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

- 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)