Where do the eigenvalues belong to?

Dear all,

I am currently working on a dsge model with credit risk and different bonds whose issuance is costly.
When I assume that agents act myopically (they do not encounter that the decision of choosing long-term bonds today will also affect their rollover costs in the next period), my model seems to work fine giving me plausible results for this case. When my agents do not act myopically anymore and encounter the effect of their decisions today on future costs, the model still seems to be fine, however, I get two imaginary eigenvalues with the same real part and the imaginary part differing only in the sign (one is negative one positive, but still the same number in absolute values).

Is this same major issue I should worry about? Or is it just a calibration issue? How can I find out to which variable my eigenvalues belong to?

Thank you very much for your help!

Those are generalized eigenvalues. They are allow to be complex (unless they lead to weird oscillating behavior). If there is nothing really suspicious in your results, you should not worry.

Thank you very much for the fast reply. For now the model looks fine, however, if I ever cross such weird oscillating behavior in some extensions of the model, is there some way to fix this problem? Is it then mistake in the model equations? Or some problem of another nature?

Usually, you have a timing error in that case. Only in a few models it is driven by a weird parameterization of e.g. a fiscal rule with too much debt feedback.