Steady state computation, singular Jacobian

Dynare help (legacy posts)
1

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
Spain_ext.mod (38.8 KB)

2

Use

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:

[quote]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.[/quote]

3

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!!

4

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.

// 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

5

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.

6

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:

[quote]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.[/quote]

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
Spain_ext_rgiven2.mod (38.8 KB)

7

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.

8

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

9

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.

10

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?

11

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