In first order, impulse response is by default, a difference from deterministic steady states.

In second order, we compute IRF by differencing simulated series and repeat many times. Now I wonder how I should interpret those impulse responses. Because now the IRF is the difference between two series, it is no longer a difference from deterministic steady state but from, what we call, stochastic steady state. Is this right way to interpret this?

FYI, Second order IRF is computed as follows : (from DynareWiki)

"…In Dynare, at order 1, we don’t need to care about the possible values of shocks except for the impulsion, because in a linear model the average effect of symmetric shocks is always 0. This is not true for orders of approximation 2 and above. In that case, we compute the IRF for shock e in the following manner:

1.draw a series of random shocks for 140 periods

2.Perform simulation Y1

3. Add one standard deviation to the simulated series for shock e in period 101

4.Perform simuluation Y2

5.The IRF for this experiment is equal to Y2-Y1

6.Results obtained in 5) is affected by idiosyncratic shocks other than the one impulse in period 101. In order to average over the effect of these idiosyncratic shocks, we 7.perform 50 replications of steps 1) to 5) and report the average.

8.Initial 100 warming periods is the default value of option DROP

9.40 periods for the IRF is the default value of option IRF

10. 50 replications is the default value of option REPLIC