# Problem in solving a NK DSGE model with debt

Hi,
When I’m running my model, it gives me the following errors:

``````There are 12 eigenvalue(s) larger than 1 in modulus for 11 forward-looking variable(s)

The rank condition ISN'T verified!

Error using print_info (line 42)
Blanchard Kahn conditions are not satisfied: no stable equilibrium
Error in stoch_simul (line 98)
print_info(info, options_.noprint, options_);
Error in NK_lumpsumtaxes (line 379)
info = stoch_simul(var_list_);
Error in dynare (line 180)
evalin('base',fname) ;
``````

I know this is not a new question and I checked all other questions and answers provided in the forum but still cannot figure out my problem. Here are the two equations causing the above problems:

``````  var pi          //inflation
r           //gross nominal interest rate
y           //real output
tau         //lump-sum tax  rate
b           //real bond
gamma       //trend growth rate of the economy
;

parameters      gbar       // constant govt spending
psi_tau    // the sensitivity of taxes to real debt
rho_tau    // tax persistence
sbbar      // steady state govt debt to GDP ratio
taubar     // steady state lump-sum tax  rate
;
Model;
//. GBC
b + tau*y = (r(-1)/pi)*(b(-1)/exp(gamma)) + gbar;
//. Lump-sum tax
tau = (tau(-1)^rho_tau)*((taubar*(((b(-1)/y(-1))/sbbar)^psi_tau))^(1-rho_tau));
``````

I didn’t use predetermined_variables command. I’m running a traditional NK model just like the NK_baseline.mod in examples. Before I introduced fiscal variables into the model, everything is fine. However, when I introduced the above two equations into the model, the errors show up. To make things simple, I set govt spending constant and only have lump-sum taxes. My tax rule follows Leeper’s specification to stabilize real debt, which includes a response of tax to real debt.
Is there anything wrong with the timing of debt? Or is the problem due to fiscal rule set-up or parameterization?

Best,

Hi, I am not familiar with this kind of models… You do not show the parameter values, and I don’t understand the right hand side of the last equation (the role and timing of y/b). You probably will not obtain a lot of feedbacks if you do not post a mod file.

Best,
Stéphane.

1 Like

There are a lot of potential issues.

1. Make sure that the sign of the feedback coefficient is correct and that indebtedness has the correct sign. What is the value of `sbbar`? You could check this by changing the sign of `psi_tau`
2. Why is your lump-sum tax multiplying output in the budget constraint?
3. Check whether it is a problem with the parameterization. My experience is that the coefficient needs to be not to small and not too big. Simply try different values and see whether the number of eigenvalues moves into the right direction.
1 Like

Hi Stepan,
The right hand side of the tax rule (the role and timing of y/b) denotes a response of tax to the debt-to-GDP ratio to stabilize debt, followed by Leeper’s fiscal rule specification.
NK_lumpsumtaxes.mod (8.7 KB)

Please see the attachment of my mod.file.
Highly appreciate that!

Best,

Hi Jpfeifer,
For question 2, tau is lump-sum tax rate, tau multiplying output denotes tax revenue in the budget constraint.

Highly appreciate that!

Best,NK_lumpsumtaxes.mod (8.7 KB)

Your feedback coefficient is too small. The file works with
`psi_tau = 0.5;`
Also, there is no such thing as a lump-sum tax rate. Either it is a tax rate or lump sum taxes.

1 Like

Thank you so much! Yes, it works now.
You’re right, it’s a tax rate. Sorry for my wrong expression.

Thanks again!

Best,