First order approximation in Dynare notation


i was working trough the presentation of Mr. Juillard ( … -order.pdf) and got 2 Question:

  1. 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.

  2. 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,

  1. As far as I understand, both are general. The Villemot (2011) version makes use of information on variables that are purely forward-looking and purely backward-looking. Exploiting this information allows greater computational efficiency, but is not essential. Michel does not exploit this info, because it has no didactical value in a presentation.

  2. That is a typo in Michel’s slides. The g_sigma term is missing there.