Correct specification of fiscal rules in a non-stationary environment

Hi, I was wondering how to correctly specify fiscal rules in a non-stationary environment with TFP trend, when using Dynare’s deflating capabilities?

Usually, fiscal rules are specified to be activated if there are some deviation from the steady-state:

T_t =\rho T_{t-1} + (1-\rho) \bar{T} + \phi_b \left(\frac{B_{t-1}}{Y_{t-1}} - \bar{\frac{B}{Y}} \right) +\phi_g(g_t -\bar{g})+e_t

But to my understanding, if I am using deflator of Dynare, s.t. var(deflator=z) Tt gt Bt; Dynare will assume the rule of this form
\frac{T_t}{z_t} =\rho \frac{T_{t-1}}{z_{t-1}}\frac{z_{t-1}}{z_t} + (1-\rho) \bar{T} \frac{1}{z_t} + \phi_b \frac{1}{z_t}\left(\frac{B_{t-1}}{Y_{t-1}} - \bar{\frac{B}{Y}} \right) +\phi_g(\frac{g_t}{z_t} -\frac{\bar{g}}{z_t})+e_t

which seems rather unusual rule. Please correct me if I am wrong, but to recover the “conventional” rule, does one should already detrend the rule even though command var(deflator=z) Tt gt Bt; is used?

\frac{T_t}{z_t} =\rho \frac{T_{t-1}}{z_{t-1}} + (1-\rho) \bar{T} + \phi_b \left(\frac{B_{t-1}}{Y_{t-1}} - \bar{\frac{B}{Y}} \right) +\phi_g(\frac{g_t}{z_t} -\bar{g})+e_t

Note that for \bar{T}, I am using steady_state(T), that comes from the steady-state file (already detrended).

Also, could you happen to know some papers that specify fiscal rules in a non-stationary environment?

Thanks a lot!

I would need to check what happens in this case. Can you provide me with the file? I guess that T(-1) would be detrended by z(-1), so that would not be an issue. But I would like to check what happens with the steady state operator.

I’ve send you via private message. Thanks