Steady state computation, singular Jacobian

[maa14]

Dear all,

I'm trying to propose an extension of the Gerali, Neri, Sessa and Signoretti (JMCB,2010) "Credit and banking in a DSGE model of the Euro Area" in order to introduce banks' entry/exit (as proposed by Jaimovich and Floetotto, JME 2008).

I changed the relevant equations in order to introduce changing number of banks and now I cannot manage to solve the steady state, and therefore neither do any estimation. It seems that the problematic equations are the ones I changed/added because the error is: "An infinite element was encountered when trying to solve equation(s) 32, 33, 34, 64
with respect to the variable(s): data_BE, data_HP, data_N, N."

It's a quite complex model but the changed equations are easy to find searching for EXTENSION in the mod file.

Thanks in advance for your help!!
MAA

[jpfeifer]

Use

Code: Select all

steady(solve_algo=4,maxit=10000);


with the most recent snapshot and a steady state will be found. However, there is still a collinearity issue:

MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 3 colinear relationships between the variables and the equations
Relation 1
Colinear variables:
c_p
h_p
d_p
l_p
lam_p
J_R
pie_wp
c_i
h_i
b_i
l_i
lam_i
s_i
pie_wi
I
c_e
k_e
l_pd
l_id
b_ee
y_e
lam_e
s_e
u
d_b
b_h
b_e
r_d
r_bh
r_be
R_b
K_b
pie
x
C
Y
D
BE
BH
B
w_p
w_i
q_h
K
PIW
r_ib
r_k
Y1
rr_e
aux1
bm
spr_b
data_rBH
data_rBE
data_rD
data_rIB
data_PIW
data_PIE
Relation 2
Colinear variables:
h_p
d_p
l_p
J_R
j_B
pie_wp
c_i
h_i
b_i
l_i
lam_i
s_i
pie_wi
I
c_e
k_e
l_pd
l_id
b_ee
y_e
lam_e
s_e
u
d_b
b_h
b_e
r_d
r_bh
r_be
R_b
pie
C
Y
D
BE
BH
B
w_p
w_i
q_h
K
PIW
r_ib
r_k
Y1
rr_e
aux1
bm
spr_b
data_rBH
data_rBE
data_rD
data_rIB
data_PIW
data_PIE
Relation 3
Colinear variables:
d_p
l_p
J_R
j_B
pie_wp
c_i
h_i
b_i
l_i
lam_i
s_i
pie_wi
I
c_e
k_e
l_pd
l_id
b_ee
y_e
lam_e
s_e
u
d_b
b_h
b_e
r_d
r_bh
r_be
R_b
pie
C
Y
D
BE
BH
B
w_p
w_i
K
PIW
r_ib
r_k
Y1
rr_e
aux1
bm
spr_b
data_rBH
data_rBE
data_rD
data_rIB
data_PIW
data_PIE
Relation 1
Colinear equations
32 33 34 64

Relation 2
Colinear equations
32 33 34 64

Relation 3
Colinear equations
32 33 34 64

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.

[maa14]

Dear jpfeifer,

Thank you very much for your reply. I tried with the latest snapshot and steady state was computed. Nevertheless, I do not see how the eq 32,33,34,64 can be collinear. I guess that this problem is causing the error with the Generalized Schur decomposition. Any hint on how to proceed will be more than welcomed.

Thanks again for your help!!

[maa14]

Anyone suggesting some solution for the collinearity problem?

I don't see how those equations can be collinear.....I just changed the pricing equations (32,33,34) and add the exogenous process of the new observable (eq 64) to the baseline model. I really don't see it.

Code: Select all

// eq 32
 - 1/exp(N)
     - kappa_d  * ( exp(r_d)/exp(r_d(-1)) - 1  )  * exp(r_d)/exp(r_d(-1)) - kappa_d/2  * ( exp(r_d)/exp(r_d(-1)) - 1  )^2
     + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_d  * ( exp(r_d(+1))/exp(r_d) - ( exp(r_d)/exp(r_d(-1)))^ind_d )   * ( (exp(r_d(+1))/exp(r_d))^2 )   * (exp(d_b(+1))/exp(d_b)) = 0;//

// eq 33
  1/exp(N)
     - kappa_bh  * ( exp(r_bh)/exp(r_bh(-1)) - 1  )  * exp(r_bh)/exp(r_bh(-1)) - kappa_bh/2  * ( exp(r_bh)/exp(r_bh(-1)) - 1  )^2
     + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_bh  * ( exp(r_bh(+1))/exp(r_bh) - ( exp(r_bh)/exp(r_bh(-1)))^ind_bh )   * ( (exp(r_bh(+1))/exp(r_bh))^2 )   * (exp(b_h(+1))/exp(b_h)) = 0;//

// eq 34
 1/exp(N)
     - kappa_be  * ( exp(r_be)/exp(r_be(-1)) - 1  )  * exp(r_be)/exp(r_be(-1)) - kappa_be/2  * ( exp(r_be)/exp(r_be(-1)) - 1  )^2
     + beta_p * ( exp(lam_p(+1))/exp(lam_p) ) * kappa_be  * ( exp(r_be(+1))/exp(r_be) - ( exp(r_be)/exp(r_be(-1)))^ind_be )   * ( (exp(r_be(+1))/exp(r_be))^2 )   * (exp(b_e(+1))/exp(b_e)) = 0;//

exp(N)        = (1-rho_N)       *    N_ss          + rho_N      * exp(N(-1))       + e_N; // eq 64



Thanks!!
M

[jpfeifer]

I cannot answer your question. But if you can exclude a problem due to Walras Law, the problem often comes from a timing problem (a forgotten or wrong (+1) for example). In that case, the steady state will solve, but the model will have collinearity issues.

[maa14]

Thanks a lot for your answer!!

I had a mistake on the initial conditions and it seems that the colinearity problem is solved. But now the following appears:

STEADY: The Jacobian contains Inf or NaN. The problem arises from:

Derivative of Equation 32 with respect to Variable N (initial value of N: -532.998)
Derivative of Equation 33 with respect to Variable N (initial value of N: -532.998)
Derivative of Equation 34 with respect to Variable N (initial value of N: -532.998)

STEADY: The problem most often occurs, because a variable with
STEADY: exponent smaller than 1 has been initialized to 0. Taking the derivative
STEADY: and evaluating it at the steady state then results in a division by 0.

I don't understand why uses that initial value if I define in initval block N= 0.002440489. Do you have any clue why this could happen?

Thanks a lot again!!!!
M

[jpfeifer]

Sorry, but I cannot replicate your error message. Which Dynare version are you using? Currently it looks as if your initial values are not good enough to find the steady state at all.

[maa14]

yes, sorry. I'm using the latest snapshot from 2014-05-21

[jpfeifer]

I still cannot replicate the issue, Rather, it seems there is still a mistake in the model or the initial values are simply too poor.

[maa14]

Ok, thanks. I'll check the model again and the initial values too. Regarding the difference on the stated initial value on the error (-533) with respect to the initial value given at initval block (0.002). Do you know which can be the source of such difference?

[federico]

Hi everyone,

I working on a very similar model and I'm experiencing the same collinearity problem.

I'm able to find quite easily the steady state and the obtained values are plausible and i think that I can eliminate
a timing problem.

Even with the estimation I obtain resonable values for the deep parameters.

So my question is if there could be other non trivial problem that could generate a collinearity issue?

Thanx