Colinear relationships SOE Model

Stochastic simulations
1

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.

2

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;
3

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

4

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

5

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?

6

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

7

Thank you for the clarifications and willingness to help.