Perfect Foresight Model with Habits: The generalized Schur (QZ) decomposition failed

Perfect foresight simulations
1

Hello! I am trying to solve a perfect foresight model with habits in the utility function. I have attached the mod file for your reference. The habit parameter in the code is “kahab”. So, if kahab = 0, there are no habits, but if kahab >0, there are habits.

My code works fine if kahab = 0, i.e., without habits. However, the moment i choose a non-zero value for habits, I get the following error:

The generalized Schur (QZ) decomposition failed. For more information, see the documentation for Lapack function
dgges: info=30, n=16. You can also run model_diagnostics to get more information on what may cause this problem.
Error in check (line 48)
print_info(info, 0, options_);
Error in twohh_manix.driver (line 776)
oo_.dr.eigval = check(M_,options_,oo_);
Error in dynare (line 310)
evalin(‘base’,[fname ‘.driver’]);

On doing the model diagnostics, I get the following:

MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 2 collinear relationships between the variables and the equations
Relation 1
Collinear variables:
k
hr
cp
cr
r
wr
wp
h
p
y
srate
rel_w
c
Relation 2
Collinear variables:
k
hr
cp
cr
r
wr
wp
h
p
y
srate
rel_w
c
Relation 1
Collinear equations
1 2 3 5 6 7 8 10 11 12 13 14 15 21
Relation 2
Collinear equations
2 3 8 11 12 13 14 15 21
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.

I cannot understand why I get a Walras Law error for a non-zero habit parameter when the code works fine without habits. Can someone kindly suggest a way forward? Many thanks for considering my request.

My code is attached. We just need to comment out the steady state values without habits if choosing kahab = 0.1. And if kahab = 0, we comment out the steady state values corresponding to kahab = 0.1.
twohh_manix_dynare_forum.mod (7.4 KB)

Regards,
Pawan

2

This looks like a numerical issue. Your steady state values have widely differing scales:

k_ast = 3174.9638312349803 ;
lambda1_ast = 3.243632264128509e-08 ;

That may cause numerical over- and underflow. Habits often make this issue worse.

3

Dear jpfeifer,

Thanks for your reply! In this deterministic model, K_ast is Capital whereas lambda1_ast is the lagrange multiplier.

Can you please recommend a way of fixing this over-/underflow issue?

Is there an example perfect foresight dynare code with habits?

Thanks,
Pawan

4

It may be caused by a parameter choice like

barh = 2496;
5

I see! But since I am calibrating my model to annual data, barh is basically total labor endowment available to the agent available in one period. So I don’t know how to work around this.

Is there any other possible issue? The model works without habits, but crashes the moment I include habits (QZ decomposition error)

Regards,
Pawan

6

The straightforward way is usually to normalize the time endowment to 1.

7

Thank you so much!

Will try this and update

8

model.mod (5.7 KB)
Dear professor,I meet the similar error, I’m not sure if it’s the model itself (collinear) or something else. Please check it for me, thank you.

9

How can

Ph = 1/mph;
mph = epsilonh/(epsilonh-1);
log(Ph/Phss) = rhomp*log(Ph(-1)/Phss) - eps_mp;

be correct? The first two equations define Ph to be constant.

11

I don’t see a material change in the issue. You still have the three inconsistent equations. I think there is something economically wrong with your setup. Why is the elasticity of substitution now a variable?