Stable/explosive eigenvalues & variables

Dynare help (legacy posts)
1

Hi everyone,

Is there a way to find out in Dynare, which variables pertain to a stable eigenvalue (i.e. which variables are predetermined) and which variables pertain to an explosive eigenvalue (i.e. which variables are non-predetermined)? The model summary as well as eigenvalues_ don’t provide specific information on that.
Thanks in advance for your help.

Juerg

2

Juerg,

you want a life very easy, but that would be boring. Eigenvalues correspond to unitary combinations of the variables, not directly to the variables. So, if I were so desparate to know the connection, I would look at the qz decomposition. I think that the algerba in Dynare is very similar (up to a handling of variables occurring in both times) to algebra for the first order approximation described in kord.pdf in dynare++ documentation. Hopefully you will be able to to get the link between eigenvalues and linear combinations of the variables. However, I still don’t understand how you want to recognize what linear combination is wrong (the bad eignevalue) and how to correct it when/if you know it.

perhaps this helps and good luck anyway

ondra k.

3

Thank you for your comment.

I was, obviously, not really clear. I just wanted to know, if there was a way to find out, which variables are treated by Dynare as predetermined ones and which are treated as non-predetermined ones when checking the Blanchard-Kahn conditions. (Of course, a variable cannot be simply associated with an eigenvalue; sorry for my poor English)

4

Juerg,

predetermined variables are those which appear at time t-1. Those which appear at time t+1 are forward looking. Their intersection does not need to be empty, some variables may appear at both times t-1 and t+1. Variables which appear only at time t are called static. If you get rid of the variable appearing in both times by introducing auxiliary variables (internally), then you will have predetermined variables and forward looking variables. Their numbers must correspond to the number of eigenvalues in and out of the unit circle.

Ondra K.

5

Thank you for your comments.