The generalized Schur (QZ) decomposition failed. Colinear equations issue

Dear team Dynare.
When I run my mod file, it indicates this error message:

The generalized Schur (QZ) decomposition failed. For more information, see the documentation for Lapack function dgges: info=30, n=21. You can also
run model_diagnostics to get more information on what may cause this problem.

and molde_diagnostics says it’s because of a colinear equations.

model_diagnostics(M_, options_, oo_);
MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 1 colinear relationships between the variables and the equations
Colinear variables:
epsilontheta
R
Omega
theta
epsilon
l
k
w
lr
lw
c
cr
cw
lambda
hr
hw
y
inv
a
Rk
pi
pistar
mc
g
b
tau
f1
f2
ii
Colinear equations
14 16 17 20
MODEL_DIAGNOSTICS: The presence of a singularity problem typically indicates that there is one
MODEL_DIAGNOSTICS: redundant equation entered in the model block, while another non-redundant equation
MODEL_DIAGNOSTICS: is missing. The problem often derives from Walras Law.

I’ve checked equations 14, 16, 17, 20, but I think these are still needed.

Could anyone please give me some advice to solve this issue?

Appreciate your help.

G3.mod (6.0 KB)

Which Dynare version are you using? Also, have you tried different parameterizations?

Hello, professor, thank you very much for your reply!
I tried Dynare version 4.6.0, and 5.1. both indicated the similar error message.
version 5.1 says: The generalized Schur (QZ) decomposition failed. For more information, see the documentation for Lapack function dgges: info=30, n=21. You can also
run model_diagnostics to get more information on what may cause this problem.

version 4.6.0 says: One of the eigenvalues is close to 0/0 (the absolute value of numerator and denominator is smaller than 0.0000!
If you believe that the model has a unique solution you can try to reduce the value of qz_zero_threshold.

But the model diagnstics mentioned that there is 1 colinear relationships between the variables and the equations.

I’ve replicate Gertler 1999(Government debt and social security in a life-cycle economy) and It worked I think. (with the same parameter the paper mentioned)
So I silightly extended model which I add NK calvo price setting and fiscal and monetary policy.
and something happened here.

Professor, can you please tell me how I try different parameterizations? most of parameters are the same as Gertler’s paper. I have no idea what to do. Please.

This is a very hard problem to debug. It seems the error message differs across version due to numerical issues. In any case, I tend to believe it may be something systematic. But problems like the current one are very hard to debug. If you have a baseline version that runs without any indication of a problem, it’s most probably one of the modifications that causes the error.