2nd order moments different from steady state values


I have made a model using growth rate and level of variables. When I use the stoch_simul command, the results indicated oor the empirical mean differ depending on whether I used first or second order approximation. First order values are corresponding exactly to the steady state one and are fine, but for the second order one, it is not the case.
Could someone explain me why ?

I would like to correct these deviations of the theorical mean from the steady state value, but I cannot manage to understand their origins. Could someone helps me to understand what is happenning ?


You are confusing the deterministic steady state and the ergodic distribution. See