Eigenvalues with Zero Modulus

Dynare help (legacy posts)
1

Hi All
I am playing with a DSGE model of banking and discovered something strange when I used the check command. Many eigenvalues are zero or very close to zero in modulus. For example,

     Modulus             Real        Imaginary

           0                0                0
           0               -0               -0
           0               -0               -0
           0               -0               -0
           0               -0               -0
   2.956e-18        2.871e-18       -7.009e-19
    9.48e-18        9.471e-18       -4.143e-19
   6.683e-17       -6.682e-17        8.935e-19
   1.116e-16         1.08e-16        2.829e-17
   2.254e-16        2.254e-16        5.296e-19
   2.992e-16        -2.99e-16        1.143e-17
   5.572e-16        5.565e-16       -2.657e-17

I am not sure what the implications are. The Blanchard-Kahn conditions are associated with forward looking variables and eigenvalues above unity. But zero eigenvalues…are they problematic? My guess is that it indicates that many variables do not play a role in the dynamics. Perhaps I am wrong.
Have others experienced the same ‘problem’?

cheers
Reuben

2

In terms of modulus, 0 is just a number like any other and indicates nothing problematic. But you are right that a 0 eigenvalue indicates that the model will have less endogenous propagation than one where the eigenvalue would be ceteris paribus bigger in modulus.