Taylor rule problem in 2 agents model_nonlinear

[Dean]

Dear all, I might encountering the same problem as

Basic New Keynesian model - nonlinear

Dear Dynare forum, I would like to ask, whether somebody could share with me a link to some lecture notes, that provides derivation of simple three equations New Keynesian model in full nonlinear form. Thanks in advance! Best, Honza

When I change the Taylor rule from

(Rb/Rbar)=(((Rb(-1))/Rbar)^(gammaR)*((PI/PIbar)^(gammaPI)*((Y/Ybar)/(Y(-1)/Ybar))^(gammaY))^(1-gammaR))*eps_m 

to

Rb/Rbar=((Rb(-1))/Rb)^(gammaR)*((PI/PIbar)^(gammaPI)*(Y/Ybar)^(gammaY))^(1-gammaR)*eps_m;

my model works, but otherwise not, gives the following message:

There are 13 eigenvalue(s) larger than 1 in modulus
for 12 forward-looking variable(s)

The rank condition ISN’T verified!

MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.

I tried to change to other type of Taylor rule like

Rb=1/betta*PI^(gammaPI)*(Y/Ybar)^(gammaY)*eps_m

but still not working.

Could you please help me and give some suggestions
ModelX0.mod (8.4 KB)

[jpfeifer]

Your model exhibits explosiveness. You should try to understand why.

[Dean]

Dear @jpfeifer, thank you! Might it be related to government spending and fiscal rules?
As is it here:

Baseline DSGE + government

I am not sure I understand @punnoosejacob’s answer. Conceptually, an model economy does not need to be saddle path stable or have a non-stationarity. So even a small open economy does not have to be closed. That being said, we usually think that saddle path stable equilibria are the ones that interest us. In that case, there is a transversality+No-Ponzi condition that rules out explosive paths for debt. From that point of view, the models needs to include a condition that assures that debt does…

I tried to work it out with different rules and shut down shocks but still have this issue.
Should I assume government debt (B) to be 0 at steady state? If so, I cannot use taylor type fiscal rules. Could you please suggested any other type of fiscal rules? I run out of ideas :((

STEADY-STATE RESULTS when I use wrong Taylor rule for monetary policy.

Y 1.50429
C 1.05625
CR 1.05625
CNR 1.05625
B 36.6369
B_R 73.2739

B and B_R seem very high.

[jpfeifer]

What happens if you use lump sum taxes to close the model? Does the explosiveness vanish?

[Dean]

Dear @jpfeifer Yes, I have lump sum tax and corresponding lump sum tax rule in the model.
In order to balance the budget constraint of Ricardian household I put a manually calculated: STEADY_STATE(ss_tax)
and for Non-Ricardian: T_NR.
and in the aggregation:
T=lambda*T_NR+(1-lambda)*T_R
Since I have it already, it does not change the explosiveness(

[jpfeifer]

A tax rule for lump sum taxes may still be too slow to prevent explosiveness. What happens if the lump sum adjustment is instantaneous.

[Dean]

@jpfeifer If I just leave T_R for Ricardian it gives:
Error using print_info (line 32)
One of the eigenvalues is close to 0/0 (the absolute value of numerator and denominator is smaller than 0.0000!
If you believe that the model has a unique solution you can try to reduce the value of qz_zero_threshold.

If I understand you correctly

[jpfeifer]

That is strange, because it indicates a singularity. You may need to start from a simpler model that works.

[Dean]

Dear Prof. @jpfeifer , I really appreciate your help in dynare forum’s questions. I made a simplified version by dropping wage rigidity and replacing public spending rules with more “simpler” form:
ghat=rhoG*ghat(-1)+eps_g;
where
ghat=(G-Gbar)/Ybar;

and tax rules as well.

It works, but can I use it? Many papers that I saw employ Leeper/Taylor type rules though linearized one.

[jpfeifer]

This suggests that the problem is indeed with the fiscal rules. You may go for Leeper/Taylor rules as you call them, but they may need a different parameterization.

[Dean]

Thank you, Professor