# Basic RBC model with distortionary Taxes

Dear all,

I am trying to expand the basic RBC model to allow for distortionary taxes on labor income but without lump sum tax.

As far as I know, when government lump sum financing is ruled out, you need to consider both the government budget constraint featuring public debt dynamics and a fiscal policy rule featuring a distortionary tax pattern preventing public debt from exploding.

Starting from a basic RBC drawn from Prof. Pfeifer’s web page, I just added the government budget constraint (where as far as I know public debt should be a state variable) and a fiscal policy rule where the distortionary tax evolves proportionally to the public debt to GDP ratio, i.e.:

``````[name='Government budget constraint']
r(-1)*d(-1) + g_ss*exp(ghat) = tau*w*l + d - d(-1);

[name='Fiscal policy rule']
tau = (1-rho_tau)*tauss + rho_tau*tau(-1) + (1-rho_tau)*gam_tau*(d/y - 0.505818181818180);
``````

(note that 0.505818181818180 is just the ss debt to GDP ratio).

Given a reasonable calibration of the fiscal policy response (gam_tau = 0.025) and other fiscal policy-related parameters, I find that the BK conditions are not satisfied as there are 4 eigenvalues larger than 1 in modulus for 3 forward variables.

Note that

1. if you run the model with the forwarded gvt budget constraint (i.e. making public debt a jump variable) the BK conditions are satisfied and the model works (although it’s bizarre that public debt is a jump variable…)

This is very weird, can anyone help? What am I missing?

See the attached mod file

Thank you very much

Fabio

rbc.mod (7.7 KB)

1 Like

rbc_fiscal.mod (34.3 KB)
Dear all,

I found out that the issues I was experiencing were mainly due to bad fiscal-related parameter choices.

To make it short, the model satisfies the BK conditions for

1. relatively low levels of public debt to GDP ratio (I would recommend setting it below 0.6 to have reasonable dynamics; mind also that debt to GDP also pins down the distortionary tax size in the SS)

2. The fiscal policy response parameter (gam_tau_n in the code) must be approximately in the 0.3-0.8 range (at least according to my standard fiscal policy rule tieing the distortionary tax on labor to teh debt to GDP ratio)

3. the fiscal policy rule persistence must be set to relatively low levels (at most at rho_tau_n=0.8), as higher values induce some complex eigenvalues triggering oscillatory dynamics and/or violation of BK.

I attach here a mod file where you can see several comparison exercises based on several different calibrations of fiscal policy parameters for a basic RBC model.

I hope this can help someone approaching fiscal policy modeling in this class of models.

Of course, feel free to jump in if I miss something or if you find some mistakes in the code

Best regards

Fabio

Sorry for not replying earlier. What you describe sounds right. Calibrating fiscal rules is tricky. There must be sufficient feedback, but not too much.

Thank you very much for your response Professor Pfeifer