BK conditions satisfied in count but rank condition fails (indeterminacy)

1

Hi everyone,

I am encountering an issue with the Blanchard & Kahn conditions in Dynare and would really appreciate your help.

From the model output, I obtain:

  • Number of eigenvalues with modulus greater than 1: 6

  • Number of forward-looking variables: 6

However, Dynare reports:

Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.

This is confusing to me, since the count condition appears to be satisfied, yet the rank condition fails.

Below are the eigenvalues:

Modulus        Real        Imaginary
1.694e-16      1.694e-16   0
2.339e-16      2.339e-16   0
4.578e-16     -4.578e-16   0
0.1488         0.1488      0
0.2864        -0.2864      0
0.6513         0.6513      0
1.038          1.038       0
1.099          1.099       0
157.6          157.6       0
1.179e+08     -8359        1.179e+08
1.179e+08     -8359       -1.179e+08
1.03e+18      -1.03e+18    0

Dynare also reports:

There are 6 eigenvalue(s) larger than 1 in modulus 
for 6 forward-looking variable(s)

The rank condition ISN'T verified!

Additional diagnostics:

  • model_diagnostics reports no obvious issues

  • The steady state is solved using fsolve with small residuals

  • Solver message:

    Equation solved, solver stalled.

    fsolve stopped because the relative size of the current step is less than the tolerance…

My questions are:

  1. Can very large eigenvalues (e.g. 1e+08 or 1e+18) generate numerical instability that leads to rank failure?

  2. Does this typically indicate a singularity or collinearity problem in the forward-looking block, even if model_diagnostics does not detect it?

  3. In general, under what conditions can the count condition be satisfied but the rank condition still fail?

I suspect this may be related to the structure of my model (possibly a very “stiff” static block combined with a small number of forward-looking equations), but I am not sure how to diagnose it formally.

Any suggestions on how to debug this (e.g. checking the Jacobian, identifying redundant equations, or rescaling variables) would be greatly appreciated.

Thanks a lot!