I would like to use different initial values for the state variables of my model from the steady-state that my model ends up, to do this i use:
I want to simulate the model and produce simulated series for the endogenous variables of it (2nd order approximation).
I do this WITH and WITHOUT using the “simul_replic” option (when i use simul_replic i take into account all the simulated series produced by using the function “get_simul_replications” created by J. Pfeifer, see sites.google.com/site/pfeiferecon/dynare).
The results differ substantially.
Which approach should i use?
Please keep in mind that the initial point of departure plays an important role in my exercise.
I think that when i use simul_replic option (see WITH) the effect of the initial values weakens as i increase the number in “simul_replic” option. Is this true?
You are correct that histval in the context of stochastic simulations allows setting the starting values for the simulation (by default, it is the deterministic steady state). , But remember that only the state variables in the starting point are relevant. For example, saying y=1 as the starting value won’t work, because y is a function of the states like capital or TFP.
Note that this does not apply to IRFs. If you want to start IRF simulations from a particular starting point, you have to do this directly using the simult_ function. See e.g. [Simulate a model using smoothed shocks). There you can provide starting values (insteady of ys, which is the steady state).
In general, for all types of simulations you will face a particular problem if you want to use pruning. With pruning, your state space becomes larger because you need to keep track of both the first and second order terms whose sum makes up the starting values for the states (and there are infinitely many combinations of first and second order terms that result in a particular starting value for the states). Currently, there is not yet a way to provide those terms separately.
Regarding your initial question: due to the non-linear state space, the average simulation with simul_replic is the correct one. The other one is conditional on a particular sequence of shocks. Ideally, you want to integrate out these shock sequences by averaging (similar to GIRFs).