Dynare's third-order approximation

Stochastic simulations
1

Hi everyone, I have a question about dynare’s third-order approximation. According to the formula in dynare manual :

yt=ys+G0+G1zt+G2(zt⊗ zt)+G3*(zt⊗ zt⊗ zt)

so when all the state variables in a steady state, and all shocks are equal to 0, zt should be zero vector, then turned to yt = ys + G0.
When all state variables are in steady state and the shock is 0, yt should be equal to ys, but G0 is also a non-zero vector.
So there seems to be a contradiction? What is the reason for this?

I think about this because I would like to read out the policy functions in the case of a third order approximation.

2

Starting with second order, a model with 0 shocks will not converge to the deterministic steady state as its fixed point but rather the stochastic steady state.