I attempt to simulate a permanent change in wage income tax using the most basic NK model (no capital, no wage rigidity, only price adjustment cost). However, it seems that Dynare fails to generate any dynamic. I checked the simulation result and found that Dynare doesn’t recognize the initial value (initial steady state) I set as the period 0 state to start with, as shown in the picture:

To verify my conjecture, I also attempted the case of a transitory shock where wage income tax increases from period 1 to period 5, the same issue happens again as the period 0 value is 0.05 rather than 0:

You are working with a model that does not feature any state variables. Initial values do not matter. There is only degenerate dynamics for your experiment. The model will immediately jump to its new steady state.

As there is no physical capital in this model, I assume households can use the nominal bond to smooth their consumption. I also include the first order condition with respect to the nominal bond in the list of equilibrium conditions. I struggle to understand why it can not act as a state variable in this case. Is it because, by assumption, the bond is of zero net supply at equilibrium?

If this is the case, is it correct to say that the only way to generate transition dynamics with respect to the tax change in this kind of model is to assume some lag structure in the exogenous variable, for example, assuming the tax rate follows an AR process?