steadystate (dynare 4) the stochastic steady state?
In case they are not, how can I recover the stochastic steady state?

It depends on what you mean by stochastic steady state, since the definition of what is this point is not universal.

If you mean the point where the agents decide to stay, in the absence of shocks, but taking into account the likelihood of future shocks, then Dynare doesnâ€™t compute this point. Note that oo_.steady_state is the deterministic steady state, i.e. the point where the agents decide to stay, in the absence of shocks, and ignoring future shocks.

If you mean the mean of the ergodic distribution of endogenous variables, then you can retrieve it in oo_.mean

I meant actually the point where agents decide to stay in absence of shocks but taking into account the likelihood of future shocks.
Thanks a lot for your reply