Problems with colinear and eigenvalues

bn_0801 · September 17, 2020, 6:58am

Hi everyone!

I’ve been working on a model based on César Carrera* and Hugo Vega (2012). I divided the production side into 2 different categories to compare the structural liquidity difference. However, the model_diagnostics keep warning as:
“MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 1 colinear relationships between the variables and the equations”
I solved part of this problem, but currently there is no progress any more.
And every time I try to modify this model, the colinear variables remains and equation issue gets worse.

Could any one give any suggestion about it?

Appreciate your help
MS_Bank_Liquidity_Baseline1.mod (10.6 KB)

jpfeifer · September 17, 2020, 12:32pm

In Dynare 4.6.2 I get:

ERROR: If the model is declared linear the second derivatives must be equal to zero.
The following equations have non-zero second derivatives:
* Eq # 38 [N_p]
* Eq # 39 [39]
* Eq # 57 [57]

bn_0801 · September 18, 2020, 12:49am

Thank you Prof. Pfeifer for viewing this topic.
I ran the code on ver. 4.5.6 and it didn’t show similar problem. Maybe i should upgrade my dynare and fix this issue.
Before that, the current result is
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:
S
Ps
Colinear equations
column 1 to 22

 1     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23

column 23 to 44

24    25    26    27    28    29    31    32    35    36    37    38    39    40    41    42    44    45    46    47    48    50

MODEL_DIAGNOSTICS: The singularity seems to be (partly) caused by the presence of a unit root
MODEL_DIAGNOSTICS: as the absolute value of one eigenvalue is in the range of ±1e-6 to 1.
MODEL_DIAGNOSTICS: If the model is actually supposed to feature unit root behavior, such a warning is expected,
MODEL_DIAGNOSTICS: but you should nevertheless check whether there is an additional singularity problem.
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.

Residuals of the static equations:

Equation number 1 : 0
Equation number 2 : 0
Equation number 3 : 0
Equation number 4 : 0
Equation number 5 : 0
Equation number 6 : 0
Equation number 7 : 0
Equation number 8 : 0
Equation number 9 : 0
Equation number 10 : 0
Equation number 11 : 0
Equation number 12 : 0
Equation number 13 : 0
Equation number 14 : 0
Equation number 15 : 0
Equation number 16 : 0
Equation number 17 : 0
Equation number 18 : 0
Equation number 19 : 0
Equation number 20 : 0
Equation number 21 : 0
Equation number 22 : 0
Equation number 23 : 0
Equation number 24 : 0
Equation number 25 : 0
Equation number 26 : 0
Equation number 27 : 0
Equation number 28 : 0
Equation number 29 : 0
Equation number 30 : 0
Equation number 31 : 0
Equation number 32 : 0
Equation number 33 : 0
Equation number 34 : 0
Equation number 35 : 0
Equation number 36 : 0
Equation number 37 : 0
Equation number 38 : 0
Equation number 39 : 0
Equation number 40 : 0
Equation number 41 : 0
Equation number 42 : 0
Equation number 43 : 0
Equation number 44 : 0
Equation number 45 : 0
Equation number 46 : 0
Equation number 47 : 0
Equation number 48 : 0
Equation number 49 : 0
Equation number 50 : 0

STEADY-STATE RESULTS:

C 0
MUC 0
P 0
R_D 0
Pi 0
H 0
H_s 0
H_p 0
W_s 0
W_p 0
CSH 0
DIV 0
S 0
Ps 0
R_ws 0
R_wp 0
MC_s 0
MC_p 0
Y_s 0
Y_p 0
K_s 0
K_p 0
A 0
P_s 0
P_p 0
Pi_s 0
Pi_p 0
Y 0
X_s 0
X_p 0
Q_s 0
Q_p 0
Re_s 0
Re_p 0
L_s 0
L_p 0
N_p 0
Ce_p 0
omegabar 0
RR 0
R_RR 0
D 0
IB 0
RL_s 0
RL_p 0
R_ib 0
P_b 0
B_nb 0
B_cb 0
T 0

EIGENVALUES:
Modulus Real Imaginary

           0               -0                0
           0                0                0
   3.935e-17       -3.935e-17                0
   1.422e-16       -1.422e-16                0
   1.757e-16        1.757e-16                0
   3.996e-16       -3.996e-16                0
   6.746e-16        6.746e-16                0
   1.273e-15       -1.273e-15                0
   4.218e-15       -4.218e-15                0
     0.08347         -0.08347                0
     0.09529          0.09529                0
        0.25             0.25                0
        0.25             0.25                0
         0.5              0.5                0
      0.8525           0.8525                0
         0.9              0.9                0
      0.9009           0.8873           0.1557
      0.9009           0.8873          -0.1557
        0.99             0.99                0
           1                1                0
       1.004            1.004                0
       1.007            1.007                0
       1.059            1.051           0.1321
       1.059            1.051          -0.1321
       1.182            1.182                0
       1.992           -1.992                0
       4.027            4.027                0
       4.027            4.027                0
       7.311           -7.311                0
   2.395e+16        2.395e+16                0
   8.339e+18        8.339e+18                0
   7.165e+19        7.165e+19                0

There are 12 eigenvalue(s) larger than 1 in modulus
for 10 forward-looking variable(s)

The rank condition ISN’T verified!

misusing print_info (line 42)
Blanchard Kahn conditions are not satisfied: no stable equilibrium

error stoch_simul (line 100)
print_info(info, options_.noprint, options_);

error MS_Bank_linear1 (line 692)
info = stoch_simul(var_list_);

error dynare (line 235)
evalin(‘base’,fname) ;

42 error([‘Blanchard Kahn conditions are not satisfied: no stable’ …

bn_0801 · September 18, 2020, 5:46am

Dear Prof Pfeifer
I tried to run my code on ver. 4.6.2
However the result seem be the same as it in older version.
Here’s the error info:
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:
S
Ps
Colinear equations
1 至 22 列

 1     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23

23 至 44 列

24    25    26    27    28    29    31    32    35    36    37    38    39    40    41    42    44    45    46    47    48    50

MODEL_DIAGNOSTICS: The singularity seems to be (partly) caused by the presence of a unit root
MODEL_DIAGNOSTICS: as the absolute value of one eigenvalue is in the range of ±1e-6 to 1.
MODEL_DIAGNOSTICS: If the model is actually supposed to feature unit root behavior, such a warning is expected,
MODEL_DIAGNOSTICS: but you should nevertheless check whether there is an additional singularity problem.
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.

Residuals of the static equations:

Equation number 1 : 0 : MUC
Equation number 2 : 0 : 2
Equation number 3 : 0 : 3
Equation number 4 : 0 : 4
Equation number 5 : 0 : CSH
Equation number 6 : 0 : 6
Equation number 7 : 0 : R_ws
Equation number 8 : 0 : R_wp
Equation number 9 : 0 : W_s
Equation number 10 : 0 : W_p
Equation number 11 : 0 : Y_s
Equation number 12 : 0 : Y_p
Equation number 13 : 0 : MC_s
Equation number 14 : 0 : MC_p
Equation number 15 : 0 : A
Equation number 16 : 0 : Pi_s
Equation number 17 : 0 : Pi_p
Equation number 18 : 0 : 18
Equation number 19 : 0 : 19
Equation number 20 : 0 : 20
Equation number 21 : 0 : P
Equation number 22 : 0 : Pi
Equation number 23 : 0 : K_s
Equation number 24 : 0 : K_p
Equation number 25 : 0 : Q_s
Equation number 26 : 0 : Q_p
Equation number 27 : 0 : Re_s
Equation number 28 : 0 : Re_p
Equation number 29 : 0 : 29
Equation number 30 : 0 : 30
Equation number 31 : 0 : N_p
Equation number 32 : 0 : 32
Equation number 33 : 0 : L_p
Equation number 34 : 0 : 34
Equation number 35 : 0 : 35
Equation number 36 : 0 : 36
Equation number 37 : 0 : 37
Equation number 38 : 0 : RL_s
Equation number 39 : 0 : 39
Equation number 40 : 0 : 40
Equation number 41 : 0 : 41
Equation number 42 : 0 : 42
Equation number 43 : 0 : 43
Equation number 44 : 0 : R_D
Equation number 45 : 0 : 45
Equation number 46 : 0 : RR
Equation number 47 : 0 : R_RR
Equation number 48 : 0 : 48
Equation number 49 : 0 : 49
Equation number 50 : 0 : Y

STEADY-STATE RESULTS:

C 0
MUC 0
P 0
R_D 0
Pi 0
H 0
H_s 0
H_p 0
W_s 0
W_p 0
CSH 0
DIV 0
S 0
Ps 0
R_ws 0
R_wp 0
MC_s 0
MC_p 0
Y_s 0
Y_p 0
K_s 0
K_p 0
A 0
P_s 0
P_p 0
Pi_s 0
Pi_p 0
Y 0
X_s 0
X_p 0
Q_s 0
Q_p 0
Re_s 0
Re_p 0
L_s 0
L_p 0
N_p 0
Ce_p 0
omegabar 0
RR 0
R_RR 0
D 0
IB 0
RL_s 0
RL_p 0
R_ib 0
P_b 0
B_nb 0
B_cb 0
T 0

EIGENVALUES:
Modulus Real Imaginary

           0               -0                0
           0                0                0
   4.488e-18       -4.488e-18                0
    1.06e-16         1.06e-16                0
   1.837e-16        1.837e-16                0
   1.847e-16        1.847e-16                0
   4.305e-16        4.305e-16                0
   7.375e-16        7.375e-16                0
   5.699e-15       -5.699e-15                0
     0.08347         -0.08347                0
     0.09529          0.09529                0
        0.25             0.25                0
        0.25             0.25                0
         0.5              0.5                0
      0.8525           0.8525                0
         0.9              0.9                0
      0.9009           0.8873           0.1557
      0.9009           0.8873          -0.1557
        0.99             0.99                0
           1                1                0
       1.004            1.004                0
       1.007            1.007                0
       1.059            1.051           0.1321
       1.059            1.051          -0.1321
       1.182            1.182                0
       1.992           -1.992                0
       4.027            4.027                0
       4.027            4.027                0
       7.311           -7.311                0
   8.256e+16        8.256e+16                0
   1.224e+17       -1.224e+17                0
   3.609e+19        3.609e+19                0

There are 12 eigenvalue(s) larger than 1 in modulus
for 10 forward-looking variable(s)

The rank condition ISN’T verified!

错误使用 print_info (line 32)
Blanchard & Kahn conditions are not satisfied: no stable equilibrium.

出错 stoch_simul (line 103)
print_info(info, options_.noprint, options_);

出错 MS_Bank_linear1.driver (line 834)
[info, oo_, options_, M_] = stoch_simul(M_, options_, oo_, var_list_);

出错 dynare (line 293)
evalin(‘base’,[fname ‘.driver’]) ;

32 error(message);

jpfeifer · September 18, 2020, 8:16am

Did you correctly set the path? It should now say:

Starting Dynare (version 4.6.2).

bn_0801 · September 19, 2020, 6:20am

Sorry, I didn’t paste entire info.
I modified the code a bit, but the issue still exist.
MS_Bank_linear1.mod (9.5 KB)

Using 64-bit preprocessor
Starting Dynare (version 4.6.2).
Calling Dynare with arguments: none
Starting preprocessing of the model file …
Found 50 equation(s).
Evaluating expressions…done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 2).
Processing outputs …
done
Preprocessing completed.

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:
S
Ps
Colinear equations
1 至 22 列

 1     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23

23 至 40 列

24    25    26    27    28    31    32    35    36    38    41    42    44    45    46    47    48    50

MODEL_DIAGNOSTICS: The singularity seems to be (partly) caused by the presence of a unit root
MODEL_DIAGNOSTICS: as the absolute value of one eigenvalue is in the range of ±1e-6 to 1.
MODEL_DIAGNOSTICS: If the model is actually supposed to feature unit root behavior, such a warning is expected,
MODEL_DIAGNOSTICS: but you should nevertheless check whether there is an additional singularity problem.
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.

Residuals of the static equations:

Equation number 1 : 0 : MUC
Equation number 2 : 0 : 2
Equation number 3 : 0 : 3
Equation number 4 : 0 : 4
Equation number 5 : 0 : CSH
Equation number 6 : 0 : 6
Equation number 7 : 0 : R_ws
Equation number 8 : 0 : R_wp
Equation number 9 : 0 : W_s
Equation number 10 : 0 : W_p
Equation number 11 : 0 : Y_s
Equation number 12 : 0 : Y_p
Equation number 13 : 0 : MC_s
Equation number 14 : 0 : MC_p
Equation number 15 : 0 : A
Equation number 16 : 0 : Pi_s
Equation number 17 : 0 : Pi_p
Equation number 18 : 0 : 18
Equation number 19 : 0 : 19
Equation number 20 : 0 : 20
Equation number 21 : 0 : P
Equation number 22 : 0 : Pi
Equation number 23 : 0 : K_s
Equation number 24 : 0 : K_p
Equation number 25 : 0 : Q_s
Equation number 26 : 0 : Q_p
Equation number 27 : 0 : Re_s
Equation number 28 : 0 : Re_p
Equation number 29 : 0 : 29
Equation number 30 : 0 : 30
Equation number 31 : 0 : N_p
Equation number 32 : 0 : 32
Equation number 33 : 0 : L_p
Equation number 34 : 0 : 34
Equation number 35 : 0 : 35
Equation number 36 : 0 : 36
Equation number 37 : 0 : 37
Equation number 38 : 0 : RL_s
Equation number 39 : 0 : 39
Equation number 40 : 0 : 40
Equation number 41 : 0 : 41
Equation number 42 : 0 : 42
Equation number 43 : 0 : 43
Equation number 44 : 0 : R_D
Equation number 45 : 0 : 45
Equation number 46 : 0 : RR
Equation number 47 : 0 : R_RR
Equation number 48 : 0 : 48
Equation number 49 : 0 : 49
Equation number 50 : 0 : Y

STEADY-STATE RESULTS:

C 0
MUC 0
P 0
R_D 0
Pi 0
H 0
H_s 0
H_p 0
W_s 0
W_p 0
CSH 0
DIV 0
S 0
Ps 0
R_ws 0
R_wp 0
MC_s 0
MC_p 0
Y_s 0
Y_p 0
K_s 0
K_p 0
A 0
P_s 0
P_p 0
Pi_s 0
Pi_p 0
Y 0
X_s 0
X_p 0
Q_s 0
Q_p 0
Re_s 0
Re_p 0
L_s 0
L_p 0
N_p 0
Ce_p 0
omegabar 0
RR 0
R_RR 0
D 0
IB 0
RL_s 0
RL_p 0
R_ib 0
P_b 0
B_nb 0
B_cb 0
T 0

EIGENVALUES:
Modulus Real Imaginary

           0               -0                0
           0                0                0
   3.048e-17       -3.048e-17                0
   4.122e-17        4.122e-17                0
   4.865e-17       -4.865e-17                0
   6.055e-17       -6.055e-17                0
   2.132e-16       -2.132e-16                0
   8.801e-16        8.801e-16                0
   4.939e-15        4.939e-15                0
     0.08347         -0.08347                0
     0.09529          0.09529                0
        0.25             0.25                0
        0.25             0.25                0
         0.5              0.5                0
      0.8525           0.8525                0
         0.9              0.9                0
      0.9009           0.8873           0.1557
      0.9009           0.8873          -0.1557
        0.99             0.99                0
           1                1                0
       1.004            1.004                0
       1.007            1.007                0
       1.059            1.051           0.1321
       1.059            1.051          -0.1321
       1.182            1.182                0
       1.992           -1.992                0
       4.027            4.027                0
       4.027            4.027                0
       7.311           -7.311                0
   5.671e+17        5.671e+17                0
   1.579e+18       -1.579e+18                0
   2.556e+18       -2.556e+18                0

There are 12 eigenvalue(s) larger than 1 in modulus
for 10 forward-looking variable(s)

The rank condition ISN’T verified!

错误使用 print_info (line 32)
Blanchard & Kahn conditions are not satisfied: no stable equilibrium.

出错 stoch_simul (line 103)
print_info(info, options_.noprint, options_);

出错 MS_Bank_linear1.driver (line 834)
[info, oo_, options_, M_] = stoch_simul(M_, options_, oo_, var_list_);

出错 dynare (line 293)
evalin(‘base’,[fname ‘.driver’]) ;

jpfeifer · September 21, 2020, 8:00am

Given that your are missing two stable eigenvalues, there is most probably some issue with your timing or a mistake in the equations. I can only recommend starting with a simpler version of the model that works.

bn_0801 · September 28, 2020, 10:00am

Thank you for your help, Prof.

I solved the colinear issue by replacing variables(DIV, Ps and S) by some new ones (as their linear combination).

I think it may be necessary to double check the timing, because now it says
"There are 16 eigenvalue(s) larger than 1 in modulus
for 14 forward-looking variable(s)

The rank condition ISN’T verified!"MS_Bank_linear2.mod (9.4 KB)

Regards