No Eigenvalues larger than 1


#1

Dear all,

I have a little conceptual question on eigenvalues:
What does it mean if the model does not feature any eigenvalue larger than 1?

I am working on a model that features indetereminacy and I applied the Farmer et al. (2015) method to be able to solve the model in dynare. However, the model is such that the only forward looking variable is the indeterminate one and there are no eigenvalues larger than 1. The dynamics of the model look fine once the redefinition of Farmer et al. is applied, still I was wondering if there is no timing mistake hidden and what this eigenvalue result actually means.

Thank you for your help! :slight_smile:


#2

To get a unique determinate bounded solution, you need one eigenvalue bigger than 1 for each forward-looking variable. The explosive eigenvalues are needed to rule out all explosive unbounded paths. If you do not have such an eigenvalue, then all paths are stable and you cannot select a single one by appealing to boundedness. Thus, it is expected that an indeterminate model with only 1 forward-looking variable does not have an explosive eigenvalue.