Dear Johannes (and other Dynare users),
I’m currently trying to back out the state space representation of a third order approximation from Dynare’s storage structure and am concerned that the manual (link: dynare.org/manual/index_26.html) has an important typo in the discussion of the G2 matrix in the third-order approximation.
The concern is in the following line:
The reason that there may be a typo is that when I run an exercise using a simple RBC model, I found that only by multiplying ALL of the unfolded version of G2 by 2 can I match the second-order matrices C, D and E as defined in the second-order approximation section of the manual (i.e. 2*oo_.dr_2 returns a folded version of the structures oo_dr.ghxx, oo_dr.ghuu and oo_dr.ghxu). If this is correct (i.e. these matrices should be equivalent) then the manual should state that all elements in the folded matrix must be multiplied by 2 (not only those columns associated with non-squared terms of the approximation).
Also, if my above intuition is right then a second issue arises in the discussion about the G3 matrix. More precisely, do we multiply cross-product terms of order 1 by 6, cross-product terms of order 2 by 3 and leave terms of order 3 as they are? If not, what would be the correct way of recovering the coefficients? A guess based on the previous case of the G2 matrix would be that we simply need to multiply all values in the G3 matrix by 3.
Thankyou for your time,