Second order approximation and the IRF explosive

  1. I don’t understand your problem. fhat is minus the unconditional welfare (as we are using a minimizer). When I run your code,
fhat =    -6.9770

When I run

options_.noprint=0;
info = stoch_simul(var_list_);

I get

APPROXIMATED THEORETICAL MOMENTS
VARIABLE            MEAN  STD. DEV.   VARIANCE
y                 1.1225     0.0018     0.0000
...
v                 6.9770     0.0016     0.0000

So the value of v and fhat are consistent.
2. The values of the mean are displayed if you reset the noprint option (as shown in point 1). They are stored in oo_.mean