Hi Valerio88,
FIRST AND FOREMOST, I am deeply indebted to you for your patient answer! and sorry for my late reply.
Your first paragraph is very clear. I understand. So we just follow usual Dynare practice, it will do the rest thing for us.
Then I’m a little missed. First I don’t find the command simult_ or simult, do you mean stoch_simul ? Perhaps I have to read the manual and more codes to concrete our discussion.
If I understand correctly, when I just want to an illustrative IRF, then without assigning initial values, Dynare may (latently) guess one, generating the whole sequence. But when I want to precise values for each element in the sequence, say \{C_t\}_{t=0}^{\infty}, that is, I want to collect them for further various computations, then I need specify initial values, which are customized and subject to / depends on my particular purpose.
But for example, if I want to calculate the standard deviation of C_t, \sigma_c. Which way should I adopt? In practice, I think the first way is enough. Yet based on your reply and my understanding, it seems to be the second way… Another example, (I’m not sure about it, just for illustration), in welfare analysis, if I want to compute: \sum\beta^t\log C_t, then which method shall I employ? I often heard “XXX is very sensitive to initial guess”. Does this example belongs to the situation?
==============================
The second snapshot comes from
Kitano and Takaku(2017), Capital Controls, Monetary Policy, and Balance Sheets in a Small Open Economy.
The equilibrium definition is very common across the literature.
The first one comes from an old unpublished paper, whose “ex ante” notion I believe is based on some Sutherland’s work.