I have a few general questions about Second Order approximations.
- What would be the best go-to paper/guide to learn the general procedure? (preferably with examples and not a description of the general matrix procedure only).
- Can you solve a DSGE model that combines first and second order approximations?
- Any matlab codes or (dynare codes) that can approximate a non-linear system into a second order approximation would be much appreciated.
Note: I know dynare can solve Second Order Approximations by just setting order=2, but I need to do this by hand for several equations as it is important for me to understand the behavior of certain dynamics. Thus, simply plugging in the non-linear model into dynare wouldn’t be of use for me (hence this thread)
Thanks Johannes. I may be missing something here, but a first and second order linear approximations don’t have any non linearities right? What I meant in 2 is that I want to combine a first and second order approximation into the equilibrium of the system. I don’t want to exploit the original non-linear system.
A second order approximation is not linear. There will be quadratic terms.
Yes that was silly on my part.
Back to my previous question, can I mix linear and non-linear equations in dynare. With respect to my case, first and second order approximations?
Yes, of course, with the caveat mentioned above.
Are you aware of any code in dynare that does this that I could reference?
Not really. What people sometimes do is have a nonlinear mod-file with
order=2 where some linearized equations are appended.