Hello,
i was working trough the presentation of Mr. Juillard (dynare.org/events/paris1005 … order.pdf) and got 2 Question:

The notation is different to Villemot (2011), in that we do not differentiate between forward and backward looking variables. As far as I understand the difference the Juillard version only approximates the “necessary” equations, whereas the Villemot version is more general, in that it approximates all transition functions, even if we might have them in closed form. Any clarifying comment is greatly appreciated.

On Slide 7, moving from line 2 to 3, i get the term
** (f_y+ g_y g_sigma + f_y+ g_sigma + f_y0 g_sigma ) sigma **
instead of the stated
(f_y+ g_y g_sigma + f_y0 g_sigma ) sigma .
The solution g_sigma = 0, doesn’t change, but I don’t get the intuition.
Thanks a lot for comments,
Fabian