# Colinear relationships SOE Model

Hi everyone,
I’ve extended a closed economy model with government to a two-country one, similar to Gali and Monacelli (2005). But, I ended up having with colinearity problems. As the model has worked when economy was closed, I don’t know if it is just a parametrization or model definition problem.

ModelOpenBi.mod (13.6 KB)

there is 8 colinear relationships between the variables and the equations
Relation 1
Colinear variables:
C
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 2
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 3
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 4
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 5
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 6
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 7
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A
Gamma
Relation 8
Colinear variables:
W_real
N
MC
Y
I
Pi
V
Phi_v
M
Pi_x_D
x_1_D
x_2_D
Pi_D
Pi_P_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
Pi_P_F
d_F
Q
dS
TOT
PSI_f
Pi_x
Y_x
I_x
B
tau
G
A

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.

One issue seems to be

for example in

``````log(A/steady_state(A))=rho_A*log(A(-1)/steady_state(A))+sigma_A*e_A;
``````

I changed the code and simplified the equations to reduce some variables, but the problem was not resolved. Now, the diagnosis points to 1 collinear relationship. I’m a little lost because I don’t know exactly which equation other than 23 to pay attention to.

There are 11 eigenvalue(s) larger than 1 in modulus
for 10 forward-looking variable(s)

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:
C
W_real
N
MC
Y
I
Pi
Pi_x_D
x_1_D
x_2_D
Pi_D
d_D
Pi_F
Pi_x_F
x_1_F
x_2_F
d_F
Q
dS
TOT
PSI_f
B
tau
G
Colinear equations

Your model has a unit root, so that collinear relationship is not unexpected.

So the problem here is not the collinearity, but the violation of BK conditions? And this can be related to another problem besides the unit root?

Yes, it could simply be a matter of the parameterization or a timing error.

Thank you for the clarifications and willingness to help.